Finite Group DatabasebetaFinite Group Databasebeta| order | 27500 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 30000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C11×C625 |
| multiplicative | (ℤ/41253)ˣ, (ℤ/55004)ˣ, (ℤ/82506)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C125 | C22×C5×C11 |
| socle, prime radical | C22×C5×C11 | C125 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
50 conjugacy classes of subgroups.
27500 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.