Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #11143 |
838 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)(58,61,64,79)(59,66,69,84)(60,71,73,76)(62,78,63,77)(65,80,82,86)(67,75,68,83)(70,85,81,89)(72,88,74,87);(58,60,62,72,64,73,63,74)(59,65,67,70,69,82,68,81)(61,76,77,88,79,71,78,87)(66,80,83,89,84,86,75,85);(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)(58,59,63,67,64,69,62,68)(60,70,74,82,73,81,72,65)(61,75,78,66,79,83,77,84)(71,86,88,85,76,80,87,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=d,c^2=h,d^2=h,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^52,c^b=cf,f^b=fh,d^c=dh,e^c=eh,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, 77111);