Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#6629071 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C23×D4 |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
62773 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72252512, #72311257, C2×#72252578, … |
| maximal normal subgroup of | C2×#72252512, #72311257, C2×#72252578, … |
Past the SmallGroups library coverage — no SmallGroups id.