Finite Group DatabasebetaFinite Group Databasebeta| order | 20580 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 592704 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C7 |
| abelian | C22×C3×C5×C7×C49 |
| multiplicative | (ℤ/21113)ˣ, (ℤ/24059)ˣ, (ℤ/24353)ˣ, (ℤ/42226)ˣ, (ℤ/48118)ˣ, (ℤ/48706)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C7 | C22×C3×C5×C72 |
| socle, prime radical | C22×C3×C5×C72 | C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
360 conjugacy classes of subgroups.
20580 conjugacy classes. The character table is too large to display.
| automorphism group of | C43×C491 |
| outer automorphism group of | C43×C491 |
Past the SmallGroups library coverage — no SmallGroups id.