Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C213×C4 |
| direct product | C2×#72318410 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C23×D4 |
| commutator | C2×C4 | C24×C42 |
| Frattini, cosocle | C2×C42 | C26 |
| socle | C24 | C22×C4×D4 |
| prime radical | C24×D8 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C2×C4×#405 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
39724 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
440 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.