Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C212×C4 |
| direct product | C2×#72264021 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×#379 |
| commutator | C22×C4 | C23×C42 |
| Frattini, cosocle | C24×C4 | C25 |
| prime radical | C23×D42 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C22 ▷ C1 | |
At least 6654 conjugacy classes of subgroups; only the 4456 normal subgroups are shown.
296 conjugacy classes. The character table is too large to display.
| maximal quotient of | C2×#72280588 |
Past the SmallGroups library coverage — no SmallGroups id.