Finite Group DatabasebetaFinite Group Databasebeta| order | 7080 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3712 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C5×C59 |
| multiplicative | (ℤ/7799)ˣ, (ℤ/8267)ˣ, (ℤ/10623)ˣ, (ℤ/10629)ˣ, (ℤ/14164)ˣ, (ℤ/15598)ˣ, (ℤ/16534)ˣ, (ℤ/21246)ˣ, (ℤ/21258)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C5×C59 |
| socle, prime radical | C22×C3×C5×C59 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
7080 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.