Finite Group DatabasebetaFinite Group Databasebeta| order | 19628 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C4×C701⋊C7 |
| unambiguous semidirect product | (C4×C701)⋊C7 |
| Fitting, Hall | C4×C701 ⋊ C7 |
| derived, Sylow | C701 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C701⋊C7 |
| commutator, hypocenter | C701 | C4×C7 |
| Frattini | C2 | C2×C701⋊C7 |
| Fitting | C4×C701 | C7 |
| socle, cosocle | C2×C701 | C2×C7 |
| prime radical | C2×C701⋊C7 | C2 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2804 |
428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19628, 3);