Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2069 ⋊ C2 |
| Sylow | C53 ⋊ #30237 |
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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 — 4 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)(54,57,60,72,59,71,58,70)(55,62,73,83,64,78,63,77)(56,67,66,80,69,82,68,81)(61,74,75,85,76,84,65,79);(56,66)(57,70)(58,60)(61,65)(62,77)(63,73)(68,69)(71,72)(74,84)(75,76)(78,83)(80,81);(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)(54,56,59,69)(55,61)(57,67,71,82)(58,68,60,66)(62,74)(63,65)(64,76)(70,81,72,80)(73,75)(77,79)(78,84)(83,85);(54,55,58,63,59,64,60,73)(56,65,66,61,69,75,68,76)(57,62,70,77,71,78,72,83)(67,79,80,74,82,85,81,84)Polycyclic presentation:
2^8,53|a^2=fg,b^2=f,d^2=eh,e^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,g^a=gh,c^b=cg,g^b=gh,i^b=i^52,d^c=de,e^c=eh,g^c=gh,i^d=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 281714);