D₃×#10596473 #72241535

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂⁴×C₃² ⋊ C₂²×D₃

5854 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 4 generators on 14 points:

(2,4)(5,7,8)(9,10,11)(12,13,14);(1,2)(3,4)(6,7);(6,7)(10,11)(13,14);(13,14)

maximal subgroup of	D₃×#13181790, D₃×#72215293
maximal quotient of	D₃×#72215293

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

gap> G := Group((2,4)(5,7,8)(9,10,11)(12,13,14), (1,2)(3,4)(6,7), (6,7)(10,11)(13,14), (13,14));