Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13465 |
384 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,4,5,3)(2,6,7,8)(9,11,12,18)(10,15,13,21)(14,23,20,19)(16,24,22,17)(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77);(1,3,5,4)(2,6,7,8)(9,10,12,13)(11,17,18,24)(14,22,20,16)(15,23,21,19)(25,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27);(1,2,5,7)(3,8,4,6)(10,13)(11,15)(14,20)(17,19)(18,21)(23,24)Polycyclic presentation:
2^8,53|a^2=dh,b^2=d,c^2=d,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,c^b=cf,e^b=eg,f^b=fh,e^c=eh,f^c=fh,g^c=gh,i^c=i^52,f^e=fh863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89255);