Finite Group DatabasebetaFinite Group Databasebeta| order | 19656 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 135862272 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C23×C33×C7×C13 |
| multiplicative | (ℤ/23779)ˣ, (ℤ/30573)ˣ, (ℤ/34461)ˣ, (ℤ/34839)ˣ, (ℤ/47558)ˣ, (ℤ/61146)ˣ, (ℤ/68922)ˣ, (ℤ/69678)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1792 conjugacy classes of subgroups.
19656 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.