Finite Group DatabasebetaFinite Group Databasebeta| order | 19600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 80640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C42×C25×C49 |
| multiplicative | (ℤ/19897)ˣ, (ℤ/24625)ˣ, (ℤ/39794)ˣ, (ℤ/49250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, socle, prime radical, cosocle | C22×C5×C7 | C22×C5×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
135 conjugacy classes of subgroups.
19600 conjugacy classes. The character table is too large to display.
| automorphism group of | C101×C197 |
| outer automorphism group of | C101×C197 |
Past the SmallGroups library coverage — no SmallGroups id.