Finite Group DatabasebetaFinite Group Databasebeta| order | 19071 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C163 · Schur multiplier (H2) = C3 |
| direct product | C3×C13⋊C3×C163 |
| unambiguous semidirect product | C13⋊(C32×C163) |
| unambiguous semidirect product | (C3×C13)⋊(C3×C163) |
| Fitting, socle | C3×C13×C163 ⋊ C3 |
| derived, Sylow | C13 ⋊ C32×C163 |
| Hall | C13×C163 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C163 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C32×C163 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C163 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C163 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6357 |
3423 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13⋊C3×C163, C3×(C13⋊C3)⋊D163, C3×C13⋊C3×D163, … |
| maximal normal subgroup of | C3×D13⋊C3×C163, C3×(C13⋊C3)⋊D163, C3×C13⋊C3×D163, … |
| maximal quotient of | C2×C3×C13⋊C3×C163 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19071, 13);