Finite Group DatabasebetaFinite Group Databasebeta| order | 27072 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1695744 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C16×C47 |
| multiplicative | (ℤ/33677)ˣ, (ℤ/43299)ˣ, (ℤ/67354)ˣ, (ℤ/86598)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C23×C32×C47 |
| socle, prime radical | C23×C32×C47 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
588 conjugacy classes of subgroups.
27072 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.