Finite Group DatabasebetaFinite Group Databasebeta| order | 19992 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10752 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C17×C49 |
| multiplicative | (ℤ/20291)ˣ, (ℤ/21671)ˣ, (ℤ/24995)ˣ, (ℤ/40582)ˣ, (ℤ/43342)ˣ, (ℤ/49990)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C7 | C22×C3×C7×C17 |
| socle, prime radical | C22×C3×C7×C17 | C2×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96 conjugacy classes of subgroups.
19992 conjugacy classes. The character table is too large to display.
| automorphism group of | C103×C197, C13×C1667 |
| outer automorphism group of | C103×C197, C13×C1667 |
Past the SmallGroups library coverage — no SmallGroups id.