Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#1912 ⋊ C2 |
| Sylow | C53 ⋊ #23898 |
1718 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)(58,72)(62,70)(65,84)(67,78)(69,71)(74,82)(79,85)(81,83);(54,57)(55,61)(56,64)(58,71)(59,68)(60,73)(62,78)(63,77)(65,83)(66,80)(67,70)(69,72)(74,85)(75,76)(79,82)(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)(54,56,59,66)(55,60,63,75)(57,64,68,80)(58,65,72,84)(61,76,77,73)(62,74,70,82)(67,85,78,79)(69,81,71,83);(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)(56,60)(57,67)(58,70)(59,63)(61,69)(62,72)(64,79)(65,82)(66,75)(68,78)(71,77)(73,81)(74,84)(76,83)(80,85)Polycyclic presentation:
2^8,53|b^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^52,c^b=cg,i^b=i^52,e^c=eh,f^c=fh,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, 201138);