Finite Group DatabasebetaFinite Group Databasebeta| order | 22272 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 458752 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C4×C29×C32 |
| multiplicative | (ℤ/28615)ˣ, (ℤ/32515)ˣ, (ℤ/36231)ˣ, (ℤ/41805)ˣ, (ℤ/44672)ˣ, (ℤ/48308)ˣ, (ℤ/57230)ˣ, (ℤ/65030)ˣ, (ℤ/72462)ˣ, (ℤ/83610)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C16 | C23×C3×C29 |
| socle, prime radical | C23×C3×C29 | C2×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
540 conjugacy classes of subgroups.
22272 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.