C₃×D₇⋊A₄ #92756

order	504
isoclinism	isoclinic class of D₇⋊A₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×D₇⋊A₄
unambiguous semidirect product	(C₃×D₇)⋊A₄

	subgroup	G/H
center, hypercenter	C₃	D₇⋊A₄
commutator, cosocle, hypocenter	C₂²×C₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇	C₂×C₃
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₃

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 84

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 182);