Finite Group DatabasebetaFinite Group Databasebeta| order | 27216 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 117573120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C3×C7×C81 |
| multiplicative | (ℤ/56072)ˣ, (ℤ/63896)ˣ, (ℤ/83592)ˣ, (ℤ/84108)ˣ, (ℤ/95256)ˣ, (ℤ/95844)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C27 | C24×C32×C7 |
| socle, prime radical | C24×C32×C7 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2412 conjugacy classes of subgroups.
27216 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.