Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1976 ⋊ C2 |
| Sylow | C53 ⋊ #21559 |
868 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)(54,58,59,70,61,69,60,56)(55,62,65,77,66,78,64,67)(57,72,73,83,74,84,75,68)(63,76,79,85,80,82,71,81);(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)(54,57)(55,63)(56,68)(58,72)(59,73)(60,75)(61,74)(62,76)(64,71)(65,79)(66,80)(67,81)(69,84)(70,83)(77,85)(78,82);(54,56,59,58,61,70,60,69)(55,62,64,67,66,78,65,77)(57,68,73,72,74,83,75,84)(63,76,71,81,80,82,79,85);(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)(54,55,59,65,61,66,60,64)(56,67,58,62,70,77,69,78)(57,71,73,63,74,79,75,80)(68,82,72,81,83,76,84,85)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,d^2=g,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,d^b=dh,f^c=fh,i^c=i^52,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 176521);