Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2140 ⋊ C2 |
| Sylow | C53 ⋊ #13442 |
398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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)(54,56,57,70,74,84,58,68,61,72,59,76,60,71,73,82)(55,63,62,69,77,83,75,85,67,80,65,81,66,79,64,78);(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)(56,69)(57,64)(58,65)(59,75)(60,77)(61,67)(62,73)(63,70)(66,74)(68,79)(71,85)(72,81)(76,80)(78,84)(82,83);(55,62)(56,68)(57,73)(58,59)(60,74)(64,77)(65,67)(66,75)(69,78)(70,84)(71,76)(72,82)(79,83)(81,85)Polycyclic presentation:
2^8,53|c^2=d,d^2=gh,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fg,g^a=gh,c^b=cf,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^52,f^c=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89123);