Finite Group DatabasebetaFinite Group Databasebeta| order | 14190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D7095 |
| unambiguous semidirect product | C3⋊D2365 |
| unambiguous semidirect product | C5⋊D1419 |
| unambiguous semidirect product | C11⋊D645 |
| unambiguous semidirect product | C43⋊D165 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C11×C43 | C2 |
| LCS | G ▷ C3×C5×C11×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 7095 |
A minimal faithful permutation representation — 2 generators on 62 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);(2,3)(5,8)(6,7)(10,19)(11,18)(12,17)(13,16)(14,15)(21,62)(22,61)(23,60)(24,59)(25,58)(26,57)(27,56)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)Polycyclic presentation:
2,3,5,11,43|b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^423549 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D165, D11×D645, D15×D473, … |
| maximal normal subgroup of | D43×D165, D11×D645, D15×D473, … |
| maximal quotient of | Dic7095, C2×D7095 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14190, 19);