Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C82 · Schur multiplier (H2) = C29×C8 |
| direct product | C2×C8×#12067 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C8 | #442 |
| commutator | C8 | C23×C82 |
| Frattini, cosocle | C42×C8 | C25 |
| socle | C24 | C4×#442 |
| prime radical | C23×D16 | C42 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C8 ◁ C2×C42×C8 ◁ C2×C8×#322 ◁ G | |
| LECS | G ▷ C42×C8 ▷ C22×C4 ▷ C2 ▷ C1 | |
15571 conjugacy classes of subgroups.
736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×AGL(1,ℤ/32) |
| maximal normal subgroup of | C2×C8×AGL(1,ℤ/32) |
| maximal quotient of | C2×C8×AGL(1,ℤ/32) |
Past the SmallGroups library coverage — no SmallGroups id.