D₃×#12585 #72254129

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

Fitting	C₃×#12585 ⋊ C₂
Sylow	C₃ ⋊ C₂×#12585

5156 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 4 generators on 23 points:

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

maximal subgroup of	D₃×#147782, D₃×#494622, D₃×#146488, …
maximal normal subgroup of	D₃×#147782, D₃×#494622, D₃×#146488, …

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

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