C₃×D₇×C₂²⋊A₄ #72244615

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

C₃×D₇×C₂²⋊A₄

	subgroup	G/H
center, hypercenter	C₃	D₇×C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴×C₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃×C₇	C₂×C₃
LCS	G ▷ C₂⁴×C₇
UCS	C₁ ◁ C₃

648 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 3 generators on 18 points:

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,3)(4,5)(6,7)(12,15)(13,14)(16,17,18), (1,2,4,6,7,5,3)(9,11,10)(13,15,14), (8,11)(9,10));