Finite Group DatabasebetaFinite Group Databasebeta| order | 14910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D7455 |
| unambiguous semidirect product | C3⋊D2485 |
| unambiguous semidirect product | C5⋊D1491 |
| unambiguous semidirect product | C7⋊D1065 |
| unambiguous semidirect product | C71⋊D105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C71 | C2 |
| LCS | G ▷ C3×C5×C7×C71 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 86 |
| transitive degree | μt(G) = 7455 |
A minimal faithful permutation representation — 2 generators on 86 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);(2,3)(5,8)(6,7)(10,15)(11,14)(12,13)(17,86)(18,85)(19,84)(20,83)(21,82)(22,81)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)Polycyclic presentation:
2,3,5,7,71|b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^703729 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D71×D105, D7×D1065, D15×D497, … |
| maximal normal subgroup of | D71×D105, D7×D1065, D15×D497, … |
| maximal quotient of | Dic7455, C2×D7455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14910, 21);