Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24 |
| direct product | C22×D3×#1094 |
2142 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 2142 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 20 points:
(3,4)(6,8,7)(9,10,11)(12,15,20,14,18,16,17,13,19);(1,2)(5,8)(6,7)(13,15,18)(16,20,19);(10,11)240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67×#1094 |
| maximal normal subgroup of | C2×#67×#1094 |
| maximal quotient of | C2×#67×#1094 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,4)(6,8,7)(9,10,11)(12,15,20,14,18,16,17,13,19), (1,2)(5,8)(6,7)(13,15,18)(16,20,19), (10,11));