Finite Group DatabasebetaFinite Group Databasebeta| order | 37582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18791 |
| unambiguous semidirect product | C19⋊D989 |
| unambiguous semidirect product | C23⋊D817 |
| unambiguous semidirect product | C43⋊D437 |
| Fitting, socle, derived, Hall | C19×C23×C43 ⋊ C2 |
| Hall | C23×C43 ⋊ D19 |
| Hall | C19×C43 ⋊ D23 |
| Hall | C19×C23 ⋊ D43 |
| Sylow | C43 ⋊ D437 |
| Sylow | C23 ⋊ D817 |
| Sylow | C19 ⋊ D989 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C23×C43 | C2 |
| LCS | G ▷ C19×C23×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 18791 |
A minimal faithful permutation representation — 2 generators on 85 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);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)Polycyclic presentation:
2,19,23,43|b^a=b^18,c^a=c^22,d^a=d^429397 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37582, 8);