Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1379 ⋊ C2 |
| Sylow | C53 ⋊ #13019 |
496 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(59,67)(61,78)(62,63)(64,79)(66,83)(68,88)(69,71)(70,80)(72,86)(73,74)(75,81)(76,82)(84,87)(85,89);(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)(54,56,57,55)(58,60)(59,66)(61,74)(62,75)(63,81)(64,82)(65,77)(67,83)(68,72)(69,84)(70,89)(71,87)(73,78)(76,79)(80,85)(86,88);(54,55,57,56)(58,59,63,69,79,88,78,68,65,71,61,67,64,70,62,80)(60,72,75,86,82,84,74,66,77,85,73,89,76,83,81,87)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,d^2=gh,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^52,d^c=dg,e^c=egh,f^c=fg,g^c=gh,i^c=i^521502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86673);