Dic₃×PSU(3,𝔽₂)⋊C₃ #72228431

order	2592
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×PSU(3,𝔽₂)⋊C₃
commutator, hypocenter	C₃×PSU(3,𝔽₂)	C₃×C₄
Fitting, socle	C₂×C₃³	C₂×SL(2,𝔽₃)
prime radical	C₂×C₃×PSU(3,𝔽₂)⋊C₃	C₂
cosocle	C₂×C₃×PSU(3,𝔽₂)	C₂×C₃
LCS	G ▷ C₃×PSU(3,𝔽₂)
UCS	C₁ ◁ C₂

203 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 203 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.

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

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 16 points:

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

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

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