Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C215 |
| direct product | C2×#72280847 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #20586 |
| commutator | C23×C4 | C24×C4 |
| Frattini, cosocle | C22×#41 | C25 |
| socle | C22 | #392111 |
| prime radical | C2×#10586169 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#62811 ◁ G | |
| LECS | G ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1 | |
At least 10845 conjugacy classes of subgroups; only the 4408 normal subgroups are shown.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72292698 |
| maximal normal subgroup of | C2×#72292698 |
| maximal quotient of | #72302979 |
Past the SmallGroups library coverage — no SmallGroups id.