Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#13105092 |
| Fitting | C2×C42×C52 ⋊ C22 |
| Sylow | C52 ⋊ C2×#535 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D52 |
| commutator, cosocle | C22×C52 | C25 |
| Frattini | C22 | C23×D52 |
| Fitting | C2×C42×C52 | C22 |
| socle | C23×C52 | C24 |
| hypercenter | C2×C42 | D52 |
| hypocenter | C52 | C2×#535 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
4290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
308 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.