Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #19405 |
590 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)(71,78)(75,83)(77,84)(82,85);(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)(70,72,74,81)(71,77,78,84)(73,80,76,79)(75,82,83,85);(54,56,63,67,58,65,57,64)(55,59,66,69,61,68,60,62)(70,71,76,83,74,78,73,75)(72,77,79,85,81,84,80,82);(54,55,58,61)(56,62,65,69)(57,66,63,60)(59,67,68,64)(71,75)(72,79)(73,76)(78,83)(80,81)(82,85)Polycyclic presentation:
2^8,53|a^2=gh,b^2=eg,c^2=h,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,d^b=dh,f^c=fh,i^c=i^52881 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 154925);