Finite Group DatabasebetaFinite Group Databasebeta| order | 8000 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | AGL(1,𝔽5)×#87830 |
| derived, Sylow | C53 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C53 | C43 |
| Fitting, socle | C2×C53 | C2×C42 |
| prime radical, cosocle | C2×D5×C5⋊D5 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
1340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
140 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.