Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C23×#3264 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C23×C4×D4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
141765 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C23×D4×AGL(1,ℤ/8), C23×#61451, C22×#6383947, … |
| maximal normal subgroup of | C23×D4×AGL(1,ℤ/8), C23×#61451, C22×#6383947, … |
| maximal quotient of | C22×#6574130, C22×#6577212, C22×#6574842, … |
Past the SmallGroups library coverage — no SmallGroups id.