C₂×C₃×D₄×C₃⋊D₉ #72276119

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

Aliases

C₂×C₃×D₄×C₃⋊D₉

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

2765 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:

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

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

maximal subgroup of	C₂×D₄×#92299
maximal quotient of	C₂×D₄×#92299

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

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