Finite Group DatabasebetaFinite Group Databasebeta| order | 22968 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 13440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C9×C11×C29 |
| multiplicative | (ℤ/23423)ˣ, (ℤ/24263)ˣ, (ℤ/28715)ˣ, (ℤ/34479)ˣ, (ℤ/46846)ˣ, (ℤ/48526)ˣ, (ℤ/57430)ˣ, (ℤ/68958)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C3×C11×C29 |
| socle, prime radical | C22×C3×C11×C29 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96 conjugacy classes of subgroups.
22968 conjugacy classes. The character table is too large to display.
| automorphism group of | C59×C397, C19×C1277 |
| outer automorphism group of | C59×C397, C19×C1277 |
Past the SmallGroups library coverage — no SmallGroups id.