Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#511790 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #32898 |
| commutator, Frattini, cosocle | C22×D4 | C24×C5 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C23×C5 ◁ C23×C5×D4 ◁ G | |
6038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
265 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | D5×#511790, AGL(1,𝔽5)×#511790 |
| maximal subgroup of | D5×#511790, C5×AGL(2,ℤ/4), C5×#72209772 |
| maximal normal subgroup of | D5×#511790 |
Past the SmallGroups library coverage — no SmallGroups id.