Finite Group DatabasebetaFinite Group Databasebeta| order | 7650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D255 |
| unambiguous semidirect product | C3⋊(C5×D255) |
| unambiguous semidirect product | C5⋊(C5×C3⋊D51) |
| unambiguous semidirect product | C17⋊(C5×C3⋊D15) |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C2 |
| derived | C32×C5×C17 ⋊ C2×C5 |
| Hall | C52×C17 ⋊ C3⋊D3 |
| Hall | C32×C52 ⋊ D17 |
| Hall | C32×C17 ⋊ C5×D5 |
| Sylow | C52 ⋊ C3⋊D51 |
| Sylow | C17 ⋊ C5×C3⋊D15 |
| Sylow | C32 ⋊ C5×D85 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D255 |
| commutator, hypocenter | C32×C5×C17 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C2 |
| LCS | G ▷ C32×C5×C17 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
1920 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D17×C3⋊D15, C5×D5×C3⋊D51, C5×C3⋊D3×D85, … |
| maximal normal subgroup of | C5×D17×C3⋊D15, C5×D5×C3⋊D51, C5×C3⋊D3×D85, … |
| maximal quotient of | C5×C3⋊Dic255, C2×C5×C3⋊D255 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7650, 66);