Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 77309411328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C43 |
| abelian | C22×C3×C42×C5×C32 |
| multiplicative | (ℤ/85360)ˣ, (ℤ/91520)ˣ, (ℤ/116400)ˣ, (ℤ/117120)ˣ, (ℤ/124800)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C16 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C22×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
46752 conjugacy classes of subgroups.
30720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.