Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1395 ⋊ C2 |
| Sylow | C53 ⋊ #13103 |
646 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 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)(54,57,61,74)(55,62,66,81)(56,68,69,84)(58,75,77,71)(59,73,60,72)(63,82,78,79)(64,80,65,70)(67,83,76,85);(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)(54,56,67,55)(57,68,83,62)(58,65,59,78)(60,63,77,64)(61,69,76,66)(70,73,79,75)(71,80,72,82)(74,84,85,81);(54,55,60,65,61,66,59,64)(56,58,63,76,69,77,78,67)(57,70,73,62,74,80,72,81)(68,83,79,71,84,85,82,75)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh,i^c=i^52,f^d=fh710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87175);