Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2202 ⋊ C2 |
| Sylow | C53 ⋊ #13678 |
400 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 400 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)(54,56,59,66)(55,61,63,79)(57,69,67,84)(58,72,71,65)(60,74,68,85)(62,77,81,78)(64,73,82,70)(75,76,80,83);(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)(54,55)(56,61)(57,68)(58,62)(59,63)(60,67)(64,83)(65,78)(66,79)(69,85)(70,80)(71,81)(72,77)(73,75)(74,84)(76,82);(55,60)(57,67)(58,71)(61,76)(62,75)(63,68)(64,82)(69,84)(74,77)(78,85)(79,83)(80,81)Polycyclic presentation:
2^8,53|c^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fg,d^b=dh,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=fh464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90304);