Finite Group DatabasebetaFinite Group Databasebeta| order | 19701 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C19701 |
| abelian | C9×C11×C199 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C3×C11×C199 |
| socle, prime radical | C3×C11×C199 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
19701 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×C11×C199, C9×C11×D199, C9×D11×C199, … |
| maximal normal subgroup of | C2×C9×C11×C199, C9×C11×D199, C9×D11×C199, … |
| maximal quotient of | C2×C9×C11×C199 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19701, 1);