Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C53×#1384 ⋊ C2 |
| Sylow | C53 ⋊ #7422 |
150 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 41 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)(55,60)(56,67)(57,68)(58,75)(61,63)(62,79)(64,81)(65,66)(69,82)(70,84)(71,77)(72,73)(74,78)(76,80)(83,85);(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)(56,66,69,60)(57,71)(58,74)(59,65)(61,67,79,82)(62,72)(63,68)(64,75)(70,78,85,81)(73,80)(76,83,77,84)Polycyclic presentation:
2^8,53|a^2=d,c^2=fgh,e^2=g,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fgh,g^a=gh,c^b=cf,d^b=defgh,e^b=egh,f^b=fgh,g^b=gh,i^b=i^52,d^c=dh863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57134);