Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 74317824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C7 |
| abelian | C22×C32×C72×C16 |
| multiplicative | (ℤ/34013)ˣ, (ℤ/35819)ˣ, (ℤ/43473)ˣ, (ℤ/43731)ˣ, (ℤ/49539)ˣ, (ℤ/49833)ˣ, (ℤ/57964)ˣ, (ℤ/66052)ˣ, (ℤ/68026)ˣ, (ℤ/71638)ˣ, (ℤ/86946)ˣ, (ℤ/87462)ˣ, (ℤ/99078)ˣ, (ℤ/99666)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C23×C32×C72 |
| socle, prime radical | C23×C32×C72 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2940 conjugacy classes of subgroups.
28224 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.