Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D245 |
| unambiguous semidirect product | C5⋊(C13⋊C3×D49) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C13×C49 | C2×C3 |
| Frattini | C7 | C13⋊C3×D35 |
| socle | C5×C7×C13 | C3×D7 |
| LCS | G ▷ C5×C13×C49 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
868 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13⋊C3×D245, (C5⋊(D13⋊C3))⋊D49, D5×C13⋊C3×D49, … |
| maximal normal subgroup of | D13⋊C3×D245, (C5⋊(D13⋊C3))⋊D49, D5×C13⋊C3×D49, … |
| maximal quotient of | C13⋊C3×Dic245, C2×C13⋊C3×D245 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 41);