Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C4×#72213207 |
| derived | (C22⋊A4)⋊C9 ⋊ C2×C3×C4 |
2314 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 2314 conjugacy classes of subgroups — too many to draw. Only its 97 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) = 108 |
A minimal faithful permutation representation — 3 generators on 21 points:
(2,8,9,4,5,6)(3,7)(14,17,16,15)(18,19,21,20);(1,5,4,3,9,6,7,2,8)(10,11,12,13)(19,20,21);(15,16,17)(19,20,21)200 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,8,9,4,5,6)(3,7)(14,17,16,15)(18,19,21,20), (1,5,4,3,9,6,7,2,8)(10,11,12,13)(19,20,21), (15,16,17)(19,20,21));