Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D5×#23996 |
| Fitting | C5×#23996 ⋊ C2 |
| Sylow | C5 ⋊ C2×#23996 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D5×#2404 |
| commutator, cosocle | C24×C5 | C25 |
| Frattini | C24 | C24×D5 |
| Fitting | C5×#23996 | C2 |
| socle | C2×C5 | C2×#2404 |
| hypercenter | #23996 | D5 |
| hypocenter | C5 | C2×#23996 |
| LCS | G ▷ C24×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #23996 | |
9400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#6499874, AGL(1,𝔽5)×#23996, #72269864 |
| maximal normal subgroup of | D5×#6499874, AGL(1,𝔽5)×#23996, #72269864 |
Past the SmallGroups library coverage — no SmallGroups id.