Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11337 |
686 conjugacy classes of subgroups.
| 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)(58,61,62,77,64,78,63,76)(59,66,67,74,68,85,79,84)(60,70,72,75,73,86,71,87)(65,80,81,89,82,88,69,83);(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)(58,60,62,71,64,73,63,72)(59,65,67,69,68,82,79,81)(61,75,76,86,78,87,77,70)(66,83,84,80,85,89,74,88);(54,55,56,57)(58,59)(60,69)(61,74)(62,79)(63,67)(64,68)(65,71)(66,77)(70,80)(72,82)(73,81)(75,83)(76,85)(78,84)(86,88)(87,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=d,c^2=e,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,c^b=cf,e^b=eh,d^c=dh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78249);