Finite Group DatabasebetaFinite Group Databasebeta| order | 31752 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7900913664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33×C7 |
| abelian | C23×C32×C72×C9 |
| multiplicative | (ℤ/38227)ˣ, (ℤ/40033)ˣ, (ℤ/49149)ˣ, (ℤ/56007)ˣ, (ℤ/56889)ˣ, (ℤ/76454)ˣ, (ℤ/80066)ˣ, (ℤ/98298)ˣ, (ℤ/112014)ˣ, (ℤ/113778)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C33×C72 |
| socle, prime radical | C23×C33×C72 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8000 conjugacy classes of subgroups.
31752 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.