Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2061 ⋊ C2 |
| Sylow | C53 ⋊ #26848 |
718 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)(54,56,57,60)(55,59,58,61)(62,66,67,85,69,81,68,76)(63,72,73,84,74,92,86,93)(64,77,78,65,79,82,87,83)(70,71,75,80,89,91,88,90);(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)(59,61)(62,65,67,82,69,83,68,77)(63,71,73,80,74,91,86,90)(64,76,78,66,79,85,87,81)(70,72,75,84,89,92,88,93);(62,64,67,78,69,79,68,87)(63,70,73,75,74,89,86,88)(65,81,82,76,83,66,77,85)(71,84,80,92,91,93,90,72);(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)(56,59)(57,58)(60,61)(62,63)(64,75)(65,80)(66,84)(67,86)(68,73)(69,74)(70,78)(71,82)(72,85)(76,92)(77,91)(79,88)(81,93)(83,90)(87,89)Polycyclic presentation:
2^8,53|b^2=e,c^2=e,d^2=f,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,i^a=i^52,c^b=cg,g^b=gh,g^c=gh,i^c=i^52,i^d=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 239522);