Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1387 ⋊ C2 |
| Sylow | C53 ⋊ #12945 |
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 6784 |
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)(58,60)(59,66)(61,72)(62,77)(63,80)(64,74)(65,81)(67,70)(68,87)(69,86)(71,78)(73,75)(76,89)(79,85)(82,88)(83,84);(54,56,57,55)(59,65)(61,62)(63,75)(66,81)(67,68)(69,83)(70,87)(71,89)(72,77)(73,80)(76,78)(79,82)(84,86)(85,88);(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)(54,55,57,56)(58,59)(60,70)(61,65)(62,67)(63,79)(64,69)(66,72)(68,75)(71,87)(73,81)(74,88)(76,83)(77,85)(78,82)(80,84)(86,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,i^a=i^52,d^b=dg,e^b=egh,g^b=gh,d^c=dgh,e^c=egh,g^c=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86231);