Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×C4×#12067 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | #442 |
| commutator | C8 | C23×C4×C8 |
| Frattini, cosocle | C2×C4×C8 | C25 |
| socle | C24 | C2×#442 |
| prime radical | C23×D16 | C2×C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C2×C43 ◁ C2×C4×#322 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
8524 conjugacy classes of subgroups.
368 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.