Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2143 ⋊ C2 |
| Sylow | C53 ⋊ #13027 |
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 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:
(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)(55,63)(57,75)(58,69)(59,70)(60,78)(61,73)(62,79)(64,68)(65,80)(66,82)(67,81)(71,77)(72,76)(74,85)(83,84);(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)(55,62,67,82)(57,75)(58,69)(59,70)(60,78)(61,73)(63,79,81,66)(64,80,74,83)(65,85,84,68)(71,77)(72,76);(54,55,59,64,60,66,77,84,61,67,57,74,76,79,58,65)(56,68,71,81,72,80,70,82,73,85,69,63,78,83,75,62)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^52,d^c=dg,e^c=eg,f^c=fg,g^c=gh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86728);