Finite Group DatabasebetaFinite Group Databasebeta| order | 2496 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C22×D4×D13⋊C3 |
| Fitting | C22×D4×C13 ⋊ C2×C3 |
| Hall | C22×D4×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C23×D4 |
| Sylow | C13 ⋊ C23×C3×D4 |
2724 conjugacy classes of subgroups; only the 928 normal subgroups are shown.
This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 928 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 5 generators on 21 points:
(10,14,15,11,12,16)(13,19,20,17,18,21);(3,4)(9,10,13,15,14,18,20,21,19,12,16,17,11);(1,2);(5,6,7,8);(6,8)160 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((10,14,15,11,12,16)(13,19,20,17,18,21), (3,4)(9,10,13,15,14,18,20,21,19,12,16,17,11), (1,2), (5,6,7,8), (6,8));