Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#3025 ⋊ C2 |
| Sylow | C53 ⋊ #23885 |
1662 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)(54,58,61,57)(55,63,66,80)(56,69,71,68)(59,73,60,74)(62,78,79,77)(64,72,65,75)(67,83,81,82)(70,84,76,85);(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)(54,57,61,58)(55,63,66,80)(56,68,71,69)(59,74,60,73)(62,77,79,78)(64,72,65,75)(67,82,81,83)(70,85,76,84);(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)(55,62)(57,68)(58,69)(59,76)(60,70)(61,71)(63,78)(64,81)(65,67)(66,79)(72,82)(73,85)(74,84)(75,83)(77,80);(54,55)(56,67)(57,72)(58,75)(59,65)(60,64)(61,66)(62,70)(63,74)(68,77)(69,78)(71,81)(73,80)(76,79)(82,84)(83,85)Polycyclic presentation:
2^8,53|c^2=h,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,c^b=cg,e^b=eh,i^b=i^52,e^c=eh,f^c=fh,i^c=i^52,e^d=eh,f^d=fh,i^d=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 201012);