Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | D5×C13×C49⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C13×C49⋊C3) |
| unambiguous semidirect product | (D5×C49)⋊(C3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D5×C49⋊C3 |
| commutator, cosocle, hypocenter | C5×C49 | C2×C3×C13 |
| Frattini | C7 | D5×C13×ΓL(1,𝔽8) |
| Fitting | C5×C13×C49 | C2×C3 |
| socle | C5×C7×C13 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
988 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 34);