C₂×C₃×#88668 #72276101

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

Aliases

Fitting	C₂³×C₃²×C₉ ⋊ C₂²
Sylow	C₃²×C₉ ⋊ C₂²×D₄

1937 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 144

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

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

306 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((3,4,5)(6,7)(14,16)(15,19)(17,20)(18,21), (10,12)(13,20,21,15,14,16,19,18,17), (1,2), (7,8)(9,10)(11,12));