Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2991 ⋊ C2 |
| Sylow | C53 ⋊ #18018 |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 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)(56,62)(59,65)(63,68)(66,69)(70,74,76,72)(71,79,80,81)(73,82,75,83)(77,84,85,78);(54,56,57,63,58,62,64,68)(55,59,60,66,61,65,67,69)(70,73,76,75)(71,78,80,84)(72,82,74,83)(77,79,85,81);(70,72,76,74)(71,77,80,85)(73,82,75,83)(78,79,84,81);(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)(54,55,57,60,58,61,64,67)(56,59,63,66,62,65,68,69)(70,71,76,80)(72,81,74,79)(73,78,75,84)(77,83,85,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=f,d^2=g,e^2=g,f^2=h,b^a=be,e^a=eg,i^a=i^52,e^b=eg,d^c=dgh1370 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 140774);