Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4×C5 |
| direct product | C5⋊D5×#535 |
| Fitting | C52×#535 ⋊ C2 |
| Sylow | C52 ⋊ C2×#535 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C25 |
| Fitting | C52×#535 | C2 |
| hypercenter | #535 | C5⋊D5 |
| hypocenter | C52 | C2×#535 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #535 | |
7584 conjugacy classes of subgroups.
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #535×#1043, C5⋊D5×#3498, C5⋊D5×#3484, … |
| maximal normal subgroup of | #535×#1043, C5⋊D5×#3498, C5⋊D5×#3484, … |
Past the SmallGroups library coverage — no SmallGroups id.