Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C13×D49 |
| Fitting, Hall | C3×C5×C13×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C3×C5×C13 |
| Hall | C5×C13×C49 ⋊ C2×C3 |
| Hall | C3×C13×C49 ⋊ C2×C5 |
| Hall | C3×C5×C49 ⋊ C2×C13 |
| Hall | C13×C49 ⋊ C2×C3×C5 |
| Hall | C5×C49 ⋊ C2×C3×C13 |
| Hall | C3×C49 ⋊ C2×C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C13 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C3×C5×C13 |
| Frattini | C7 | C3×C5×C13×D7 |
| Fitting | C3×C5×C13×C49 | C2 |
| socle | C3×C5×C7×C13 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C3×C5×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9555 |
5070 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D13×D49, C3×D5×C13×D49, C3×D49×D65, … |
| maximal normal subgroup of | C3×C5×D13×D49, C3×D5×C13×D49, C3×D49×D65, … |
| maximal quotient of | C3×C5×C13×Dic49, C2×C3×C5×C13×D49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 7);