Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#72285720 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #35527 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| socle | C22 | #4928982 |
| prime radical | C2×#6451776 | C2 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 7340 conjugacy classes of subgroups; only the 5128 normal subgroups are shown.
224 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.