Finite Group DatabasebetaFinite Group Databasebeta| order | 2430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#11717694 |
| Fitting, socle, Sylow | C35 ⋊ D5 |
| derived | C34⋊C5 ⋊ C2×C3 |
| Hall | C3×C34⋊C5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11717694 |
| commutator, cosocle, hypocenter | C34⋊C5 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C35 | D5 |
| LCS | G ▷ C34⋊C5 | |
| UCS | C1 ◁ C3 | |
528 conjugacy classes of subgroups.
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72209678 |
| maximal quotient of | C3×#13108499 |
Past the SmallGroups library coverage — no SmallGroups id.