Finite Group DatabasebetaFinite Group Databasebeta| order | 27744 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 835584 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C289 |
| multiplicative | (ℤ/52035)ˣ, (ℤ/55504)ˣ, (ℤ/69380)ˣ, (ℤ/104070)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C17 | C23×C3×C17 |
| socle, prime radical | C23×C3×C17 | C22×C17 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
27744 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.