Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#1286 ⋊ C2 |
| Sylow | C53 ⋊ #9196 |
478 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(54,57,58,59)(55,60,56,61)(62,65,67,77)(63,69,70,76)(64,73,74,88)(66,80,72,78)(68,81,83,91)(71,87,85,84)(75,90,79,89)(82,93,86,92);(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)(54,56,58,55)(57,61,59,60)(62,64,72,75,67,74,66,79)(63,68,71,86,70,83,85,82)(65,73,78,90,77,88,80,89)(69,81,87,92,76,91,84,93);(54,55,59,60,58,56,57,61)(62,63,66,71,67,70,72,85)(64,68,75,82,74,83,79,86)(65,76,78,87,77,69,80,84)(73,81,89,92,88,91,90,93)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=h,d^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,f^c=fg,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 65595);