Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1695 ⋊ C2 |
| Sylow | C53 ⋊ #19253 |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
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)(54,57,58,59)(55,62,60,66)(56,64,65,67)(61,69,68,63)(70,74,76,75)(71,72,79,78)(73,81,82,83)(77,84,85,80);(54,56)(55,61)(57,64)(58,65)(59,67)(60,68)(62,69)(63,66)(70,73)(71,77)(72,80)(74,83)(75,81)(76,82)(78,84)(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)(55,60)(61,68)(62,66)(63,69)(70,72,75,79,76,78,74,71)(73,80,81,85,82,84,83,77);(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)(56,63)(57,62)(58,60)(59,66)(61,64)(65,69)(67,68)(70,71,76,79)(72,75,78,74)(73,80,82,84)(77,83,85,81)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,d^2=h,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^52,d^b=dg,i^b=i^52,d^c=dg,f^c=fh,i^d=i^52641 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 153338);