Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#3293 ⋊ C2 |
| Sylow | C53 ⋊ #13682 |
384 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 47 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)(57,66)(58,72)(59,75)(60,69)(61,76)(63,79)(64,78)(65,82)(67,71)(68,74)(70,84)(73,85)(77,81)(80,83);(54,55,60,65)(56,62,69,82)(57,70,58,61)(59,64,74,77)(63,71,83,73)(66,84,72,76)(67,80,85,79)(68,81,75,78);(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)(55,61)(56,66)(57,58)(59,74)(62,78)(63,64)(65,70)(67,75)(68,85)(69,72)(76,80)(77,83)(79,84)(81,82)Polycyclic presentation:
2^8,53|b^2=h,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fg,i^a=i^52,d^b=dh,e^b=efgh,g^b=gh,d^c=df,e^c=eh,f^c=fh,g^c=gh,e^d=egh,f^d=fh,f^e=fh779 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90332);