Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#360 ⋊ C2 |
| Sylow | C53 ⋊ #13002 |
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(55,57)(58,61,65,64)(59,67,70,69)(60,72,75,81)(62,76,63,77)(66,82,83,87)(68,84,78,86)(71,85,88,89)(73,79,74,80);(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)(58,60)(59,66,70,83)(61,72)(62,79)(63,80)(64,81)(65,75)(67,82,69,87)(68,85,78,89)(71,84,88,86)(73,77)(74,76);(54,55)(56,57)(58,59,63,68,64,69,76,86,65,70,62,78,61,67,77,84)(60,71,74,82,72,85,80,83,75,88,73,87,81,89,79,66)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,c^2=h,d^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dg,f^b=fg,g^b=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86564);