Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1888 ⋊ C2 |
| Sylow | C53 ⋊ #13426 |
512 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 73 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) = 1696 |
A minimal faithful permutation representation — 3 generators on 73 points:
(1,3,4,2)(5,6)(7,14)(8,17)(9,12)(10,13)(11,16)(15,19)(18,20)(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)(3,4)(6,11)(8,16)(10,19)(12,17)(14,20)(15,18)(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);(2,3)(6,10)(7,13)(8,16)(11,19)(12,14)(17,20)Polycyclic presentation:
2^8,53|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,i^b=i^52,e^c=eh,f^c=fh,g^c=gh,f^e=fh863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89027);