C₇²×S₄ #11924325

order	1176
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₇² · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₇²×S₄
unambiguous semidirect product	A₄⋊(C₂×C₇²)

Fitting, socle	C₂²×C₇² ⋊ D₃
derived	A₄ ⋊ C₂×C₇²

	subgroup	G/H
center, hypercenter	C₇²	S₄
commutator, cosocle, hypocenter	A₄	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₂²×C₇²	D₃
LCS	G ▷ A₄
UCS	C₁ ◁ C₇²

110 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 196

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3,4,5,6,7)(15,16,17,18);(8,9,10,11,12,13,14)(15,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 240);