Finite Group DatabasebetaFinite Group Databasebeta| order | 27072 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 94961664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C8×C47 |
| multiplicative | (ℤ/63224)ˣ, (ℤ/63392)ˣ, (ℤ/81288)ˣ, (ℤ/81504)ˣ, (ℤ/94836)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C24×C32×C47 |
| socle, prime radical | C24×C32×C47 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2028 conjugacy classes of subgroups.
27072 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.