Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C220×C4 |
| direct product | C23×C4×#127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C4 | C23 |
| commutator | C22 | C26×C4 |
| Frattini, cosocle | C23 | C27 |
| prime radical | C24×#127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
253365 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D4×#127, C23×C4×D42, C23×#59816, … |
| maximal normal subgroup of | C23×D4×#127, C23×C4×D42, C23×#59816, … |
| maximal quotient of | C23×C4×#392, C22×C22⋊C4×#127, C22×#517979, … |
Past the SmallGroups library coverage — no SmallGroups id.