Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×D3×#6900 |
| Fitting | C2×C3×#6900 ⋊ C2 |
| Sylow | C3×#6900 ⋊ C22 |
1098 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 315 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 324 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(13,19,20,18,16,17,15,14,21)(22,23);(2,3)(4,10,11,9,7,8,6,5,12);(5,7,10)(8,12,11)(14,16,19)(17,21,20)306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#92314, C22×D3×#6900, C2×D3×#92265, … |
| maximal normal subgroup of | C2×D3×#92314, C22×D3×#6900, C2×D3×#92265, … |
| maximal quotient of | C22×D3×#6900, D32×#6900 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(13,19,20,18,16,17,15,14,21)(22,23), (2,3)(4,10,11,9,7,8,6,5,12), (5,7,10)(8,12,11)(14,16,19)(17,21,20));