Finite Group DatabasebetaFinite Group Databasebeta| order | 19628 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic701⋊C7 |
| derived, Sylow | C701 ⋊ C4×C7 |
| Hall | C701⋊C7 ⋊ C4 |
| Hall | Dic701 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D701⋊C7 |
| commutator, hypocenter | C701 | C4×C7 |
| Fitting, socle, cosocle | C2×C701 | C2×C7 |
| prime radical | C2×C701⋊C7 | C2 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2804 |
Polycyclic presentation:
2,7,701,2|a^2=d,c^a=c^700,c^b=c^19128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19628, 2);