Finite Group DatabasebetaFinite Group Databasebeta| order | 17556 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic627 |
| unambiguous semidirect product | C3⋊(C7×Dic209) |
| unambiguous semidirect product | C11⋊(C7×Dic57) |
| unambiguous semidirect product | C19⋊(C7×Dic33) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D627 |
| commutator, hypocenter | C3×C11×C19 | C4×C7 |
| Frattini | C2 | C7×D627 |
| Fitting, socle, prime radical | C2×C3×C7×C11×C19 | C2 |
| cosocle | C2×C3×C11×C19 | C2×C7 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 ◁ C2×C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17556 |
4410 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17556, 16);