D₃×#72209641 #72231522

order	9216
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂⁷

Aliases

Fitting	C₃×#62817 ⋊ C₂×D₃
derived	C₃×#11710730 ⋊ C₂²

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×#87588
commutator, cosocle, hypocenter	C₃×#11710730	C₂²
Fitting	C₃×#62817	C₂×D₃
socle	C₂²×C₃	C₂×#87588
LCS	G ▷ C₃×#11710730
UCS	C₁ ◁ C₂²

41154 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 41154 conjugacy classes of subgroups — too many to draw. Only its 85 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 — 3 generators on 19 points:

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

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

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