Finite Group DatabasebetaFinite Group Databasebeta| order | 27540 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 124416 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C5×C17×C27 |
| multiplicative | (ℤ/27913)ˣ, (ℤ/28489)ˣ, (ℤ/32137)ˣ, (ℤ/41319)ˣ, (ℤ/55826)ˣ, (ℤ/56978)ˣ, (ℤ/64274)ˣ, (ℤ/82638)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C22×C32×C5×C17 |
| socle, prime radical | C22×C32×C5×C17 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
280 conjugacy classes of subgroups.
27540 conjugacy classes. The character table is too large to display.
| automorphism group of | C103×C271 |
| outer automorphism group of | C103×C271 |
Past the SmallGroups library coverage — no SmallGroups id.