Finite Group DatabasebetaFinite Group Databasebeta| order | 17430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D8715 |
| unambiguous semidirect product | C3⋊D2905 |
| unambiguous semidirect product | C5⋊D1743 |
| unambiguous semidirect product | C7⋊D1245 |
| unambiguous semidirect product | C83⋊D105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C83 | C2 |
| LCS | G ▷ C3×C5×C7×C83 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 8715 |
A minimal faithful permutation representation — 2 generators on 98 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98);(2,3)(5,8)(6,7)(10,15)(11,14)(12,13)(17,98)(18,97)(19,96)(20,95)(21,94)(22,93)(23,92)(24,91)(25,90)(26,89)(27,88)(28,87)(29,86)(30,85)(31,84)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)Polycyclic presentation:
2,3,5,7,83|b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^824359 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D83×D105, D7×D1245, D15×D581, … |
| maximal normal subgroup of | D83×D105, D7×D1245, D15×D581, … |
| maximal quotient of | Dic8715, C2×D8715, D26145 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17430, 17);