Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C22×#61454 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C22×C4×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
69441 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #72264537, #72264998, C22×#10576928 |
| maximal normal subgroup of | #72264537, #72264998, C22×#10576928 |
| maximal quotient of | C22×#6383947, C22×#6439849, C22×#6439857, … |
Past the SmallGroups library coverage — no SmallGroups id.