Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7457 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#7457 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #1368 |
| commutator | C16 | C2×C4×C8 |
| Frattini, cosocle | C2×#346 | C23 |
| socle | C22 | C2×#1368 |
| prime radical | C23 | C2×#365 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ C42×C8 ◁ C4×#346 ◁ G | |
| LECS | G ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
336 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AGL(1,ℤ/32), #72223660, C8×#7457, … |
| maximal normal subgroup of | C4×AGL(1,ℤ/32), #72223660, C8×#7457, … |
| maximal quotient of | C8×#7457, C2×C4×#7457, AGL(1,𝔽5)×#7457 |
Past the SmallGroups library coverage — no SmallGroups id.