D₃×#72210357 #72258378

order	20736
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁸

Aliases

Fitting	C₂⁴×C₃³ ⋊ C₂³×D₃
derived	C₃³×C₂²⋊A₄ ⋊ C₂⁴

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃³×C₂²⋊A₄	C₂⁴
Frattini	C₂²	D₃³×S₄
Fitting	C₂⁴×C₃³	C₂³×D₃
socle	C₂²×C₃³	C₂³×S₄
LCS	G ▷ C₃³×C₂²⋊A₄
UCS	C₁

At least 18492 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 17 points:

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

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

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