Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1827 ⋊ C2 |
| Sylow | C53 ⋊ #21783 |
1230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57,59,71)(55,62,63,69)(56,66,68,81)(58,70,73,85)(60,74,65,79)(61,76,77,82)(64,78,75,83)(67,80,72,84);(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)(54,56)(55,61)(57,66)(58,72)(59,68)(60,64)(62,76)(63,77)(65,75)(67,73)(69,82)(70,84)(71,81)(74,78)(79,83)(80,85);(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)(54,56)(55,60)(57,66)(58,72)(59,68)(61,75)(62,74)(63,65)(64,77)(67,73)(69,79)(70,84)(71,81)(76,83)(78,82)(80,85);(54,55)(56,65,68,60)(57,69,71,62)(58,64)(59,63)(61,67,77,72)(66,74)(70,83,85,78)(73,75)(76,80)(79,81)(82,84)Polycyclic presentation:
2^8,53|a^2=g,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^b=gh,i^b=i^52,f^c=fh,g^c=gh,i^c=i^52,g^d=gh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 178765);