C₄×D₃×#5935 #72260125

order	4608
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₃×C₄×H(5,𝔽₂) ⋊ C₂×D₃
derived	C₃×#997 ⋊ C₂²×C₄

7536 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 7536 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 15 points:

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

maximal subgroup of	D₃×AGL(1,𝔽₅)×#5935
maximal quotient of	D₃×AGL(1,𝔽₅)×#5935

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

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