Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13172 |
274 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,60,70,84,63,72,62,69,64,73,75,85,61,71,76,86)(59,66,80,89,65,77,67,81,68,82,78,79,74,87,83,88);(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)(54,56,57,55)(58,59)(60,66)(61,74)(62,67)(63,65)(64,68)(69,81)(70,80)(71,87)(72,77)(73,82)(75,78)(76,83)(79,85)(84,89)(86,88);(54,55,57,56)(59,65)(60,69)(61,63)(62,75)(66,79)(67,83)(68,74)(70,76)(71,85)(72,84)(73,86)(77,81)(82,89)(87,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,c^2=egh,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,d^b=dh,i^b=i^52,i^c=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87632);