Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#607665 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator, Frattini, cosocle | C24 | C26 |
| prime radical | C2×#14715 | C2 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
75901 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72233551, C2×#72233572, C2×#72233548, … |
| maximal normal subgroup of | C2×#72233551, C2×#72233572, C2×#72233548, … |
| maximal quotient of | C2×C4×#14715, C22×#607665 |
Past the SmallGroups library coverage — no SmallGroups id.