Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C34 |
| direct product | D5×#66472 |
| Fitting, socle, derived, Hall | C34×C5 ⋊ C2×C4 |
| Sylow | C34 ⋊ C4×D5 |
| Sylow | C5 ⋊ C2×#66472 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C34×C5 | C2×C4 |
| prime radical | D5×C3⋊(C3⋊(C3⋊D3)) | C2 |
| cosocle | C5×C3⋊(C3⋊(C3⋊D3)) | C22 |
| LCS | G ▷ C34×C5 | |
| UCS | C1 | |
1192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#10620198, D5×#10620206, AGL(1,𝔽5)×#66472, … |
| maximal normal subgroup of | D5×#10620198, D5×#10620206, AGL(1,𝔽5)×#66472, … |
Past the SmallGroups library coverage — no SmallGroups id.