Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#3162 ⋊ C2 |
| Sylow | C53 ⋊ #19065 |
920 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 155 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) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 points:
(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)(54,57,59,58)(55,61,62,66)(56,64,65,67)(60,68,69,63)(70,73,75,74)(71,77,79,78)(72,81,83,82)(76,80,84,85);(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)(57,58)(61,66)(63,68)(64,67)(70,72)(71,76)(73,82)(74,81)(75,83)(77,85)(78,80)(79,84);(54,56,59,65)(55,60,62,69)(57,64,58,67)(61,68,66,63)(70,72)(71,76)(73,81)(74,82)(75,83)(77,80)(78,85)(79,84);(54,55,59,62)(56,63,65,68)(57,61,58,66)(60,67,69,64)(70,71)(72,80)(73,77)(74,78)(75,79)(76,82)(81,84)(83,85)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,d^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,e^a=eg,f^a=fgh,e^b=eg,f^b=fh,d^c=dg,e^c=eh,f^c=fgh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 151485);