Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1271 ⋊ C2 |
| Sylow | C53 ⋊ #7788 |
418 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 81 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) = 6784 |
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)(55,58)(56,61)(59,60)(62,64,66,65)(63,67,68,69)(70,73)(71,76)(72,78)(74,80)(75,81)(77,83)(79,85)(82,84);(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)(62,63)(64,67)(65,69)(66,68)(70,72)(71,75)(73,78)(74,79)(76,81)(77,82)(80,85)(83,84);(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)(54,55)(56,58)(57,60)(59,61)(63,67)(64,65)(68,69)(70,71,74,77)(72,75,79,82)(73,76,80,83)(78,84,85,81)Polycyclic presentation:
2^8,53|a^2=g,c^2=f,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,i^a=i^52,d^b=df,e^b=eg,i^b=i^52,d^c=dg,e^c=eh,i^c=i^521025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 58607);