Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2×C5 |
| direct product | D3×C31×C5⋊D5 |
| unambiguous semidirect product | (C5×D3)⋊(D5×C31) |
| Fitting, socle, Hall | C3×C52×C31 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C22×C31 |
| Hall | C52×C31 ⋊ C2×D3 |
| Hall | C3×C31 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D3×C31 |
| Sylow | C3 ⋊ C2×C31×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×C5⋊D5 |
| commutator, hypocenter | C3×C52 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C31 | |
160 conjugacy classes of subgroups.
1302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 191);