D₃×#7179 #72258781

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₃×#7179 ⋊ C₂
Sylow	C₃ ⋊ C₂×#7179

1292 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 23 points:

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

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

maximal subgroup of	D₃×#136361
maximal normal subgroup of	D₃×#136361

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

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