Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#2018 ⋊ C2 |
| Sylow | C53 ⋊ #23892 |
1674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,57)(55,63)(56,68)(58,74)(59,73)(60,75)(61,78)(62,65)(64,82)(66,77)(67,69)(70,84)(71,85)(72,76)(79,83)(80,81);(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)(55,62)(56,67)(58,73)(59,74)(60,75)(61,77)(63,65)(64,82)(66,78)(68,69)(70,85)(71,84)(72,76)(79,81)(80,83);(54,56)(55,61)(57,68)(58,70)(59,69)(60,71)(62,81)(63,78)(64,79)(65,80)(66,76)(67,73)(72,77)(74,84)(75,85)(82,83);(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)(56,66)(57,72)(58,76)(59,64)(60,65)(61,69)(62,74)(63,73)(67,83)(68,78)(70,80)(71,79)(75,82)(77,84)(81,85)Polycyclic presentation:
2^8,53|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,e^b=eh,g^b=gh,f^c=fh,g^c=gh,i^c=i^52,e^d=eh,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 201090);