Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2804 ⋊ C2 |
| Sylow | C53 ⋊ #13377 |
648 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(9,11)(10,15)(12,18)(13,19)(14,21)(16,17)(20,24)(22,23)(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);(1,3,4,8)(2,5,6,7)(10,14)(13,20)(15,21)(17,23)(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);(1,2,4,6)(3,7,8,5)(9,10)(11,17)(12,14)(13,16)(15,19)(18,23)(20,22)(21,24)Polycyclic presentation:
2^8,53|a^2=dh,b^2=dh,b^a=bd,c^a=ce,f^a=fgh,c^b=cf,e^b=eg,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, 88707);