Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #10115 |
466 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 87 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)(54,56)(55,59)(57,67)(58,63)(60,69)(61,68)(62,65)(64,66)(70,73,75,71)(72,79,81,85)(74,84,76,78)(77,80,83,82);(57,66)(60,65)(62,69)(64,67)(70,72,75,81)(71,77,73,83)(74,82,76,80)(78,85,84,79);(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)(54,55,58,61)(56,62,63,69)(57,65,66,60)(59,67,68,64)(70,71)(72,79)(73,75)(74,84)(76,78)(77,80)(81,85)(82,83)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,c^b=cf,d^b=dg,e^b=eh,f^b=fg,d^c=dh,e^c=eh,f^c=fg,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 71100);