Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C227 |
| direct product | C24×#575 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C28 |
| socle | C25 | C22×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C4 ▷ C2 ▷ C1 | |
837557 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72239231, C24×#2010, C22×#393936 |
| maximal normal subgroup of | C2×#72239231, C24×#2010, C22×#393936 |
Past the SmallGroups library coverage — no SmallGroups id.