Finite Group DatabasebetaFinite Group Databasebeta| order | 2496 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C13⋊C3×#453 |
| Fitting, Hall | C13×#453 ⋊ C3 |
| Sylow | C13 ⋊ C3×#453 |
336 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 81 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) = 104 |
A minimal faithful permutation representation — 3 generators on 21 points:
(2,3,5)(4,7,10)(6,9,8)(11,13,12)(14,15)(16,18)(17,19)(20,21);(1,2,4,3,6,10,7,11,13,5,8,12,9)(15,18)(16,21)(19,20);(15,19)(16,21)112 conjugacy classes — view the full character table.
| maximal subgroup of | #453×D13⋊C3, C13⋊C3×#5935 |
| maximal normal subgroup of | #453×D13⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3,5)(4,7,10)(6,9,8)(11,13,12)(14,15)(16,18)(17,19)(20,21), (1,2,4,3,6,10,7,11,13,5,8,12,9)(15,18)(16,21)(19,20), (15,19)(16,21));