Finite Group DatabasebetaFinite Group Databasebeta| order | 19152 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 995328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C7×C19 |
| multiplicative | (ℤ/29541)ˣ, (ℤ/33537)ˣ, (ℤ/33663)ˣ, (ℤ/39388)ˣ, (ℤ/44716)ˣ, (ℤ/44884)ˣ, (ℤ/57492)ˣ, (ℤ/59082)ˣ, (ℤ/67074)ˣ, (ℤ/67326)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C7×C19 |
| socle, prime radical | C23×C32×C7×C19 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
19152 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.