Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1365 |
| unambiguous semidirect product | C3⋊(C7×D455) |
| unambiguous semidirect product | C5⋊(C7×D273) |
| unambiguous semidirect product | C7⋊(C7×D195) |
| unambiguous semidirect product | C13⋊(C7×D105) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1365 |
| commutator, cosocle, hypocenter | C3×C5×C7×C13 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C13 | C2 |
| LCS | G ▷ C3×C5×C7×C13 | |
| UCS | C1 ◁ C7 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2730 |
4788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D13×D105, C7×D7×D195, C7×D15×D91, … |
| maximal normal subgroup of | C7×D13×D105, C7×D7×D195, C7×D15×D91, … |
| maximal quotient of | C7×Dic1365, C2×C7×D1365 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 180);