Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9298 |
442 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 442 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) = 85 |
| transitive degree | μt(G) = 3392 |
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)(55,60)(57,65)(59,66)(61,62)(64,69)(67,68)(70,72,75,83)(71,77,79,85)(73,82,74,81)(76,80,78,84);(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)(55,59,61,68)(57,64)(58,63)(60,66,62,67)(65,69)(71,76)(73,74)(77,80)(78,79)(81,82)(84,85);(54,55)(56,59,63,68)(57,60)(58,61)(62,65)(64,66,69,67)(70,71,74,76,75,79,73,78)(72,80,82,77,83,84,81,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=gh,d^2=gh,e^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=egh,f^b=fh,d^c=dgh,e^c=eh,f^c=fgh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66285);