Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#344 ⋊ C2 |
| Sylow | C53 ⋊ #11035 |
1238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61)(59,66)(60,70)(62,78)(63,77)(64,76)(65,80)(67,74)(68,85)(69,86)(71,88)(72,75)(73,87)(79,83)(81,89)(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)(58,60,64,73)(59,65,67,69)(61,75,76,88)(62,72,63,71)(66,82,74,89)(68,84,79,81)(70,78,87,77)(80,85,86,83);(54,55,56,57)(58,59,63,68,64,67,62,79)(60,69,72,84,73,65,71,81)(61,74,78,85,76,66,77,83)(70,80,88,82,87,86,75,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,c^b=cf,f^b=fh,g^b=gh,i^b=i^52,d^c=dh,f^c=fh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76445);