Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1978 ⋊ C2 |
| Sylow | C53 ⋊ #13439 |
418 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 95 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)(55,57)(58,60,61,72,76,86,78,89,64,74,62,79,63,73,75,87)(59,66,67,71,80,85,77,88,70,83,68,84,69,82,65,81);(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)(59,65)(60,72)(61,75)(62,78)(63,76)(67,69)(68,80)(70,77)(71,81)(73,89)(74,79)(82,85)(84,88)(86,87);(54,55)(56,57)(58,59)(60,71)(61,65)(62,77)(63,80)(64,70)(66,72)(67,75)(68,78)(69,76)(73,88)(74,84)(79,83)(81,86)(82,89)(85,87)Polycyclic presentation:
2^8,53|c^2=d,d^2=gh,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,g^a=gh,c^b=cf,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^52,e^c=eh,f^c=fh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89107);