Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13042 |
744 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 73 points:
(5,7,9,14)(6,11,12,19)(8,15,16,13)(10,17,18,20)(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73);(1,3,4,2)(6,10)(11,17)(12,18)(19,20)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(1,2,4,3)(5,6,8,10)(7,11,13,17)(9,12,16,18)(14,19,15,20)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,e^b=egh,d^c=dg,f^c=fg,i^c=i^52,e^d=eh,f^e=fh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86832);