Finite Group DatabasebetaFinite Group Databasebeta| order | 3280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | D4×D41⋊C5 |
| Fitting | D4×C41 ⋊ C2×C5 |
| Hall | D4×D41 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×D4 |
| Sylow | C41 ⋊ C2×C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D41⋊C5 |
| commutator, socle, cosocle | C2×C41 | C23×C5 |
| Fitting | D4×C41 | C2×C5 |
| hypercenter | D4 | D41⋊C5 |
| hypocenter | C41 | C2×C5×D4 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ D4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 164 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#4223⋊C5, S4×D41⋊C5 |
| maximal normal subgroup of | D4×#4223⋊C5 |
Past the SmallGroups library coverage — no SmallGroups id.