Finite Group DatabasebetaFinite Group Databasebeta| order | 7650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×D17×C52⋊C3 |
| unambiguous semidirect product | C17⋊(C2×C3×C52⋊C3) |
| unambiguous semidirect product | (C52×D17)⋊C32 |
| unambiguous semidirect product | (C3×C52×D17)⋊C3 |
| Fitting, socle | C3×C52×C17 ⋊ C2×C3 |
| derived, Hall | C52×C17 ⋊ C2×C32 |
| Hall | C3×C17×C52⋊C3 ⋊ C2 |
| Hall | C52×D17 ⋊ C32 |
| Sylow | C52 ⋊ C32×D17 |
| Sylow | C17 ⋊ C2×C3×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D17×C52⋊C3 |
| commutator, hypocenter | C52×C17 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C2×C3 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
330 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19099756, C3×D17×#3874, C3×#13133353⋊C3, … |
| maximal normal subgroup of | C3×#19099756, C3×D17×#3874, C3×#13133353⋊C3, … |
| maximal quotient of | C3×Dic17×C52⋊C3, C2×C3×D17×C52⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7650, 44);