Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9937 |
526 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 85 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) = 3392 |
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)(56,62)(58,64)(59,65)(61,68)(63,69)(66,67)(70,73,76,72)(71,78,81,77)(74,85,75,83)(79,84,80,82);(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)(54,56,58,63)(55,59,61,66)(57,62,64,69)(60,67,68,65)(70,72)(71,77)(73,76)(74,85)(75,83)(78,81)(79,84)(80,82);(54,55)(56,59)(57,60)(58,61)(62,65)(63,66)(64,68)(67,69)(70,71,76,81)(72,82,73,84)(74,80,75,79)(77,85,78,83)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,c^b=cf,d^b=dg,d^c=dh,e^c=eg,i^c=i^52863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 69922);