Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C226 |
| direct product | C24×#529 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C4 | C23 |
| commutator, Frattini, cosocle | C22 | C28 |
| prime radical | C24×#121 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
553749 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×#3481, C24×#3543, C24×#3519, … |
| maximal normal subgroup of | C24×#3481, C24×#3543, C24×#3519, … |
| maximal quotient of | C23×#34943, C23×#36621, C23×#36107, … |
Past the SmallGroups library coverage — no SmallGroups id.