Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C53×H(3,ℤ/4) ⋊ C2 |
| Sylow | C53 ⋊ #10759 |
1202 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)(60,71)(62,76)(63,78)(64,77)(65,79)(67,82)(68,75)(69,83)(70,84)(72,86)(73,88)(74,87)(80,89)(81,85);(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)(54,55,56,57)(58,60,63,73,64,74,62,72)(59,65,69,81,68,80,67,70)(61,71,78,88,77,87,76,86)(66,79,83,85,75,89,82,84);(58,59)(60,70)(61,75,77,66)(62,69)(63,67)(64,68)(65,72)(71,85,87,84)(73,80)(74,81)(76,82,78,83)(79,86,89,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^b=i^52,f^c=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74981);