Finite Group DatabasebetaFinite Group Databasebeta| order | 19701 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C9×C199⋊C11 |
| unambiguous semidirect product | (C9×C199)⋊C11 |
| Fitting, Hall | C9×C199 ⋊ C11 |
| derived, Sylow | C199 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C199⋊C11 |
| commutator, hypocenter | C199 | C9×C11 |
| Frattini | C3 | C3×C199⋊C11 |
| Fitting | C9×C199 | C11 |
| socle, cosocle | C3×C199 | C3×C11 |
| prime radical | C3×C199⋊C11 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
261 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9×C199⋊C11, C9×D199⋊C11, D9×C199⋊C11, … |
| maximal normal subgroup of | C2×C9×C199⋊C11, C9×D199⋊C11, D9×C199⋊C11, … |
| maximal quotient of | C2×C9×C199⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19701, 3);