Finite Group DatabasebetaFinite Group Databasebeta| order | 19628 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14584149⋊C7 |
| Fitting, socle, derived, Sylow | C701 ⋊ C4×C7 |
| Hall | C701⋊C7 ⋊ C4 |
| Hall | #14584149 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C701 | C4×C7 |
| prime radical | D701⋊C7 | C2 |
| cosocle | D701 | C2×C7 |
| LCS | G ▷ C701 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 701 |
Polycyclic presentation:
2,7,2,701|a^2=c,d^a=d^135,d^b=d^19,d^c=d^70053 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19628, 8);