Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#11716874 |
| Fitting | C2×C3×C4×C52 ⋊ C4 |
| Hall | C3×C52 ⋊ #95 |
| Sylow | C52 ⋊ C3×#95 |
608 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 600 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3)(9,11)(13,14,15,16)(18,19,20,21);(4,5,6,7)(8,9)(10,11)(17,18,21,19,20);(12,13,16,14,15)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13104791, C3×#13104711, C3×C22⋊C4×#1043, … |
| maximal normal subgroup of | C3×#13104791, C3×#13104711, C3×C22⋊C4×#1043, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(9,11)(13,14,15,16)(18,19,20,21), (4,5,6,7)(8,9)(10,11)(17,18,21,19,20), (12,13,16,14,15));