Finite Group DatabasebetaFinite Group Databasebeta| order | 17710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D8855 |
| unambiguous semidirect product | C5⋊D1771 |
| unambiguous semidirect product | C7⋊D1265 |
| unambiguous semidirect product | C11⋊D805 |
| unambiguous semidirect product | C23⋊D385 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C11×C23 | C2 |
| LCS | G ▷ C5×C7×C11×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 8855 |
A minimal faithful permutation representation — 2 generators on 46 points:
(1,2,3,4,5)(6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(2,5)(3,4)(7,12)(8,11)(9,10)(14,23)(15,22)(16,21)(17,20)(18,19)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)Polycyclic presentation:
2,5,7,11,23|b^a=b^4,c^a=c^6,d^a=d^10,e^a=e^224429 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D385, D11×D805, D35×D253, … |
| maximal normal subgroup of | D23×D385, D11×D805, D35×D253, … |
| maximal quotient of | Dic8855, C2×D8855 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17710, 18);