Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C25×C31 ⋊ C22×C3 |
| Hall | D25×D31 ⋊ C3 |
| Hall | C25×C31⋊C3 ⋊ C22 |
| Hall | C31⋊C3 ⋊ C2×D25 |
| Sylow | C31 ⋊ C2×C3×D25 |
| Sylow | C25 ⋊ C2×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C31 | C22×C3 |
| Frattini | C5 | D5×D31⋊C3 |
| socle | C5×C31 | C2×C3×D5 |
| LCS | G ▷ C25×C31 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
154 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D25×D31⋊C3, D75×D31⋊C3, D25×C3⋊(D31⋊C3), … |
| maximal normal subgroup of | C3×D25×D31⋊C3 |
| maximal quotient of | D25×D31⋊C9, C3×D25×D31⋊C3, D75×D31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 27);