Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C5 |
| direct product | C61×#1039⋊C3 |
| unambiguous semidirect product | #1039⋊(C3×C61) |
| derived, Sylow | C52 ⋊ C3×C4×C61 |
| Hall | C61×#1039 ⋊ C3 |
| Hall | C61×C52⋊C3 ⋊ C4 |
| Hall | C52×C61 ⋊ C3×C4 |
| Hall | #1039 ⋊ C3×C61 |
| Hall | C52⋊C3 ⋊ C4×C61 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3660 |
1220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 90);