Finite Group DatabasebetaFinite Group Databasebeta| order | 20590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10295 |
| unambiguous semidirect product | C5⋊D2059 |
| unambiguous semidirect product | C29⋊D355 |
| unambiguous semidirect product | C71⋊D145 |
| Fitting, socle, derived, Hall | C5×C29×C71 ⋊ C2 |
| Hall | C29×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ D29 |
| Hall | C5×C29 ⋊ D71 |
| Sylow | C71 ⋊ D145 |
| Sylow | C29 ⋊ D355 |
| Sylow | C5 ⋊ D2059 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C29×C71 | C2 |
| LCS | G ▷ C5×C29×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 10295 |
A minimal faithful permutation representation — 2 generators on 105 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(2,5)(3,4)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)Polycyclic presentation:
2,5,29,71|b^a=b^4,c^a=c^28,d^a=d^705149 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20590, 9);