Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #11395 |
820 conjugacy classes of subgroups.
| 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)(54,57)(55,61,62,67)(56,64)(58,69)(59,68)(60,72,73,76)(63,77,78,82)(65,80)(66,81)(70,83)(71,75)(74,84,79,85);(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)(55,60,62,73)(57,64)(58,70)(59,65)(61,76,67,72)(63,79,78,74)(66,71)(68,80)(69,83)(75,81)(77,84,82,85);(54,55,58,63,59,62,71,78)(56,60,66,74,65,73,70,79)(57,67,69,82,68,61,75,77)(64,76,81,85,80,72,83,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=f,c^2=f,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,c^b=cf,d^b=dh,g^b=gh,i^b=i^52,d^c=dh,e^c=eh,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, 78536);