Finite Group DatabasebetaFinite Group Databasebeta| order | 20720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 165888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C5×C7×C37 |
| multiplicative | (ℤ/31737)ˣ, (ℤ/38865)ˣ, (ℤ/41456)ˣ, (ℤ/42316)ˣ, (ℤ/51820)ˣ, (ℤ/63474)ˣ, (ℤ/77730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C5×C7×C37 |
| socle, prime radical | C23×C5×C7×C37 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
20720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.