Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#1914 ⋊ C2 |
| Sylow | C53 ⋊ #23873 |
1686 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)(55,61)(56,65)(58,74)(59,70)(60,76)(62,79)(63,77)(64,80)(66,83)(67,82)(68,71)(69,73)(72,81)(75,84)(78,85);(58,73)(60,75)(62,71)(66,72)(68,79)(69,74)(76,84)(81,83);(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)(54,56,59,67)(55,60,63,75)(57,65,70,82)(58,72,73,66)(61,76,77,84)(62,78,71,64)(68,80,79,85)(69,83,74,81);(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)(54,55)(56,64)(57,68)(58,71)(59,63)(60,66)(61,69)(62,73)(65,76)(67,78)(70,79)(72,75)(74,77)(80,81)(82,84)(83,85)Polycyclic presentation:
2^8,53|b^2=h,e^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,g^a=gh,i^a=i^52,c^b=cg,e^b=eh,i^b=i^52,e^c=eh,e^d=eh,f^d=fh,i^d=i^52794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 200875);