Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 69120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C32×C5×C61 |
| multiplicative | (ℤ/11377)ˣ, (ℤ/12817)ˣ, (ℤ/16479)ˣ, (ℤ/22754)ˣ, (ℤ/25634)ˣ, (ℤ/32958)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
10980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 101);