Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #11542 |
460 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 69 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)(54,56,58,63)(55,60,61,67)(57,62,65,69)(59,66,64,68)(70,72,74,79)(71,76,78,84)(73,80,81,85)(75,82,77,83);(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)(55,59)(60,66)(61,64)(67,68)(71,75)(72,79)(76,83)(77,78)(80,85)(82,84);(54,55)(56,60)(57,64,65,59)(58,61)(62,68,69,66)(63,67)(70,71,73,77,74,78,81,75)(72,76,80,83,79,84,85,82)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,e^2=g,b^a=bd,d^a=df,f^a=fh,c^b=cg,e^b=ef,i^c=i^52,e^d=eh713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79086);