Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212×C42 |
| direct product | C2×#612312 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator, Frattini, cosocle | C24 | C26 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
35765 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72280420, C2×#72280397, C2×#72280482, … |
| maximal normal subgroup of | C2×#72280420, C2×#72280397, C2×#72280482, … |
Past the SmallGroups library coverage — no SmallGroups id.