Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13469 |
306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56)(55,60)(57,71)(58,75)(59,69)(61,80)(62,81)(63,83)(64,79)(65,70)(66,72)(67,84)(68,76)(73,85)(74,78)(77,82);(54,56,57,66,58,68,72,71,59,69,73,67,76,75,84,85)(55,60,61,65,63,78,70,80,64,79,62,77,74,83,82,81);(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)(54,55,58,74,59,64,76,63)(56,65,75,80,69,77,68,81)(57,70,72,61,73,82,84,62)(60,71,78,66,79,85,83,67)Polycyclic presentation:
2^8,53|a^2=de,b^2=d,d^2=g,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fg,g^a=gh,i^a=i^52,c^b=cf,e^b=eh,f^b=fh,d^c=dg,e^c=egh,f^c=fgh,g^c=gh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89284);