Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C53×#2122 ⋊ C2 |
| Sylow | C53 ⋊ #13231 |
468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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)(54,57,69,82,60,72,59,71)(55,61,74,84,64,76,63,68)(56,66,77,83,62,75,67,81)(58,70,79,80,65,78,73,85);(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)(54,56,58,55,60,62,65,64)(57,66,70,61,72,75,78,76)(59,67,73,63,69,77,79,74)(68,82,83,80,84,71,81,85);(54,55)(56,65,62,58)(57,68)(59,74)(60,64)(61,71)(63,69)(66,80,75,85)(67,73,77,79)(70,81,78,83)(72,84)(76,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=eh,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,d^b=dg,f^b=fg,g^b=gh,i^c=i^52,f^d=fh632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87913);