Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1389 ⋊ C2 |
| Sylow | C53 ⋊ #12874 |
376 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(55,62,63,70)(57,71)(58,59)(61,76,66,81)(64,65,80,75)(67,83)(68,74)(72,73)(77,79,82,78)(84,85);(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)(55,61)(57,67)(58,74)(59,68)(60,69)(62,76)(63,66)(64,77)(65,79)(70,81)(71,83)(72,85)(73,84)(75,78)(80,82);(54,55,58,65,60,63,59,75)(56,66,68,79,69,61,74,78)(57,70,72,80,73,62,71,64)(67,76,83,82,84,81,85,77)Polycyclic presentation:
2^8,53|a^2=f,c^2=d,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,f^b=fh,i^b=i^52,e^c=eg,f^c=fh,g^c=gh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85890);