Finite Group DatabasebetaFinite Group Databasebeta| order | 18684 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 111456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C9×C173 |
| multiplicative | (ℤ/19741)ˣ, (ℤ/28053)ˣ, (ℤ/39482)ˣ, (ℤ/56106)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C32×C173 |
| socle, prime radical | C22×C32×C173 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
100 conjugacy classes of subgroups.
18684 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1039 |
| outer automorphism group of | C19×C1039 |
Past the SmallGroups library coverage — no SmallGroups id.