Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×ΓL(1,𝔽8)⋊D13 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C5×C7×D13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | ΓL(1,𝔽8)⋊D13 |
| commutator, cosocle, hypocenter | C7×C13 | C2×C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C2×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C5×C7 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2730 |
1295 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 56);