Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C22×#147811 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #1790 |
| commutator | C22×D4 | C24×C4 |
| Frattini, cosocle | C23×D4 | C25 |
| prime radical | C22×#36702 | C2 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26 ◁ C25×D4 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C22 ▷ C2 ▷ C1 | |
At least 6223 conjugacy classes of subgroups; only the 4776 normal subgroups are shown.
224 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213329 |
| maximal normal subgroup of | C22×#72213329 |
| maximal quotient of | #72263642 |
Past the SmallGroups library coverage — no SmallGroups id.