Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×#72241337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #392675 |
| commutator | C25 | C24×C4 |
| Frattini, cosocle | C23×D4 | C25 |
| prime radical | C2×#6628896 | C2 |
| LCS | G ▷ C25 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ C22×H(7,𝔽2) ◁ G | |
| LECS | G ▷ C23×D4 ▷ C22 ▷ C2 ▷ C1 | |
162198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
212 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.