C₃×D₃×#3811 #72228882

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

Aliases

Fitting	C₂²×C₃⁴ ⋊ C₂³
Sylow	C₃⁴ ⋊ C₂²×D₄

2965 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 16 points:

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

maximal subgroup of	AGL(1,ℤ/9)×#3811, D₃×#88668⋊C₃
maximal quotient of	AGL(1,ℤ/9)×#3811, D₃×#88668⋊C₃

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

gap> G := Group((5,6,7)(9,10)(11,12,13)(14,15), (8,9,10)(12,13), (2,4), (1,2)(3,4)(15,16));