Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×C4×#6036 |
| derived, Sylow | C52 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D52 |
| commutator, hypocenter | C52 | C23×C42 |
| Frattini | C22 | C23×D52 |
| Fitting | C23×C4×C52 | C22 |
| socle | C24×C52 | C23 |
| prime radical | C24×C5⋊D5 | C22 |
| cosocle | C22×C52 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23×C4 | |
7362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C4×#87830 |
| maximal normal subgroup of | C22×C4×#87830 |
| maximal quotient of | C22×#13100501, #72242680 |
Past the SmallGroups library coverage — no SmallGroups id.