Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3097 ⋊ C2 |
| Sylow | C53 ⋊ #26271 |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 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)(54,56,57,61)(55,59,58,60)(62,66,86,93,68,82,67,76)(63,71,73,91,74,87,72,85)(64,77,79,84,80,83,78,65)(69,70,89,92,88,90,75,81);(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)(62,65,67,83,68,84,86,77)(63,70,72,81,74,90,73,92)(64,76,78,82,80,93,79,66)(69,87,75,91,88,71,89,85);(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)(55,58)(59,60)(62,64,67,78,68,80,86,79)(63,69,72,75,74,88,73,89)(65,82,83,93,84,66,77,76)(70,85,81,87,90,91,92,71);(54,55)(56,60)(57,58)(59,61)(62,63)(64,75)(65,81)(66,85)(67,73)(68,74)(69,78)(70,83)(71,76)(72,86)(77,90)(79,88)(80,89)(82,91)(84,92)(87,93)Polycyclic presentation:
2^8,53|b^2=f,c^2=f,d^2=eh,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,g^b=gh,i^b=i^52,g^c=gh,i^c=i^52,i^d=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 231175);