Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #13540 |
234 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 83 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:
(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)(54,57,58,73,59,74,61,77)(55,63,60,76,64,71,65,81)(56,67,68,82,70,80,69,83)(62,78,66,72,79,84,75,85);(54,56,61,68,59,70,58,69)(55,62,65,66,64,79,60,75)(57,72,77,84,74,85,73,78)(63,80,81,83,71,67,76,82);(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)(54,55,58,60,59,64,61,65)(56,66,68,79,70,75,69,62)(57,71,73,81,74,63,77,76)(67,72,82,84,80,85,83,78)Polycyclic presentation:
2^8,53|a^2=d,b^2=de,c^2=d,d^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,f^a=fh,i^a=i^52,c^b=cf,d^b=dh,e^b=eh,f^b=fg,g^b=gh,f^c=fgh,g^c=gh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89705);