Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#360 ⋊ C2 |
| Sylow | C53 ⋊ #13005 |
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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:
(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)(55,62)(57,69)(58,70)(59,67)(60,71)(61,76)(63,82)(64,80)(65,81)(66,83)(68,74)(72,79)(73,78)(75,85)(77,84);(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)(55,61,65,77)(57,73)(58,74)(59,75)(62,76,81,84)(63,64,72,83)(66,82,80,79)(67,85)(68,70)(69,78);(54,55,59,63,58,64,75,77,60,65,57,72,74,83,73,61)(56,66,69,84,70,62,78,79,71,80,67,76,68,81,85,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dg,e^b=eh,f^b=fg,g^b=gh,d^c=dh,e^c=eh,f^c=fh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86579);