Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C220 |
| direct product | C22×D4×#444 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C23×D4 |
| commutator | C2×C4 | C26×C4 |
| Frattini, cosocle | C22×C4 | C27 |
| socle | C24 | C22×C4×D4 |
| prime radical | C22×D4×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C23×C8×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
217852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D4×AGL(1,ℤ/16) |
| maximal normal subgroup of | C22×D4×AGL(1,ℤ/16) |
Past the SmallGroups library coverage — no SmallGroups id.