Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C82 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#149495 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8 | C42 |
| commutator | C4 | C22×C82 |
| Frattini, cosocle | C4×C16 | C24 |
| socle | C23 | C2×#346 |
| prime radical | C24 | #346 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
1001 conjugacy classes of subgroups.
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×#1398, C2×#72223673, C2×#72223674, … |
| maximal normal subgroup of | C2×C8×#1398, C2×#72223673, C2×#72223674, … |
Past the SmallGroups library coverage — no SmallGroups id.