Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#11711260 |
1538 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 48 |
A minimal faithful permutation representation — 3 generators on 20 points:
(9,14,20,10,11,19)(12,17,15,13,16,18);(1,2,3,5,4,6,7,8)(11,15)(14,18)(16,19)(17,20);(2,5)(3,7)(6,8)(11,14)(12,13)(19,20)64 conjugacy classes — view the full character table.
| maximal subgroup of | #72340821, C2×#72214513 |
| maximal normal subgroup of | C2×#72214513 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((9,14,20,10,11,19)(12,17,15,13,16,18), (1,2,3,5,4,6,7,8)(11,15)(14,18)(16,19)(17,20), (2,5)(3,7)(6,8)(11,14)(12,13)(19,20));