Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2191 ⋊ C2 |
| Sylow | C53 ⋊ #12116 |
426 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 53 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:
(1,4,7,6)(2,9,11,21)(3,13,15,22)(5,19,20,16)(8,23,24,25)(10,17,27,32)(12,28,29,26)(14,30,31,18)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84);(1,3)(2,8)(4,13)(5,18)(6,22)(7,15)(9,23)(10,26)(11,24)(12,17)(14,19)(16,31)(20,30)(21,25)(27,28)(29,32)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85);(1,2)(3,12)(4,9)(5,17)(6,21)(7,11)(8,14)(10,19)(13,28)(15,29)(16,27)(18,23)(20,32)(22,26)(24,31)(25,30)Polycyclic presentation:
2^8,53|c^2=h,d^2=fh,f^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fh,g^a=gh,d^b=df,e^b=egh,f^b=fh,i^b=i^52,d^c=dg,i^c=i^52,e^d=eh545 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81743);