Finite Group DatabasebetaFinite Group Databasebeta| order | 30576 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 193536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C13×C49 |
| multiplicative | (ℤ/46689)ˣ, (ℤ/53529)ˣ, (ℤ/54537)ˣ, (ℤ/57345)ˣ, (ℤ/61168)ˣ, (ℤ/62252)ˣ, (ℤ/71372)ˣ, (ℤ/72716)ˣ, (ℤ/76460)ˣ, (ℤ/91764)ˣ, (ℤ/93378)ˣ, (ℤ/107058)ˣ, (ℤ/109074)ˣ, (ℤ/114690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C7 | C23×C3×C7×C13 |
| socle, prime radical | C23×C3×C7×C13 | C2×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
30576 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.