Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C53×#2046 ⋊ C2 |
| Sylow | C53 ⋊ #29821 |
800 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)(65,80)(70,87)(75,92)(78,88)(79,93)(81,82)(84,90)(86,91);(56,60)(59,61)(62,65)(63,70)(64,75)(66,80)(67,82)(68,81)(69,84)(71,87)(72,88)(73,78)(74,90)(76,92)(77,93)(79,83)(85,91)(86,89);(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)(62,64)(63,69)(65,79)(66,76)(67,77)(68,83)(70,86)(71,74)(72,85)(73,89)(75,82)(78,90)(80,93)(81,92)(84,88)(87,91);(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)(56,59)(57,58)(60,61)(62,63,67,72,66,71,68,73)(64,74,77,89,76,69,83,85)(65,78,81,87,80,88,82,70)(75,91,79,84,92,86,93,90)Polycyclic presentation:
2^8,53|a^2=f,d^2=eh,f^2=h,g^2=h,b^a=be,c^a=cf,i^a=i^52,c^b=cg,g^b=gh,i^b=i^52,d^c=de,f^c=fh,g^c=gh,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 277031);