Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#128572 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #442 |
| commutator | C2×C8 | C22×C42 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| socle | C23 | #1762 |
| prime radical | C23×D8 | C2×C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#97 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
2757 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216543 |
| maximal normal subgroup of | C2×#72216543 |
Past the SmallGroups library coverage — no SmallGroups id.