Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#11716765 |
| Hall | C3×C52 ⋊ #102 |
| Sylow | C52 ⋊ C3×#102 |
252 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 21 points:
(1,2,3)(5,8)(6,11)(9,10)(12,13,15,14)(17,18,21,20);(4,5,6,9,7,10,11,8)(13,14,15,16)(18,19,21,20)96 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13104055, D3×#11716765, #72230858, … |
| maximal normal subgroup of | C3×#13104055, D3×#11716765, #72230858, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(5,8)(6,11)(9,10)(12,13,15,14)(17,18,21,20), (4,5,6,9,7,10,11,8)(13,14,15,16)(18,19,21,20));