Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13039 |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
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)(58,61)(59,68)(60,62)(63,76)(64,84)(65,75)(66,80)(67,70)(69,78)(71,88)(72,85)(73,89)(74,79)(77,82)(81,86)(83,87);(55,57)(58,60,74,76,66,77,65,84)(59,67,71,78,72,87,89,86)(61,62,79,63,80,82,75,64)(68,70,88,69,85,83,73,81);(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)(54,55,56,57)(58,59,64,70,74,89,62,81,66,72,63,83,65,71,82,69)(60,73,75,87,84,68,80,86,77,88,79,67,76,85,61,78)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^52,d^b=dg,e^b=egh,f^b=fg,g^b=gh,d^c=dgh,e^c=eg,f^c=fgh,g^c=gh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86814);