Finite Group DatabasebetaFinite Group Databasebeta| order | 27360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5308416 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C42×C5×C19 |
| multiplicative | (ℤ/32747)ˣ, (ℤ/35495)ˣ, (ℤ/37115)ˣ, (ℤ/40075)ˣ, (ℤ/41907)ˣ, (ℤ/51525)ˣ, (ℤ/55876)ˣ, (ℤ/65494)ˣ, (ℤ/70990)ˣ, (ℤ/74230)ˣ, (ℤ/80150)ˣ, (ℤ/83814)ˣ, (ℤ/103050)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C32×C5×C19 |
| socle, prime radical | C23×C32×C5×C19 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
27360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.