Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C22×#18044 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C22×D4 |
| commutator | C2×C4 | C25×C4 |
| Frattini, cosocle | C42 | C26 |
| socle | C24 | C2×C4×D4 |
| prime radical | C24×D8 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C4×M16 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
18621 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#6345807, C22×#484097, C22×#484058, … |
| maximal normal subgroup of | C22×#6345807, C22×#484097, C22×#484058, … |
| maximal quotient of | C22×#484097, C22×#484106, C2×#72216752, … |
Past the SmallGroups library coverage — no SmallGroups id.