Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#493079 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#442 |
| commutator | C8 | C23×C42 |
| Frattini, cosocle | C22×C8 | C25 |
| prime radical | C24×D8 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C22×#405 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
8753 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72239482, #72343616 |
| maximal normal subgroup of | C2×#72239482, #72343616 |
Past the SmallGroups library coverage — no SmallGroups id.