A₄×D₂₁ #92758

order	504
isoclinism	isoclinic class of A₄×D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×D₂₁
unambiguous semidirect product	C₃⋊(A₄×D₇)

Fitting, socle, derived	C₂²×C₃×C₇ ⋊ C₂×C₃
Sylow	C₇ ⋊ D₃×A₄

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

52 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 184);