Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1977 ⋊ C2 |
| Sylow | C53 ⋊ #22459 |
1312 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)(55,63)(56,68)(58,75)(59,71)(60,72)(61,77)(62,65)(64,80)(66,76)(67,74)(69,85)(70,84)(73,81)(78,83)(79,82);(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)(55,62)(56,67)(58,71)(59,75)(60,72)(61,76)(63,65)(64,80)(66,77)(68,74)(69,84)(70,85)(73,81)(78,82)(79,83);(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)(54,56,60,70)(55,61,65,78)(57,67,72,85)(58,74,59,69)(62,76,63,82)(64,79,73,66)(68,75,84,71)(77,80,83,81);(54,55,59,64,60,65,58,73)(56,66,69,61,70,79,74,78)(57,63,71,80,72,62,75,81)(67,83,68,76,85,77,84,82)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=de,e^b=eh,i^b=i^52,g^c=gh,i^c=i^52,e^d=eh,i^d=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 185508);