Finite Group DatabasebetaFinite Group Databasebeta| order | 7650 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C17×D15 |
| unambiguous semidirect product | C3⋊(C3×C5×D5×C17) |
| unambiguous semidirect product | C5⋊(C3×C5×D3×C17) |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C3×C5×C17 |
| Hall | C52×C17 ⋊ C3×D3 |
| Hall | C32×C52 ⋊ C2×C17 |
| Hall | C32×C17 ⋊ C5×D5 |
| Sylow | C52 ⋊ C3×D3×C17 |
| Sylow | C32 ⋊ C5×D5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C17 | D15 |
| commutator, hypocenter | C3×C5 | C2×C3×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C5×C17 | |
96 conjugacy classes of subgroups.
2295 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D15×D17, C3×C5×D3×D5×C17, C3×C5×D15⋊D17, … |
| maximal normal subgroup of | C3×C5×D15×D17, C3×C5×D3×D5×C17, C3×C5×D15⋊D17, … |
| maximal quotient of | C3×C5×C17×Dic15, C2×C3×C5×C17×D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7650, 59);