Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C82 · Schur multiplier (H2) = C25×C8 |
| direct product | C2×#72223654 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #12067 |
| commutator | C16 | C22×C82 |
| Frattini, cosocle | C4×#346 | C24 |
| socle | C23 | #128688 |
| prime radical | C23×D16 | C42 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C42×C8 ◁ C2×C4×#1313 ◁ G | |
| LECS | G ▷ C4×#346 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
5793 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) |
Past the SmallGroups library coverage — no SmallGroups id.