Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×C4×AGL(1,ℤ/32) |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #12067 |
| commutator | C16 | C23×C4×C8 |
| Frattini, cosocle | C2×#346 | C25 |
| socle | C23 | C2×#12067 |
| prime radical | C22×#2263 | C2×C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C42×C8 ◁ C2×C4×#1313 ◁ G | |
| LECS | G ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
9581 conjugacy classes of subgroups.
376 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.