Finite Group DatabasebetaFinite Group Databasebeta| order | 17556 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic4389 |
| unambiguous semidirect product | C3⋊Dic1463 |
| unambiguous semidirect product | C7⋊Dic627 |
| unambiguous semidirect product | C11⋊Dic399 |
| unambiguous semidirect product | C19⋊Dic231 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D4389 |
| commutator, hypocenter | C3×C7×C11×C19 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C11×C19 | C2 |
| LCS | G ▷ C3×C7×C11×C19 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 17556 |
A minimal faithful permutation representation — 2 generators on 44 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(1,3,2,4)(6,7)(9,14)(10,13)(11,12)(16,25)(17,24)(18,23)(19,22)(20,21)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)Polycyclic presentation:
2,3,7,11,19,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^10,e^a=e^184392 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic8778, Dic13167 |
| maximal normal subgroup of | Dic8778 |
| maximal quotient of | Dic13167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17556, 20);