Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#2140 ⋊ C2 |
| Sylow | C53 ⋊ #13074 |
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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:
(2,3)(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)(54,57)(55,62)(56,68)(58,75)(59,73)(60,72)(61,78)(63,80)(64,70)(65,79)(66,81)(67,82)(69,84)(71,76)(74,85)(77,83);(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)(54,56,67,64,59,69,76,77,60,63,66,55,61,74,58,65)(57,68,82,70,73,84,71,83,72,80,81,62,78,85,75,79);(54,55)(56,66)(57,70,72,62)(58,74)(59,77)(60,64)(61,65)(63,67)(68,81,80,82)(69,76)(71,85,75,84)(73,79,78,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,e^b=eh,d^c=dh,f^c=fh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87014);