Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C82 · Schur multiplier (H2) = C25×C8 |
| direct product | C2×C8×#334 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C8 | D4 |
| commutator | C4 | C22×C82 |
| Frattini, cosocle | C43 | C24 |
| socle, prime radical | C24 | C4×C4⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C8 ◁ C2×C42×C8 ◁ G | |
| LECS | G ▷ C43 ▷ C23 ▷ C1 | |
2205 conjugacy classes of subgroups.
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×#1368, C2×C8×#1580, C2×C8×#1333 |
| maximal normal subgroup of | C2×C8×#1368, C2×C8×#1580, C2×C8×#1333 |
| maximal quotient of | C2×C8×#1368, C2×C8×#1369 |
Past the SmallGroups library coverage — no SmallGroups id.