C₂×#13048710 #72276159

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

Aliases

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

3196 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 216

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

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

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