Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1884 ⋊ C2 |
| Sylow | C53 ⋊ #21478 |
1282 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)(54,58,60,74,61,75,59,63)(55,64,65,77,66,57,72,73)(56,69,70,85,71,82,76,78)(62,79,81,84,80,68,67,83);(54,57)(55,63)(56,68)(58,65)(59,77)(60,73)(61,64)(62,78)(66,74)(67,82)(69,81)(70,83)(71,79)(72,75)(76,84)(80,85);(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)(54,56)(55,62)(57,68)(58,69)(59,76)(60,70)(61,71)(63,78)(64,79)(65,81)(66,80)(67,72)(73,83)(74,85)(75,82)(77,84);(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)(54,55,60,65,61,66,59,72)(56,67,70,62,71,81,76,80)(57,63,73,58,64,74,77,75)(68,69,83,85,79,82,84,78)Polycyclic presentation:
2^8,53|a^2=g,d^2=g,e^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^52,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,e^c=eh,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 175546);