Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | C4×#495850 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #3109 |
| commutator | C2×C8 | C23×C42 |
| Frattini, cosocle | C23×C8 | C25 |
| socle | C23 | C2×#3109 |
| prime radical | C22×#2213 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C42×#97 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
11568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
272 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.