Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#72213278 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #13088 |
| commutator | C22×C42 | C23×C4 |
| Frattini, cosocle | #2297 | C24 |
| prime radical | C2×#417807 | C2 |
| LCS | G ▷ C22×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C23×#41 ◁ C2×#35527 ◁ G | |
| LECS | G ▷ #2297 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
19012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
110 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.