Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1317 ⋊ C2 |
| Sylow | C53 ⋊ #7339 |
356 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 2 generators on 85 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(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)(54,56)(55,60)(57,70)(58,67)(59,68)(61,78)(62,76)(63,77)(64,79)(65,72)(66,74)(69,83)(71,81)(73,75)(80,84)(82,85);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,55)(56,64,66,80,68,78,67,83)(57,69)(58,73,74,62)(59,63)(60,65,75,81,77,70,76,82)(61,71,79,85)(72,84)Polycyclic presentation:
2^8,53|a^2=d,c^2=h,d^2=f,b^a=bc,c^a=ce,e^a=eg,g^a=gh,c^b=ch,d^b=deh,f^b=fh,i^b=i^52,d^c=dg,e^d=eh704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56916);