Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#72285493 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | #2433 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| socle | C22 | #607767 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C24×C8 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 9706 conjugacy classes of subgroups; only the 5968 normal subgroups are shown.
272 conjugacy classes. The character table is too large to display.
| automorphism group of | #7467 |
Past the SmallGroups library coverage — no SmallGroups id.