Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C29 · Schur multiplier (H2) = C236 |
| direct product | C27×D4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C28 | C22 |
| commutator, Frattini, cosocle | C2 | C29 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C28 ◁ G | |
| LECS | G ▷ C2 ▷ C1 | |
16149717 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#7630939, C23×D4×#120, C26×#120, … |
| maximal normal subgroup of | C22×#7630939, C23×D4×#120, C26×#120, … |
| maximal quotient of | C26×#120, C25×D42, C24×#3484, … |
Past the SmallGroups library coverage — no SmallGroups id.