Finite Group DatabasebetaFinite Group Databasebeta| order | 20880 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1032192 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C5×C29 |
| multiplicative | (ℤ/23777)ˣ, (ℤ/25193)ˣ, (ℤ/26873)ˣ, (ℤ/32391)ˣ, (ℤ/32457)ˣ, (ℤ/34551)ˣ, (ℤ/36561)ˣ, (ℤ/43276)ˣ, (ℤ/47554)ˣ, (ℤ/48748)ˣ, (ℤ/50386)ˣ, (ℤ/53746)ˣ, (ℤ/62676)ˣ, (ℤ/64782)ˣ, (ℤ/64914)ˣ, (ℤ/69102)ˣ, (ℤ/73122)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C5×C29 |
| socle, prime radical | C23×C32×C5×C29 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
20880 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C31×C59 |
| outer automorphism group of | C13×C31×C59 |
Past the SmallGroups library coverage — no SmallGroups id.