Finite Group DatabasebetaFinite Group Databasebeta| order | 22272 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9633792 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C29×C32 |
| multiplicative | (ℤ/45784)ˣ, (ℤ/52024)ˣ, (ℤ/52864)ˣ, (ℤ/66888)ˣ, (ℤ/67968)ˣ, (ℤ/68676)ˣ, (ℤ/78036)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C24×C3×C29 |
| socle, prime radical | C24×C3×C29 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1084 conjugacy classes of subgroups.
22272 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.