Finite Group DatabasebetaFinite Group Databasebeta| order | 6780 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5376 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C5×C113 |
| multiplicative | (ℤ/7037)ˣ, (ℤ/10173)ˣ, (ℤ/13564)ˣ, (ℤ/14074)ˣ, (ℤ/20346)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40 conjugacy classes of subgroups.
6780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6780, 9);