Finite Group DatabasebetaFinite Group Databasebeta| order | 19701 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C3 |
| direct product | C3×C11×C199⋊C3 |
| unambiguous semidirect product | (C11×C199)⋊C32 |
| unambiguous semidirect product | (C3×C11×C199)⋊C3 |
| Fitting, socle | C3×C11×C199 ⋊ C3 |
| derived, Sylow | C199 ⋊ C32×C11 |
| Hall | C11×C199 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | C199⋊C3 |
| commutator, cosocle, hypocenter | C199 | C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C199 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
2277 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×D199⋊C3, C3×C11⋊(D199⋊C3), C3×D11×C199⋊C3, … |
| maximal normal subgroup of | C3×C11×D199⋊C3, C3×C11⋊(D199⋊C3), C3×D11×C199⋊C3, … |
| maximal quotient of | C2×C3×C11×C199⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19701, 10);