Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11266 |
560 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)(54,57,58,73,60,74,59,75)(55,62,63,80,65,81,64,71)(56,67,68,72,70,85,69,84)(61,76,66,82,78,83,77,79);(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)(54,56,58,69,60,70,59,68)(55,61,64,66,65,78,63,77)(57,72,73,67,74,84,75,85)(62,79,71,76,81,82,80,83);(54,55,59,63,60,65,58,64)(56,66,68,61,70,77,69,78)(57,71,73,81,74,80,75,62)(67,83,84,79,85,76,72,82)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,c^2=d,d^2=h,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,d^b=dh,f^b=fh,i^b=i^52,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, 77820);