Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #8750 |
538 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 91 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:
(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)(54,57)(55,60,61,65)(56,63)(58,66)(59,67,62,68)(64,69)(70,73)(71,76)(72,78)(74,81)(75,82)(77,80)(79,85)(83,84);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56)(55,59)(57,63)(58,64)(60,67)(61,62)(65,68)(66,69)(70,72,74,79)(71,75,77,83)(73,78,81,85)(76,82,80,84);(54,55)(56,62,64,59)(57,65)(58,61)(60,66)(63,67,69,68)(70,71)(72,75)(73,80,81,76)(74,77)(78,84,85,82)(79,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=d,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^b=fg,e^c=eg,f^c=fh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 63077);