Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1656 ⋊ C2 |
| Sylow | C53 ⋊ #18990 |
862 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 862 conjugacy classes of subgroups — too many to draw. Only its 141 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) = 6784 |
A minimal faithful permutation representation — 4 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)(70,72,74,79)(71,76,77,83)(73,78,80,84)(75,82,81,85);(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)(55,59)(57,66)(58,63)(60,69)(61,68)(62,64)(65,67)(73,80)(75,81)(78,84)(82,85);(54,55,58,61)(56,59,63,68)(57,65,64,60)(62,69,66,67)(70,71,74,77)(72,76,79,83)(73,81,80,75)(78,85,84,82);(56,62)(57,64)(59,67)(60,65)(63,66)(68,69)(71,75)(73,80)(76,82)(77,81)(78,84)(83,85)Polycyclic presentation:
2^8,53|b^2=h,d^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,e^a=eg,f^a=fgh,e^b=eg,f^b=fh,e^c=eh,f^c=fgh,i^d=i^52560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150761);