Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 297271296 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4 |
| abelian | C22×C32×C42×C49 |
| multiplicative | (ℤ/53781)ˣ, (ℤ/62055)ˣ, (ℤ/66885)ˣ, (ℤ/71344)ˣ, (ℤ/71708)ˣ, (ℤ/89180)ˣ, (ℤ/92196)ˣ, (ℤ/107562)ˣ, (ℤ/124110)ˣ, (ℤ/133770)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C7 | C24×C32×C7 |
| socle, prime radical | C24×C32×C7 | C22×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4482 conjugacy classes of subgroups.
28224 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.