Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #18530 |
962 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
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)(55,60)(59,68)(61,65)(62,69)(71,78)(76,85)(77,79)(80,84);(71,77)(73,74)(76,84)(78,79)(80,85)(81,82);(54,56,58,64)(55,59,60,68)(57,66,67,63)(61,69,65,62)(70,72,75,83)(71,76,78,85)(73,82,74,81)(77,84,79,80);(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)(56,62)(57,65)(58,60)(59,63)(61,67)(64,69)(66,68)(70,71,75,78)(72,80,83,84)(73,79,74,77)(76,82,85,81)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,i^a=i^52,e^b=eg,f^b=fh,e^c=eh,f^c=fh1340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 145680);