Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C218 |
| direct product | C2×#72241161 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #612424 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Only the 8264 normal subgroups are shown; non-normal subgroups are omitted.
236 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.