Finite Group DatabasebetaFinite Group Databasebeta| order | 17556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C19⋊C3)⋊D7)⋊D11 |
| unambiguous semidirect product | (C11⋊(D19⋊C3))⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C19 | C22×C3 |
| LCS | G ▷ C7×C11×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1463 |
Polycyclic presentation:
2^2,3,7,11,19|e^a=e^10,f^a=f^18,d^b=d^6,e^b=e^10,f^c=f^7225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17556, 76);