Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2103 ⋊ C2 |
| Sylow | C53 ⋊ #31418 |
686 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)(59,64)(60,75)(61,79)(63,71)(66,72)(68,80)(70,73)(74,81)(76,77)(78,85)(82,84);(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)(54,57,58,69)(55,61,63,80)(56,65)(59,73,64,70)(60,74)(62,79,71,68)(66,84)(67,83)(72,82)(75,81)(76,85)(77,78);(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)(54,56,64,66,58,67,59,72)(55,60,71,76,63,77,62,75)(57,65,73,82,69,83,70,84)(61,78,79,85,80,74,68,81);(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)(57,68)(58,63)(59,71)(61,70)(62,64)(65,81)(66,75)(67,77)(69,79)(72,76)(73,80)(74,82)(78,84)(83,85)Polycyclic presentation:
2^8,53|b^2=ef,c^2=e,f^2=h,b^a=be,c^a=cf,d^a=def,f^a=fh,g^a=gh,i^a=i^52,c^b=cg,d^b=de,e^b=eh,f^b=fh,g^b=gh,i^b=i^52,f^c=fh,g^c=gh,i^c=i^52,f^d=fh,i^d=i^52710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 298008);