S₄×C₂₉ #10621967

order	696
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	S₄×C₂₉
unambiguous semidirect product	A₄⋊(C₂×C₂₉)

Fitting, socle	C₂²×C₂₉ ⋊ D₃
derived	A₄ ⋊ C₂×C₂₉

	subgroup	G/H
center, hypercenter	C₂₉	S₄
commutator, cosocle, hypocenter	A₄	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₂²×C₂₉	D₃
LCS	G ▷ A₄
UCS	C₁ ◁ C₂₉

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 116

A minimal faithful permutation representation — 2 generators on 33 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(696, 34);