Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C8 · Schur multiplier (H2) = C214 |
| direct product | C22×#17849 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C42 | C2×D4 |
| commutator | C4 | C25×C8 |
| Frattini, cosocle | C42 | C26 |
| socle | C24 | C2×C4×D4 |
| prime radical | C23×#135 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C42 ◁ C23×C4×C8 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
16613 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#483590, C22×#483881, C22×#6345865 |
| maximal normal subgroup of | C22×#483590, C22×#483881, C22×#6345865 |
| maximal quotient of | C22×#210728 |
Past the SmallGroups library coverage — no SmallGroups id.