Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#6451862 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #2404 |
| commutator, Frattini, cosocle | C24 | C26 |
| socle | C22 | C2×#2404 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
35801 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72237642, #72256338, C2×#72240432, … |
| maximal normal subgroup of | C2×#72237642, #72256338, C2×#72240432, … |
Past the SmallGroups library coverage — no SmallGroups id.