C₇×C₂₃⋊C₈ #13046220

order	1288
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₂₃⋊C₈
unambiguous semidirect product	C₂₃⋊(C₇×C₈)

Splittings

derived, Sylow	C₂₃ ⋊ C₇×C₈
Hall	C₇×C₂₃ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₇	D₂₃
commutator, hypocenter	C₂₃	C₇×C₈
Frattini	C₄	C₇×D₂₃
Fitting	C₄×C₇×C₂₃	C₂
socle, prime radical	C₂×C₇×C₂₃	C₄
cosocle	C₄×C₂₃	C₂×C₇
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₄×C₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 1288

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32,33,35,34,36,37,38);(8,9,11,13,15,17,19,21,23,25,27,29,30,28,26,24,22,20,18,16,14,12,10)

Conjugacy classes & character table

364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1288, 2);

C7×C23⋊C8 #13046220