Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×#150057 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D16 |
| commutator | C16 | C23×C8 |
| Frattini, cosocle | C4×C16 | C24 |
| socle | C23 | C2×#357 |
| prime radical | C22×#508 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8 ◁ C22×C4×C16 ◁ G | |
| LECS | G ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
1451 conjugacy classes of subgroups.
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72223668, C2×C8×#2263, C2×#72223678 |
| maximal normal subgroup of | C2×#72223668, C2×C8×#2263, C2×#72223678 |
Past the SmallGroups library coverage — no SmallGroups id.