Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C217 |
| direct product | C23×#1783 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C2×C22⋊C4 |
| commutator | C23 | C25×C4 |
| Frattini, cosocle | C22×C4 | C26 |
| prime radical | C26×D4 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
419525 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#147567, C23×#23897, C22×#147555, … |
| maximal normal subgroup of | C22×#147567, C23×#23897, C22×#147555, … |
| maximal quotient of | #72251097, C2×#72237164 |
Past the SmallGroups library coverage — no SmallGroups id.