Finite Group DatabasebetaFinite Group Databasebeta| order | 8325 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C37×C52⋊C3 |
| unambiguous semidirect product | C52⋊(C32×C37) |
| unambiguous semidirect product | (C3×C52)⋊(C3×C37) |
| Fitting, socle | C3×C52×C37 ⋊ C3 |
| derived, Sylow | C52 ⋊ C32×C37 |
| Hall | C52×C37 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | C52⋊C3 |
| commutator, hypocenter | C52 | C32×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C37 | |
32 conjugacy classes of subgroups.
1221 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8325, 15);