Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4 |
| direct product | #99×#442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×D4×C22⋊C4 |
| commutator | C22×C4 | C23×C42 |
| Frattini, cosocle | C24×C4 | C25 |
| prime radical | C22×D4×D8 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C22 ▷ C1 | |
23348 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
242 conjugacy classes — view the full character table.
| maximal subgroup of | #442×B(4,𝔽2) |
| maximal normal subgroup of | #442×B(4,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.