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C24×C7⋊C9 #11759337

order1008
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C26

Aliases

direct productC24×C7⋊C9

Splittings

derived, SylowC7 ⋊ C24×C9
HallC24×C7 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC24×C3ΓL(1,𝔽8)
commutator, hypocenterC7C24×C9
FrattiniC3C24×ΓL(1,𝔽8)
Fitting, socle, prime radicalC24×C3×C7C3
cosocleC3×C7C24×C3
LCSG ▷ C7
UCSC1 ◁ C24×C3

402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 1008

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2)(10,11,12)(13,15,14)(16,17,19,18,20,22,21,23,24);(3,4)(9,10,11,13,12,14,15);(5,6);(7,8)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 508);