Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C4×AGL(1,𝔽5)2 |
| Fitting | C2×C4×C52 ⋊ C42 |
| derived, Sylow | C52 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | AGL(1,𝔽5)2 |
| commutator, hypocenter | C52 | C2×C43 |
| Frattini | C2 | C22×AGL(1,𝔽5)2 |
| Fitting | C2×C4×C52 | C42 |
| socle | C22×C52 | C2×C42 |
| prime radical | C22×D52 | C23 |
| cosocle | C2×D52 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
2598 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
200 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.