C₃×3₋¹⁺²×C₂²⋊A₄ #72228722

order	3888
automorphism	?
homology	Abelianization (H₁) = C₃⁴ · Schur multiplier (H₂) = C₂⁴×C₃⁵

Aliases

Fitting	C₂⁴×C₃×3₋¹⁺² ⋊ C₃
Sylow	C₂⁴ ⋊ C₃²×3₋¹⁺²

2776 conjugacy classes of subgroups; only the 426 normal subgroups are shown.

normal subgroups only

This group has 2776 conjugacy classes of subgroups — too many to draw. Only its 426 normal subgroups are shown.

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

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 324

A minimal faithful permutation representation — 4 generators on 20 points:

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

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

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

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