Finite Group DatabasebetaFinite Group Databasebeta| order | 20640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 43008 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C3×C4×C5×C8×C43 |
| multiplicative | (ℤ/22373)ˣ, (ℤ/25825)ˣ, (ℤ/44746)ˣ, (ℤ/51650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C22×C3×C5×C43 |
| socle, prime radical | C22×C3×C5×C43 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
176 conjugacy classes of subgroups.
20640 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C1721 |
| outer automorphism group of | C13×C1721 |
Past the SmallGroups library coverage — no SmallGroups id.