Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2359296 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C4×C5×C7×C8 |
| multiplicative | (ℤ/22919)ˣ, (ℤ/25571)ˣ, (ℤ/26117)ˣ, (ℤ/32877)ˣ, (ℤ/45838)ˣ, (ℤ/51142)ˣ, (ℤ/52234)ˣ, (ℤ/65754)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C32×C5×C7 |
| socle, prime radical | C23×C32×C5×C7 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1944 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C41×C43 |
| outer automorphism group of | C13×C41×C43 |
Past the SmallGroups library coverage — no SmallGroups id.