C₂×D₄×C₉×D₉ #72268795

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

Aliases

C₂×D₄×C₉×D₉

Fitting	C₂×D₄×C₉² ⋊ C₂
Sylow	C₉² ⋊ C₂²×D₄

1251 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:

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

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

maximal subgroup of	C₂×D₄×D₉², C₂×C₉×#63710, C₂×#72219950
maximal normal subgroup of	C₂×D₄×D₉², C₂×C₉×#63710, C₂×#72219950

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

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