Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #13657 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#13658 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #2177 |
| commutator | C16 | C22×C42 |
| Frattini, cosocle | C22×C16 | C24 |
| socle | C22 | C2×#2177 |
| prime radical | C2×#2263 | C22 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ C42×C8 ◁ C4×#346 ◁ G | |
| LECS | G ▷ C22×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
990 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AGL(1,ℤ/32), C8×#13658, C2×C4×#13658, … |
| maximal normal subgroup of | C4×AGL(1,ℤ/32), C8×#13658, C2×C4×#13658, … |
| maximal quotient of | C8×#13658, C2×C4×#13658, AGL(1,𝔽5)×#13658 |
Past the SmallGroups library coverage — no SmallGroups id.