Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1882 ⋊ C2 |
| Sylow | C53 ⋊ #24927 |
862 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)(62,65)(63,70)(64,74)(66,79)(67,80)(68,77)(69,83)(71,87)(72,86)(73,88)(75,91)(76,90)(78,81)(82,89)(84,92)(85,93);(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)(55,59)(58,61)(62,64,67,76)(63,69,72,85)(65,74,80,90)(66,75,81,73)(68,82,71,84)(70,83,86,93)(77,89,87,92)(78,88,79,91);(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)(54,56,57,60)(55,58,59,61)(63,68)(64,73)(66,81)(70,77)(71,72)(74,88)(75,76)(78,79)(82,84)(86,87)(89,92)(90,91);(54,55)(56,58)(57,59)(60,61)(62,63)(64,69)(65,77)(66,68)(67,72)(70,78)(71,81)(73,84)(74,89)(75,82)(76,85)(79,86)(80,87)(83,88)(90,92)(91,93)Polycyclic presentation:
2^8,53|b^2=f,c^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,e^b=eh,g^b=gh,i^b=i^52,g^c=gh,i^c=i^52,e^d=eh,i^d=i^52875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 213817);