Finite Group DatabasebetaFinite Group Databasebeta| order | 19548 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 116640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C9×C181 |
| multiplicative | (ℤ/20653)ˣ, (ℤ/22813)ˣ, (ℤ/29331)ˣ, (ℤ/29349)ˣ, (ℤ/41306)ˣ, (ℤ/45626)ˣ, (ℤ/58662)ˣ, (ℤ/58698)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C32×C181 |
| socle, prime radical | C22×C32×C181 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
100 conjugacy classes of subgroups.
19548 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1087 |
| outer automorphism group of | C19×C1087 |
Past the SmallGroups library coverage — no SmallGroups id.