Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C17 · Schur multiplier (H2) = C5 |
| direct product | C9×C17×#1039 |
| derived, Sylow | C52 ⋊ C4×C9×C17 |
| Hall | C52×C9×C17 ⋊ C4 |
| Hall | C52×C17 ⋊ C4×C9 |
| Hall | C52×C9 ⋊ C4×C17 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15300 |
4284 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 59);