D₃×C₃⋊#3633 #72229090

order	2448
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₇	C₂×C₈
prime radical	C₃×D₃×D₁₇	C₄
cosocle	C₃²×#595	C₂²
LCS	G ▷ C₃²×C₁₇
UCS	C₁

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 102

A minimal faithful permutation representation — 2 generators on 23 points:

(2,3,4,6,5,7,8,10)(9,12,14,16,11,15,13,17)(19,20)(21,22);(1,2,6,11,8,13,17,15,3,7,12,16,14,4,9,10,5)(18,19,20)(22,23)

maximal subgroup of	D₃²×#3633
maximal normal subgroup of	D₃²×#3633

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

gap> G := Group((2,3,4,6,5,7,8,10)(9,12,14,16,11,15,13,17)(19,20)(21,22), (1,2,6,11,8,13,17,15,3,7,12,16,14,4,9,10,5)(18,19,20)(22,23));