Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#13107464 |
| Hall | C3×C52 ⋊ C4×M16 |
| Sylow | C52 ⋊ C3×C4×M16 |
622 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 164 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)(17,18,21,20);(5,8)(9,11)(12,16,15,13,14);(4,5,6,9,7,8,10,11)(18,19,21,20)192 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#13107464, C3×#72231051 |
| maximal normal subgroup of | D3×#13107464 |
| maximal quotient of | C3×#72231051 |
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)(17,18,21,20), (5,8)(9,11)(12,16,15,13,14), (4,5,6,9,7,8,10,11)(18,19,21,20));