C₂×S₄×AΓL(1,𝔽₉) #72242912

order	6912
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₃² ⋊ D₃×SD₁₆

4059 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 4059 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 54

A minimal faithful permutation representation — 4 generators on 15 points:

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

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

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