Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13023 |
474 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 474 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) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 points:
(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)(59,67)(61,80)(62,74)(63,75)(64,82)(65,78)(66,83)(68,88)(69,85)(70,73)(71,89)(72,87)(76,79)(77,81)(84,86);(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)(54,56,57,55)(59,66)(61,79)(62,63)(64,81)(67,83)(68,71)(69,72)(70,84)(73,86)(74,75)(76,80)(77,82)(85,87)(88,89);(54,55,57,56)(58,59,63,70,81,84,79,66,65,72,61,68,64,71,62,69)(60,73,76,87,82,85,75,86,78,88,74,67,77,83,80,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,d^2=gh,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^b=dg,e^b=egh,f^b=fg,g^b=gh,i^b=i^52,d^c=dgh,e^c=egh,f^c=fgh,g^c=gh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86700);