Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13378 |
572 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 75 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) = 1696 |
A minimal faithful permutation representation — 3 generators on 77 points:
(9,10)(11,18)(12,21)(13,16)(14,17)(15,20)(19,23)(22,24)(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);(1,3,4,8)(2,5,6,7)(10,15)(12,20)(14,23)(16,21)(18,24)(19,22)(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);(1,2,4,6)(3,7,8,5)(10,14)(11,17)(12,20)(15,23)(16,18)(21,24)Polycyclic presentation:
2^8,53|a^2=d,b^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, 88713);