Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2238 ⋊ C2 |
| Sylow | C53 ⋊ #33692 |
536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 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 — 4 generators on 85 points:
(1,2)(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)(55,61)(56,65,66,67)(57,71)(60,74,75,79)(63,76)(64,70,81,82)(68,84)(73,85,80,78);(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)(54,56)(55,60)(57,70)(58,65)(59,66)(61,75)(62,78)(63,79)(64,68)(67,72)(69,85)(71,82)(73,77)(74,76)(80,83)(81,84);(54,55,59,61)(56,60,66,75)(57,69,71,62)(58,63,72,76)(64,80,81,73)(65,79,67,74)(68,83,84,77)(70,85,82,78);(56,64)(57,68)(58,72)(60,73)(62,77)(63,76)(65,70)(66,81)(67,82)(69,83)(71,84)(74,85)(75,80)(78,79)Polycyclic presentation:
2^8,53|b^2=h,d^2=e,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,d^b=dh,f^b=fh,d^c=dg,e^c=eh,f^c=fg,g^c=gh,i^c=i^52,f^d=fh,i^d=i^52554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324835);