D₇×C₂²⋊C₉ #92631

order	504
isoclinism	isoclinic class of A₄×D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₃	A₄×D₇
commutator, hypocenter	C₂²×C₇	C₂×C₉
Fitting, socle, cosocle	C₂²×C₃×C₇	C₂×C₃
prime radical	C₂²×C₃×D₇	C₃
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₃

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 126

A minimal faithful permutation representation — 2 generators on 20 points:

(2,3,4)(6,7)(8,9)(10,11)(12,16,20,14,19,15,17,13,18);(1,4)(2,3)(5,6,8,10,11,9,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 57);