Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3200 ⋊ C2 |
| Sylow | C53 ⋊ #13355 |
704 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 704 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) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(2,8)(5,20)(7,21)(9,24)(10,11)(12,27)(13,17)(14,30)(16,26)(18,32)(22,23)(25,28)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,3)(2,7)(4,17)(5,14)(6,15)(8,23)(9,25)(10,21)(11,22)(12,16)(13,19)(18,31)(20,30)(24,28)(26,27)(29,32)(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)(78,79)(80,81)(82,83)(84,85);(1,2,6,11)(3,12,15,25)(4,16,19,9)(5,8,20,10)(7,17,22,13)(14,27,30,28)(18,26,32,24)(21,29,23,31)Polycyclic presentation:
2^8,53|a^2=h,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fgh,c^b=cf,d^b=dh,g^b=gh,i^b=i^52,d^c=dg,e^c=eh,f^d=fh704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88582);