Finite Group DatabasebetaFinite Group Databasebeta| order | 7650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C32×C5⋊D85 |
| unambiguous semidirect product | C5⋊(C32×D85) |
| unambiguous semidirect product | C17⋊(C32×C5⋊D5) |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C2 |
| derived, Hall | C52×C17 ⋊ C2×C32 |
| Hall | C32×C52 ⋊ D17 |
| Hall | C32×C17 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C32×D17 |
| Sylow | C17 ⋊ C32×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C5⋊D85 |
| commutator, hypocenter | C52×C17 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C2 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C32 | |
192 conjugacy classes of subgroups.
1926 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#13133343, C32×#13133344, C32×#13133347, … |
| maximal normal subgroup of | C32×#13133343, C32×#13133344, C32×#13133347, … |
| maximal quotient of | C32×#13133334, C2×C32×C5⋊D85 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7650, 56);