Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13532 |
312 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 312 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:
(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)(55,63)(56,58)(59,73)(60,70)(61,71)(62,65)(64,83)(66,68)(67,82)(69,76)(72,75)(74,85)(77,78)(79,81)(80,84);(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)(54,56,69,73,60,72,61,78)(55,62,79,74,67,80,66,83)(57,75,76,77,70,58,71,59)(63,65,81,85,82,84,68,64);(54,55,58,64,69,79,59,65,60,67,75,85,61,66,77,84)(56,68,70,83,78,82,76,80,72,81,57,74,73,63,71,62)Polycyclic presentation:
2^8,53|a^2=d,b^2=deg,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,f^a=fh,c^b=cf,d^b=dg,e^b=eg,g^b=gh,i^b=i^52,d^c=dgh,e^c=egh,g^c=gh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89661);