Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C218 |
| direct product | C2×#72239234 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C23×D4 |
| commutator | C22×C4 | C25×C4 |
| Frattini, cosocle | C23×C4 | C26 |
| socle | C24 | C23×C22⋊C4 |
| prime radical | C23×D4×#41 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C4×D4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 10130 conjugacy classes of subgroups; only the 19744 normal subgroups are shown.
344 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.