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C4×SL(2,𝔽8) #72228336

order2016
isoclinismisoclinic class of SL(2,𝔽8)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

direct productC4×SL(2,𝔽8)

Subgroups

subgroupG/H
center, Fitting, hypercenterC4SL(2,𝔽8)
commutator, hypocenterSL(2,𝔽8)C4
Frattini, cosocleC2C2×SL(2,𝔽8)
socle, prime radicalC2×SL(2,𝔽8)C2
LCSG ▷ SL(2,𝔽8)
UCSC1 ◁ C4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 36

A minimal faithful permutation representation — 2 generators on 13 points:

(1,3,2,4)(5,11,7,12,8,10,9,13,6);(5,10,8,13,9,7,12,11,6)

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofQ8×SL(2,𝔽8), Dic5×SL(2,𝔽8), Dic3×SL(2,𝔽8)
maximal normal subgroup ofQ8×SL(2,𝔽8)
maximal quotient ofDic5×SL(2,𝔽8), Dic3×SL(2,𝔽8)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,3,2,4)(5,11,7,12,8,10,9,13,6), (5,10,8,13,9,7,12,11,6));