Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#20259076 |
| Fitting, Hall | C3×C25×C61 ⋊ C4 |
| derived, Hall | C25×C61 ⋊ C3×C4 |
| Hall | C3×C61 ⋊ #1035 |
| Hall | C3×C25 ⋊ #6923 |
| Sylow | C61 ⋊ C3×#1035 |
| Sylow | C25 ⋊ C3×#6923 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4575 |
1155 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 44);