Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C25×D61⋊C3 |
| unambiguous semidirect product | (C2×C25×D61)⋊C3 |
| Fitting | C2×C25×C61 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C22×C3×C25 |
| Hall | C2×C25×D61 ⋊ C3 |
| Hall | C25×C61⋊C3 ⋊ C22 |
| Hall | C25×C61 ⋊ C22×C3 |
| Hall | C2×D61 ⋊ C3×C25 |
| Hall | C61⋊C3 ⋊ C22×C25 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3050 |
800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 38);