Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×D45⋊D5 |
| unambiguous semidirect product | D45⋊(D5×C17) |
| Fitting, Hall | C52×C9×C17 ⋊ C22 |
| derived, Hall | C52×C9 ⋊ C22×C17 |
| Hall | C52×C17 ⋊ C2×D9 |
| Hall | C9×C17 ⋊ D52 |
| Sylow | C52 ⋊ C2×C17×D9 |
| Sylow | C9 ⋊ D52×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D45⋊D5 |
| commutator, cosocle, hypocenter | C52×C9 | C22×C17 |
| Frattini | C3 | C17×D15⋊D5 |
| Fitting | C52×C9×C17 | C22 |
| socle | C3×C52×C17 | C2×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C17 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1530 |
1224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 208);