Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7457 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#7457 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #1368 |
| commutator | C16 | C23×C8 |
| Frattini, cosocle | #346 | C24 |
| prime radical | C24 | #365 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C22×C4×C8 ◁ C22×#346 ◁ G | |
| LECS | G ▷ #346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
673 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.