Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×#1035 |
| unambiguous semidirect product | (C31×#1035)⋊C3 |
| Fitting, derived, Hall | C25×C31 ⋊ C3×C4 |
| Hall | C31×#1035 ⋊ C3 |
| Hall | C25×C31⋊C3 ⋊ C4 |
| Sylow | C31 ⋊ C3×#1035 |
| Sylow | C25 ⋊ C4×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C31 | C3×C4 |
| Frattini | C5 | AGL(1,𝔽5)×C31⋊C3 |
| socle | C5×C31 | C3×AGL(1,𝔽5) |
| LCS | G ▷ C25×C31 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
130 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C31⋊C3×#1035, C31⋊C3×C3⋊#1035 |
| maximal normal subgroup of | C3×C31⋊C3×#1035 |
| maximal quotient of | #1035×C31⋊C9, C3×C31⋊C3×#1035, C31⋊C3×C3⋊#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 25);