Finite Group DatabasebetaFinite Group Databasebeta| order | 8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C52⋊C3×C37⋊C3 |
| unambiguous semidirect product | (C52×C37⋊C3)⋊C3 |
| unambiguous semidirect product | (C37×C52⋊C3)⋊C3 |
| unambiguous semidirect product | (C52⋊(C37⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C32 |
| Sylow | C37 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C32 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8325, 13);