Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×#66524⋊C2 |
| unambiguous semidirect product | #66524⋊(C22×C23) |
| unambiguous semidirect product | (C2×#66524)⋊(C2×C23) |
| derived, Sylow | C37 ⋊ C22×C9×C23 |
| Hall | C23×#66524 ⋊ C22 |
| Hall | C2×C23×D37 ⋊ C9 |
| Hall | C23×C37 ⋊ C22×C9 |
| Hall | #66524 ⋊ C22×C23 |
| Hall | C2×D37 ⋊ C9×C23 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15318 |
1656 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 17);