Finite Group DatabasebetaFinite Group Databasebeta| order | 19701 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13184224⋊C11 |
| derived, Sylow | C199 ⋊ C9×C11 |
| Hall | C199⋊C11 ⋊ C9 |
| Hall | #13184224 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C199⋊C3)⋊C11 |
| commutator, hypocenter | C199 | C9×C11 |
| Fitting, socle, cosocle | C3×C199 | C3×C11 |
| prime radical | C3×C199⋊C11 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,11,199,3|a^3=d,c^a=c^106,c^b=c^125117 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13184224⋊C11, #51426186 |
| maximal normal subgroup of | C2×#13184224⋊C11, #51426186 |
| maximal quotient of | C2×#13184224⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19701, 2);