Finite Group DatabasebetaFinite Group Databasebeta| order | 32768 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 531987705983139840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C218×C43 |
| abelian | C24×C42×C128 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C64 | C27 |
| socle, prime radical | C27 | C22×C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C22×C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
1621428 conjugacy classes of subgroups.
32768 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.