Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D17×C3⋊D75 |
| unambiguous semidirect product | (C3×D17)⋊D75 |
| unambiguous semidirect product | (C25×D17)⋊(C3⋊D3) |
| Fitting, derived, Hall | C32×C17×C25 ⋊ C22 |
| Hall | C17×C25 ⋊ C2×C3⋊D3 |
| Hall | C32×C25 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ C3⋊D3×D17 |
| Sylow | C17 ⋊ C2×C3⋊D75 |
| Sylow | C32 ⋊ D17×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C17×C25 | C22 |
| Frattini | C5 | D17×C3⋊D15 |
| socle | C32×C5×C17 | C2×D5 |
| LCS | G ▷ C32×C17×C25 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3825 |
1140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 94);