Finite Group DatabasebetaFinite Group Databasebeta| order | 32000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12582912000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43×C5 |
| abelian | C2×C42×C5×C8×C25 |
| multiplicative | (ℤ/62115)ˣ, (ℤ/66256)ˣ, (ℤ/80800)ˣ, (ℤ/82000)ˣ, (ℤ/82820)ˣ, (ℤ/124230)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C4×C5 | C24×C52 |
| socle, prime radical | C24×C52 | C22×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
14322 conjugacy classes of subgroups.
32000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.