C₂×D₄×C₉×C₃⋊D₃ #72275997

order	2592
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₉ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂×D₄×C₉×C₃⋊D₃

Fitting	C₂×C₃²×D₄×C₉ ⋊ C₂
Sylow	C₃²×C₉ ⋊ C₂²×D₄

2556 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 432

A minimal faithful permutation representation — 4 generators on 21 points:

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

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

maximal subgroup of	C₂×D₄×D₉×C₃⋊D₃
maximal normal subgroup of	C₂×D₄×D₉×C₃⋊D₃

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

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