Finite Group DatabasebetaFinite Group Databasebeta| order | 17556 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(ΓL(1,𝔽8)⋊Dic19) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊Dic209 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(ΓL(1,𝔽8)⋊D19) |
| commutator, hypocenter | C7×C11×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C11×C19 | C2×C3 |
| prime radical | C2×C11×C19×ΓL(1,𝔽8) | C2 |
| LCS | G ▷ C7×C11×C19 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5852 |
Polycyclic presentation:
2,3,7,11,19,2|a^2=f,c^a=c^6,d^a=d^10,e^a=e^18,c^b=c^21054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17556, 46);