Finite Group DatabasebetaFinite Group Databasebeta| order | 27108 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 162000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C9×C251 |
| multiplicative | (ℤ/31633)ˣ, (ℤ/40671)ˣ, (ℤ/63266)ˣ, (ℤ/81342)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C32×C251 |
| socle, prime radical | C22×C32×C251 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
100 conjugacy classes of subgroups.
27108 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.