Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C28 |
| direct product | C2×#129224 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#99 |
| commutator | C24 | C23×C8 |
| Frattini, cosocle | C22×M16 | C24 |
| socle | C23 | C2×#323 |
| prime radical | C27 | C8 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ C24×M16 ◁ G | |
| LECS | G ▷ C22×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
18373 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #72292969 |
| maximal normal subgroup of | #72292969 |
Past the SmallGroups library coverage — no SmallGroups id.