Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D31⋊C25 |
| unambiguous semidirect product | (C2×C3×D31)⋊C25 |
| derived, Sylow | C31 ⋊ C22×C3×C25 |
| Hall | C3×C31⋊C25 ⋊ C22 |
| Hall | C31⋊C25 ⋊ C22×C3 |
| Hall | C2×C3×D31 ⋊ C25 |
| Hall | C2×D31 ⋊ C3×C25 |
| Hall | C3×C31 ⋊ C22×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D31⋊C5 |
| commutator, hypocenter | C31 | C22×C3×C25 |
| Frattini | C5 | C2×C3×D31⋊C5 |
| Fitting, socle | C2×C3×C5×C31 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C3×C5 | |
60 conjugacy classes of subgroups.
390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 28);