Questions tagged [sporadic-groups]
The tag is meant to be used for any question related to the mathematics of sporadic groups.
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Does a code being perfect have a specific effect on its automorphism group?
I know that the Perfect Binary Golay Code is very exceptional as it is the only perfect binary code that is not one of a few infinite families (Trivial, Simple Repitition, Hamming). The automorphism ...
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Does the Lyons group have 2 111-dimensional representations or just 1?
From what I can tell about the 111-dimensional representation of the sporadic Lyons group (modulo 5), an involution negates a 56-dimensional subspace. Thus, the double cover of the alternating group $...
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What is the minimal-rank permutation representation of Th
The smallest degree permutation representation of the sporadic Thomposon group is on 143127000 points, and the second smallest is on 283599225 points. The stabilizers are (respectively) the Steinberg ...
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What is the octern subgroup of M24?
In this post, "24 points" refers to the 24 points of the Golay code, or equivalently, the 24 points of the S(5,8,24) design.
Conjugacy classes of $M_{24}$ use the same names as in the ATLAS ...
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Does the extension of L3(5) in the Lyons group split
According to the ATLAS of Finite groups, the sporadic Lyons group has a subgroup 53.L3(5), and the notation specifies that this extension does not split. However, according to the Wikipedia page on ...
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Is the involution centralizer in the Held group a split extension
According to the ATLAS of Finite groups, the centralizer of a 2B element in the sporadic Held group is 21+6.L3(2). According to the introductory section "How to read this ATLAS: Information about ...
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How does the Suzuki sporadic group act on an extraspecial group?
According to the ATLAS of Finite Groups, the centralizer of a 3B element in the Monster is the nonsplit extension 31+12.2Suz, where 31+12 is an extraspecial group, and 2Suz is the double cover of ...
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The Steiner system S(3,6,22) as a one-point extension of the projective plane of order 4
The group $PSL(3,4)$ acts on the projective plane $\mathbb{P}_2(\mathbb{F}_4),$ which is the Steiner system $S(2,5,21),$ meaning a collection of pentads (sets of size 5)—the lines of the projective ...
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Is this "coincidence" about representations of the Monster actually a coincidence?
I know that the Monster simple group's lowest dimension faithful representation (which is in characteristic $2$) has dimension $196882$ and that its lowest dimension faithful representation in ...
- 4,057
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What is a simple (not many relators) presentation of the Monster group?
I know that the Monster group is the largest sporadic finite simple group. Is there any simple presentation of the Monster group? $79$ relators or less is preferable.
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Sylow $2$-subgroup Mathieu Group $M_{24}$
I need to compute the Sylow $2$-subgroup of the Mathieu Group $M_{24}$. Unfortunately, this is hard to identify with a machine as it is of order $2^{10}$ and therefore not on the GAP library. I have ...
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