C₃×#72209832 #72231550

order	9216
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₃×#6499874 ⋊ D₃
derived	#11710730 ⋊ C₂²×C₃

	subgroup	G/H
center, socle	C₂×C₃	#72209653
commutator, cosocle, hypocenter	#11710730	C₂²×C₃
Frattini	C₂⁴	C₂×C₃×#1020
Fitting	C₃×#6499874	D₃
hypercenter	C₂²×C₃	#87588⋊C₂
LCS	G ▷ #11710730
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃

7179 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 7179 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

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

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 19 points:

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

maximal subgroup of	D₃×#72209832, C₃×#72215896
maximal normal subgroup of	D₃×#72209832

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

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