Finite Group DatabasebetaFinite Group Databasebeta| order | 35690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17845 |
| unambiguous semidirect product | C5⋊D3569 |
| unambiguous semidirect product | C43⋊D415 |
| unambiguous semidirect product | C83⋊D215 |
| Fitting, socle, derived, Hall | C5×C43×C83 ⋊ C2 |
| Hall | C43×C83 ⋊ D5 |
| Hall | C5×C83 ⋊ D43 |
| Hall | C5×C43 ⋊ D83 |
| Sylow | C83 ⋊ D215 |
| Sylow | C43 ⋊ D415 |
| Sylow | C5 ⋊ D3569 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C43×C83 | C2 |
| LCS | G ▷ C5×C43×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 17845 |
A minimal faithful permutation representation — 2 generators on 131 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)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(2,5)(3,4)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(50,131)(51,130)(52,129)(53,128)(54,127)(55,126)(56,125)(57,124)(58,123)(59,122)(60,121)(61,120)(62,119)(63,118)(64,117)(65,116)(66,115)(67,114)(68,113)(69,112)(70,111)(71,110)(72,109)(73,108)(74,107)(75,106)(76,105)(77,104)(78,103)(79,102)(80,101)(81,100)(82,99)(83,98)(84,97)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91)Polycyclic presentation:
2,5,43,83|b^a=b^4,c^a=c^42,d^a=d^828924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35690, 8);