D₃×#10620203 #72228535

order	3888
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₃⁵ ⋊ C₂×D₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₃³×C₃⋊D₃	C₂³
Fitting, socle, hypocenter	C₃⁵	C₂×D₄
LCS	G ▷ C₃³×C₃⋊D₃ ▷ C₃⁵
UCS	C₁

1424 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 15 points:

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

maximal subgroup of	D₃×(#157⋊D₃)⋊D₃
maximal normal subgroup of	D₃×(#157⋊D₃)⋊D₃

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

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