Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D425 |
| unambiguous semidirect product | (C17×D9)⋊D25 |
| unambiguous semidirect product | (D9×C25)⋊D17 |
| Fitting, derived, Hall | C9×C17×C25 ⋊ C22 |
| Hall | C17×C25 ⋊ C2×D9 |
| Hall | C9×C25 ⋊ C2×D17 |
| Hall | C9×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ D9×D17 |
| Sylow | C17 ⋊ D9×D25 |
| Sylow | C9 ⋊ C2×D425 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C17×C25 | C22 |
| Frattini | C3×C5 | D3×D85 |
| socle | C3×C5×C17 | D3×D5 |
| LCS | G ▷ C9×C17×C25 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3825 |
1284 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 27);