Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | C4×#22689 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | D42 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C23 | C2×D42 |
| prime radical | C22×#135 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
6123 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#136361 |
| maximal normal subgroup of | C4×#136361 |
Past the SmallGroups library coverage — no SmallGroups id.