Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D52×C31⋊C3 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C31⋊C3) |
| unambiguous semidirect product | (D52×C31)⋊C3 |
| Fitting, socle, derived, Hall | C52×C31 ⋊ C22×C3 |
| Hall | D52×C31 ⋊ C3 |
| Hall | C52×C31⋊C3 ⋊ C22 |
| Sylow | C31 ⋊ C3×D52 |
| Sylow | C52 ⋊ C22×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C31 | C22×C3 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
208 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#3874⋊C2, C3×D52×C31⋊C3, D5×D15×C31⋊C3, … |
| maximal normal subgroup of | C3×D52×C31⋊C3 |
| maximal quotient of | D52×C31⋊C9, C3×D52×C31⋊C3, D5×D15×C31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 129);