Finite Group DatabasebetaFinite Group Databasebeta| order | 19968 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 18874368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C4×C13×C32 |
| multiplicative | (ℤ/41128)ˣ, (ℤ/47488)ˣ, (ℤ/49960)ˣ, (ℤ/50560)ˣ, (ℤ/59952)ˣ, (ℤ/60288)ˣ, (ℤ/61056)ˣ, (ℤ/61692)ˣ, (ℤ/64896)ˣ, (ℤ/74940)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C16 | C24×C3×C13 |
| socle, prime radical | C24×C3×C13 | C2×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2568 conjugacy classes of subgroups.
19968 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.