Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13184 |
294 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(54,55,56,57)(59,65)(64,79)(66,81)(67,77)(68,84)(72,87)(80,83)(82,86);(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)(58,60,63,78,62,70,76,71)(59,64,67,83,65,79,77,80)(61,73,75,69,74,88,89,85)(66,82,72,68,81,86,87,84);(55,57)(58,59)(60,68,70,84)(61,72)(62,65)(63,77)(64,69,79,85)(66,75)(67,76)(71,86,78,82)(73,80,88,83)(74,87)(81,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=fg,c^2=eh,d^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,f^b=fh,g^b=gh,i^b=i^52,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87698);