Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#72307102 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #24196 |
| commutator, Frattini, cosocle | C22×C8 | C26 |
| socle | C22 | C2×#24196 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C24×C4 ◁ C22×#2961 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
At least 6108 conjugacy classes of subgroups; only the 4728 normal subgroups are shown.
188 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.