Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C8×#368 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8 | D8 |
| commutator | C8 | C22×C4×C8 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| socle | C23 | C4×#107 |
| prime radical | C24 | C4×Q16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8 ◁ C22×C4×C8 ◁ C22×C82 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
1281 conjugacy classes of subgroups.
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×#2179, C2×C8×#1426, C2×C8×#1419 |
| maximal normal subgroup of | C2×C8×#2179, C2×C8×#1426, C2×C8×#1419 |
Past the SmallGroups library coverage — no SmallGroups id.