Finite Group DatabasebetaFinite Group Databasebeta| order | 5040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2903040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C24×C5×C7×C9 |
| multiplicative | (ℤ/10792)ˣ, (ℤ/11176)ˣ, (ℤ/15144)ˣ, (ℤ/15336)ˣ, (ℤ/16188)ˣ, (ℤ/16764)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C24×C3×C5×C7 |
| socle, prime radical | C24×C3×C5×C7 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
804 conjugacy classes of subgroups.
5040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.