Finite Group DatabasebetaFinite Group Databasebeta| order | 23310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9×C37 · Schur multiplier (H2) = C1 |
| direct product | C7×C9×D5×C37 |
| unambiguous semidirect product | C5⋊(C2×C7×C9×C37) |
| Fitting, Hall | C5×C7×C9×C37 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C7×C9×C37 |
| Hall | C5×C9×C37 ⋊ C2×C7 |
| Hall | C5×C7×C37 ⋊ C2×C9 |
| Hall | C5×C7×C9 ⋊ C2×C37 |
| Hall | C5×C37 ⋊ C2×C7×C9 |
| Hall | C5×C9 ⋊ C2×C7×C37 |
| Hall | C5×C7 ⋊ C2×C9×C37 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11655 |
9324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23310, 9);