C₂×D₄×D₉⋊C₉ #72276205

order	2592
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₉ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₄×D₉⋊C₉

Fitting	C₂×D₄×C₉⋊C₉ ⋊ C₂
Sylow	C₉⋊C₉ ⋊ C₂²×D₄

1170 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 4 generators on 24 points:

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

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

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

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