Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D31⋊C3 |
| unambiguous semidirect product | (C5×D5×D31)⋊C3 |
| Fitting, socle, Hall | C52×C31 ⋊ C22×C3 |
| derived | C5×C31 ⋊ C22×C3×C5 |
| Hall | C5×D5×D31 ⋊ C3 |
| Hall | C52×C31⋊C3 ⋊ C22 |
| Hall | C31⋊C3 ⋊ C2×C5×D5 |
| Sylow | C31 ⋊ C2×C3×C5×D5 |
| Sylow | C52 ⋊ C2×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D31⋊C3 |
| commutator, hypocenter | C5×C31 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C31 | C22×C3 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
220 conjugacy classes — view the full character table.
| maximal subgroup of | #3874×D31⋊C3, C3×C5×D5×D31⋊C3, C5×D15×D31⋊C3, … |
| maximal normal subgroup of | C3×C5×D5×D31⋊C3 |
| maximal quotient of | C5×D5×D31⋊C9, C3×C5×D5×D31⋊C3, C5×D15×D31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 119);