Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C212 |
| direct product | C2×#123533 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | #120 |
| commutator | C24 | C22×C42 |
| Frattini, cosocle | C26 | C24 |
| prime radical | C28 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C27 ◁ G | |
| LECS | G ▷ C26 ▷ C2 ▷ C1 | |
130645 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
208 conjugacy classes — view the full character table.
| maximal quotient of | C2×#72268042 |
Past the SmallGroups library coverage — no SmallGroups id.