Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C32 |
| direct product | C5×#10620198 |
| Fitting, socle, Hall | C34×C5 ⋊ C2×C4 |
| derived, Sylow | C34 ⋊ C2×C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #10620198 |
| commutator, hypocenter | C34 | C2×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C2×C4 |
| prime radical | C5×C3⋊D32 | C2 |
| cosocle | C3⋊(C3⋊(C3⋊D3)) | C22×C5 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C5 | |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#10620198, C5×#13049813, #72269635 |
| maximal normal subgroup of | D5×#10620198, C5×#13049813, #72269635 |
Past the SmallGroups library coverage — no SmallGroups id.