Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C3 |
| direct product | C17×#11744707 |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C4 |
| derived, Hall | C32×C52 ⋊ C4×C17 |
| Hall | C52×C17 ⋊ #157 |
| Hall | C32×C17 ⋊ #1043 |
| Sylow | C52 ⋊ C17×#157 |
| Sylow | C32 ⋊ C17×#1043 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2550 |
1020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 440);