Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#480370 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#410 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C2×M16 | C25 |
| socle | C22 | C2×#1466 |
| prime radical | C22×#525 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 ◁ C2×#2873 ◁ G | |
| LECS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
6693 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72292716 |
| maximal normal subgroup of | C2×#72292716 |
Past the SmallGroups library coverage — no SmallGroups id.