Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2198 ⋊ C2 |
| Sylow | C53 ⋊ #13676 |
394 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 43 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)(54,57)(55,61)(56,64)(58,67)(59,69)(60,72)(62,75)(63,77)(65,79)(66,81)(68,71)(70,76)(73,78)(74,85)(80,82)(83,84);(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)(54,56,59,66)(55,60,63,74)(57,64,69,81)(58,65,71,82)(61,72,77,85)(62,73,70,83)(67,79,68,80)(75,78,76,84);(54,55,59,63)(56,60,66,74)(57,61,69,77)(58,70,71,62)(64,78,81,84)(65,73,82,83)(67,75,68,76)(72,80,85,79)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,f^2=h,b^a=bd,c^a=ce,f^a=fg,e^b=efgh,g^b=gh,d^c=df,f^c=fh,g^c=gh,i^c=i^52,e^d=egh,f^d=fh,f^e=fh545 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90292);