Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1529 ⋊ C2 |
| Sylow | C53 ⋊ #8484 |
706 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 706 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) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(56,61)(58,60)(62,65,67,77)(63,69,70,76)(64,73,74,89)(66,80,81,78)(68,82,72,88)(71,87,85,84)(75,91,79,90)(83,93,86,92);(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)(56,60)(57,59)(58,61)(62,64)(63,68)(65,73)(66,79)(67,74)(69,82)(70,72)(71,86)(75,81)(76,88)(77,89)(78,91)(80,90)(83,85)(84,93)(87,92);(55,58,59,60)(62,63,66,71,67,70,81,85)(64,72,75,86,74,68,79,83)(65,76,78,87,77,69,80,84)(73,88,90,93,89,82,91,92)Polycyclic presentation:
2^8,53|a^2=f,c^2=g,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,f^c=fg,i^c=i^52869 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61871);