Finite Group DatabasebetaFinite Group Databasebeta| order | 5460 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C5×C7×C13 |
| multiplicative | (ℤ/5609)ˣ, (ℤ/5633)ˣ, (ℤ/6017)ˣ, (ℤ/6377)ˣ, (ℤ/6419)ˣ, (ℤ/8193)ˣ, (ℤ/8199)ˣ, (ℤ/10924)ˣ, (ℤ/11218)ˣ, (ℤ/11266)ˣ, (ℤ/12034)ˣ, (ℤ/12754)ˣ, (ℤ/12838)ˣ, (ℤ/16386)ˣ, (ℤ/16398)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
80 conjugacy classes of subgroups.
5460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5460, 49);