Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C213×C4 |
| direct product | C22×#20491 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C24 |
| commutator | C22 | C24×C42 |
| Frattini, cosocle | C22×C4 | C26 |
| socle | C25 | C23×C4 |
| prime radical | C24×D4 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
31141 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#6444993, C22×#6383947, C22×#6373373 |
| maximal normal subgroup of | C22×#6444993, C22×#6383947, C22×#6373373 |
Past the SmallGroups library coverage — no SmallGroups id.