Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#11717048 |
| Hall | C3×C52 ⋊ C2×SD16 |
| Sylow | C52 ⋊ C2×C3×SD16 |
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 120 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3)(13,14)(15,16)(17,18)(19,20);(5,8)(6,10)(9,11)(12,13,15,16,14);(4,5,6,8,7,9,10,11)(18,19)(20,21)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13104059, D3×#11717048, #72230795, … |
| maximal normal subgroup of | C3×#13104059, D3×#11717048, #72230795, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(13,14)(15,16)(17,18)(19,20), (5,8)(6,10)(9,11)(12,13,15,16,14), (4,5,6,8,7,9,10,11)(18,19)(20,21));