Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2226 ⋊ C2 |
| Sylow | C53 ⋊ #33924 |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
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)(56,61)(59,60)(63,70)(64,74)(69,85)(71,86)(72,80)(75,89)(76,90)(91,92);(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)(54,57,58,55)(56,60,61,59)(63,69)(64,74)(66,79)(67,78)(68,81)(70,85)(71,72)(73,84)(75,91)(77,93)(80,86)(82,88)(83,87)(89,92);(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)(55,59)(57,60)(58,61)(62,64,65,74)(63,68,70,73)(66,75,77,89)(67,76,78,90)(69,84,85,81)(71,82,86,87)(72,83,80,88)(79,92,93,91);(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)(54,55,58,57)(56,60,61,59)(62,63)(64,73)(65,70)(66,69)(67,80)(68,74)(71,79)(72,78)(75,81)(76,83)(77,85)(82,91)(84,89)(86,93)(87,92)(88,90)Polycyclic presentation:
2^8,53|a^2=eh,b^2=h,c^2=eh,f^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fg,g^a=gh,i^a=i^52,c^b=ch,d^b=de,i^b=i^52,f^c=fg,g^c=gh,i^c=i^52,i^d=i^52797 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327207);