Finite Group DatabasebetaFinite Group Databasebeta| order | 7650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C3×C3⋊(C5⋊D85) |
| unambiguous semidirect product | C3⋊(C3×C5⋊D85) |
| unambiguous semidirect product | C5⋊(C3×D255) |
| unambiguous semidirect product | C17⋊(C3×C3⋊(C5⋊D5)) |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C2 |
| derived | C3×C52×C17 ⋊ C2×C3 |
| Hall | C52×C17 ⋊ C3×D3 |
| Hall | C32×C52 ⋊ D17 |
| Hall | C32×C17 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C3×D51 |
| Sylow | C17 ⋊ C3×C3⋊(C5⋊D5) |
| Sylow | C32 ⋊ C5⋊D85 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C5⋊D85) |
| commutator, hypocenter | C3×C52×C17 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C2 |
| LCS | G ▷ C3×C52×C17 | |
| UCS | C1 ◁ C3 | |
144 conjugacy classes of subgroups.
1917 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D17×C3⋊(C5⋊D5), C3×C5⋊D5×D51, C3×D3×C5⋊D85, … |
| maximal normal subgroup of | C3×D17×C3⋊(C5⋊D5), C3×C5⋊D5×D51, C3×D3×C5⋊D85, … |
| maximal quotient of | C3×C3⋊#13133334, C2×C3×C3⋊(C5⋊D85) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7650, 62);