Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C22×D4×#361 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×#102 |
| commutator | C2×C8 | C25×C4 |
| Frattini, cosocle | C22×C8 | C26 |
| prime radical | C23×D4×D8 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C23×C4×D4 ◁ C23×C8×D4 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
98312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
320 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.