Finite Group DatabasebetaFinite Group Databasebeta| order | 11820 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3136 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C11820 |
| abelian | C3×C4×C5×C197 |
| multiplicative | (ℤ/11821)ˣ, (ℤ/23642)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C3×C5×C197 |
| socle, prime radical | C2×C3×C5×C197 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
11820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11820, 1);