Finite Group DatabasebetaFinite Group Databasebeta| order | 27048 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 310464 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C23×C49 |
| multiplicative | (ℤ/48363)ˣ, (ℤ/54104)ˣ, (ℤ/64484)ˣ, (ℤ/81156)ˣ, (ℤ/96726)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C7 | C23×C3×C7×C23 |
| socle, prime radical | C23×C3×C7×C23 | C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
27048 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.