Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×#72239326 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #2297 |
| commutator | C23×C4 | C24×C4 |
| Frattini, cosocle | C24×C4 | C25 |
| socle | C23 | #13956 |
| prime radical | C2×#7629122 | C2 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×#117 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
At least 9895 conjugacy classes of subgroups; only the 7344 normal subgroups are shown.
272 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.