Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2128 ⋊ C2 |
| Sylow | C53 ⋊ #12714 |
974 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 974 conjugacy classes of subgroups — too many to draw. Only its 107 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)(54,57,60,71)(55,62,65,79)(56,67,59,75)(58,70,74,84)(61,76,77,83)(63,78,72,82)(64,80,66,69)(68,81,73,85);(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)(54,56,60,59)(55,61,65,77)(57,67,71,75)(58,68,74,73)(62,76,79,83)(63,66,72,64)(69,82,80,78)(70,81,84,85);(54,55)(56,66)(57,69,71,80)(58,72,74,63)(59,64)(60,65)(61,68,77,73)(62,67,79,75)(70,83)(76,84)(78,81)(82,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,f^b=fg,i^b=i^52,e^c=eh,f^c=fh,i^c=i^52,f^d=fh632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85129);