Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#2263 ⋊ C2 |
| Sylow | C53 ⋊ #13692 |
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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)(55,62)(57,67)(58,71)(59,74)(60,75)(61,68)(63,78)(64,81)(65,77)(66,70)(69,76)(72,85)(73,84)(79,83)(80,82);(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)(54,55,60,64,61,65,57,59)(56,62,75,81,68,77,67,74)(58,63,72,79,73,80,69,70)(66,71,78,85,83,84,82,76);(55,59)(56,66)(57,60)(58,70)(62,76)(63,69)(64,65)(67,78)(68,83)(71,74)(72,80)(73,79)(75,82)(77,85)(81,84)Polycyclic presentation:
2^8,53|b^2=dh,d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=ef,f^a=fg,g^a=gh,i^b=i^52,e^c=ef,f^c=fg,g^c=gh713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90387);