Finite Group DatabasebetaFinite Group Databasebeta| order | 32480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14450688 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C5×C7×C29 |
| multiplicative | (ℤ/56463)ˣ, (ℤ/62835)ˣ, (ℤ/67024)ˣ, (ℤ/74008)ˣ, (ℤ/75284)ˣ, (ℤ/83780)ˣ, (ℤ/111012)ˣ, (ℤ/112926)ˣ, (ℤ/125670)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C5×C7×C29 |
| socle, prime radical | C24×C5×C7×C29 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
32480 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.