C₉×D₉×C₃⋊D₃ #72228643

order	2916
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₉×D₉×C₃⋊D₃

Fitting, Sylow	C₃²×C₉² ⋊ C₂²
derived	C₃²×C₉ ⋊ C₂²×C₉

730 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

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

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 24 points:

(2,3)(5,6)(7,11,15,9,14,10,12,8,13)(16,18,22,19,23,24,17,20,21);(4,5,6)(17,19)(18,21)(20,22)(23,24);(1,2,3)

324 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₃⋊D₃×#92265, C₉×D₉⋊((C₃⋊D₃)⋊C₃), #72254051, …
maximal normal subgroup of	C₃⋊D₃×#92265, C₉×D₉⋊((C₃⋊D₃)⋊C₃), #72254051, …

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

gap> G := Group((2,3)(5,6)(7,11,15,9,14,10,12,8,13)(16,18,22,19,23,24,17,20,21), (4,5,6)(17,19)(18,21)(20,22)(23,24), (1,2,3));