Finite Group DatabasebetaFinite Group Databasebeta| order | 15990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D7995 |
| unambiguous semidirect product | C3⋊D2665 |
| unambiguous semidirect product | C5⋊D1599 |
| unambiguous semidirect product | C13⋊D615 |
| unambiguous semidirect product | C41⋊D195 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C13×C41 | C2 |
| LCS | G ▷ C3×C5×C13×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 7995 |
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)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(23,62)(24,61)(25,60)(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)Polycyclic presentation:
2,3,5,13,41|b^a=b^2,c^a=c^4,d^a=d^12,e^a=e^403999 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D41×D195, D13×D615, D15×D533, … |
| maximal normal subgroup of | D41×D195, D13×D615, D15×D533, … |
| maximal quotient of | Dic7995, C2×D7995 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15990, 19);