Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2 |
| direct product | C3×#11716763 |
| Hall | C3×C52 ⋊ #97 |
| Sylow | C52 ⋊ C3×#97 |
220 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 58 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)(9,11)(13,14,15,16)(17,18,19,20);(4,5,6,9,7,8,10,11)(12,13,16,14,15)(18,19)(20,21)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13103905, D3×#11716763, #72230521, … |
| maximal normal subgroup of | C3×#13103905, D3×#11716763, #72230521, … |
| maximal quotient of | C3×#72229663 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(5,8)(9,11)(13,14,15,16)(17,18,19,20), (4,5,6,9,7,8,10,11)(12,13,16,14,15)(18,19)(20,21));