Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2102 ⋊ C2 |
| Sylow | C53 ⋊ #32696 |
552 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)(55,62)(58,73)(61,68)(67,72)(69,85)(71,76)(75,80)(77,83);(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)(54,57)(55,61,62,68)(56,65,66,82)(58,71)(59,70)(60,74)(63,78,79,84)(64,81)(67,69,72,85)(73,76)(75,77)(80,83);(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)(55,60)(57,69)(58,72)(59,66)(61,77)(62,64)(63,80)(65,71)(67,73)(68,83)(70,85)(74,78)(75,79)(76,82)(81,84);(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)(54,55,58,63,59,62,73,79)(56,64,67,80,66,60,72,75)(57,68,71,84,70,61,76,78)(65,81,69,83,82,74,85,77)Polycyclic presentation:
2^8,53|a^2=g,c^2=ef,g^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,i^a=i^52,c^b=cg,d^b=de,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,f^c=fh,i^c=i^52,g^d=gh,i^d=i^52710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 316386);