Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1362 ⋊ C2 |
| Sylow | C53 ⋊ #11929 |
414 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 97 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) = 6784 |
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)(62,65,68,67)(63,70,72,82)(64,74,76,83)(66,77,81,80)(69,84,86,85)(71,78,88,92)(73,89,90,87)(75,79,91,93);(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)(55,58)(56,60)(62,64)(63,69)(65,74)(66,79)(67,83)(68,76)(70,84)(71,87)(72,86)(73,78)(75,80)(77,91)(81,93)(82,85)(88,89)(90,92);(54,55,56,59,57,58,60,61)(62,63)(64,73)(65,70)(66,78)(67,82)(68,72)(69,75)(71,80)(74,89)(76,90)(77,88)(79,84)(81,92)(83,87)(85,93)(86,91)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=gh,e^2=fgh,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^b=i^52,i^c=i^52812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80812);