Finite Group DatabasebetaFinite Group Databasebeta| order | 6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43 |
| direct product | C4×#13103905 |
| Sylow | C52 ⋊ C42×M16 |
4740 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 22 points:
(14,15,16,17)(18,19,20,21);(6,9)(10,12)(13,14,17,15,16);(1,2,3,4)(6,9)(10,12);(5,6,7,10,8,9,11,12)(19,20)(21,22)304 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((14,15,16,17)(18,19,20,21), (6,9)(10,12)(13,14,17,15,16), (1,2,3,4)(6,9)(10,12), (5,6,7,10,8,9,11,12)(19,20)(21,22));