Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1822 ⋊ C2 |
| Sylow | C53 ⋊ #27674 |
696 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)(62,66,68,78,69,77,67,64)(63,72,74,70,75,86,73,83)(65,80,84,92,82,91,81,76)(71,87,89,85,88,93,79,90);(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)(56,60)(58,61)(62,65)(63,71)(64,76)(66,80)(67,81)(68,84)(69,82)(70,85)(72,87)(73,79)(74,89)(75,88)(77,91)(78,92)(83,90)(86,93);(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)(54,56)(55,58)(57,60)(59,61)(62,64,67,77,69,78,68,66)(63,70,73,72,75,83,74,86)(65,76,81,91,82,92,84,80)(71,85,79,87,88,90,89,93);(54,55,57,59)(56,58,60,61)(62,63)(64,72)(65,79)(66,83)(67,74)(68,73)(69,75)(70,77)(71,81)(76,90)(78,86)(80,93)(82,89)(84,88)(85,92)(87,91)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,i^b=i^52,f^c=fh,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, 251542);