Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1418 ⋊ C2 |
| Sylow | C53 ⋊ #13667 |
294 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 55 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)(56,66)(60,73)(64,78)(65,81)(68,79)(74,77)(76,84)(80,83);(54,55)(56,65)(57,69)(58,72)(59,61)(60,64)(62,67)(63,70)(66,81)(68,84)(71,85)(73,78)(74,83)(75,82)(76,79)(77,80);(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)(56,64)(57,67)(58,70)(61,73)(62,76)(63,77)(65,69)(66,78)(68,83)(71,82)(72,74)(75,84)(79,80)(81,85)Polycyclic presentation:
2^8,53|d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,i^a=i^52,d^b=df,e^b=eh,f^b=fg,g^b=gh,d^c=dh,i^c=i^52707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90242);