Finite Group DatabasebetaFinite Group Databasebeta| order | 32768 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 412316860416 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C42×C8 |
| abelian | C22×C4×C8×C256 |
| multiplicative | (ℤ/123360)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C128 | C25 |
| socle, prime radical | C25 | C2×C4×C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C2×C4×C128 ▷ C2×C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
42612 conjugacy classes of subgroups.
32768 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.