Finite Group DatabasebetaFinite Group Databasebeta| order | 27648 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 86973087744 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C43 |
| abelian | C22×C42×C16×C27 |
| multiplicative | (ℤ/74120)ˣ, (ℤ/88944)ˣ, (ℤ/103920)ˣ, (ℤ/104640)ˣ, (ℤ/110160)ˣ, (ℤ/111180)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C8×C9 | C25×C3 |
| socle, prime radical | C25×C3 | C22×C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
36564 conjugacy classes of subgroups.
27648 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.