Finite Group DatabasebetaFinite Group Databasebeta| order | 35150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17575 |
| unambiguous semidirect product | C19⋊D925 |
| unambiguous semidirect product | C25⋊D703 |
| unambiguous semidirect product | C37⋊D475 |
| Fitting, derived, Hall | C19×C25×C37 ⋊ C2 |
| Hall | C25×C37 ⋊ D19 |
| Hall | C19×C37 ⋊ D25 |
| Hall | C19×C25 ⋊ D37 |
| Sylow | C37 ⋊ D475 |
| Sylow | C25 ⋊ D703 |
| Sylow | C19 ⋊ D925 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C19×C25×C37 | C2 |
| Frattini | C5 | D3515 |
| socle | C5×C19×C37 | D5 |
| LCS | G ▷ C19×C25×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 17575 |
A minimal faithful permutation representation — 2 generators on 81 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);(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)Polycyclic presentation:
2,5,19,37,5|b^5=e^4,b^a=b^4e,c^a=c^18,d^a=d^36,e^a=e^48789 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35150, 8);