Finite Group DatabasebetaFinite Group Databasebeta| order | 29520 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 15360 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C5×C8×C9×C41 |
| multiplicative | (ℤ/30299)ˣ, (ℤ/31939)ˣ, (ℤ/32483)ˣ, (ℤ/45387)ˣ, (ℤ/60598)ˣ, (ℤ/63878)ˣ, (ℤ/64966)ˣ, (ℤ/90774)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C22×C3×C5×C41 |
| socle, prime radical | C22×C3×C5×C41 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
132 conjugacy classes of subgroups.
29520 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.