Finite Group DatabasebetaFinite Group Databasebeta| order | 31536 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 124416 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C8×C9×C73 |
| multiplicative | (ℤ/32047)ˣ, (ℤ/33307)ˣ, (ℤ/37303)ˣ, (ℤ/47331)ˣ, (ℤ/47961)ˣ, (ℤ/64094)ˣ, (ℤ/66614)ˣ, (ℤ/74606)ˣ, (ℤ/94662)ˣ, (ℤ/95922)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C22×C32×C73 |
| socle, prime radical | C22×C32×C73 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
220 conjugacy classes of subgroups.
31536 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.