Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2159 ⋊ C2 |
| Sylow | C53 ⋊ #12940 |
424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(59,66)(61,62)(63,76)(65,81)(67,79)(68,86)(69,85)(70,83)(71,75)(72,89)(73,80)(77,78)(82,84)(87,88);(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)(54,56,57,55)(58,60)(59,65)(61,75)(62,71)(63,80)(64,74)(66,81)(67,70)(68,87)(69,84)(72,77)(73,76)(78,89)(79,83)(82,85)(86,88);(54,55,57,56)(58,59)(60,70)(61,67)(62,66)(63,79)(64,69)(65,71)(68,76)(72,83)(73,82)(74,88)(75,87)(77,86)(78,85)(80,81)(84,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,d^b=dg,e^b=eg,g^b=gh,d^c=dg,e^c=egh,g^c=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86192);