Dic₃×AGL(2,𝔽₃) #72259643

order	5184
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×AGL(2,𝔽₃)
commutator, hypocenter	C₃×PSU(3,𝔽₂)⋊C₃	C₂×C₄
Fitting, socle	C₂×C₃³	C₂×GL(2,𝔽₃)
prime radical	C₂×C₃×AGL(2,𝔽₃)	C₂
cosocle	C₂×C₃×PSU(3,𝔽₂)⋊C₃	C₂²
LCS	G ▷ C₃×PSU(3,𝔽₂)⋊C₃
UCS	C₁ ◁ C₂

568 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 36 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:

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

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

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