Finite Group DatabasebetaFinite Group Databasebeta| order | 8640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | D5×#63694⋊C3 |
| Sylow | C5 ⋊ C2×#63694⋊C3 |
2244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 180 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,3,4)(6,8)(9,10,12,13,11)(14,22,17,16,15,19,20,18,21);(10,11)(12,13);(2,3)(5,6)(7,8)(15,17)(16,20)(18,21)(19,22)232 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((1,3,4)(6,8)(9,10,12,13,11)(14,22,17,16,15,19,20,18,21), (10,11)(12,13), (2,3)(5,6)(7,8)(15,17)(16,20)(18,21)(19,22));