Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #33329 |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(56,65)(61,74)(66,79)(67,80)(72,76)(75,84)(81,82)(83,85);(54,56)(55,61)(57,66)(58,67)(59,65)(60,72)(62,75)(63,74)(64,76)(68,79)(69,81)(70,80)(71,82)(73,83)(77,85)(78,84);(55,60,63,64)(57,68)(61,72,74,76)(62,77,78,73)(66,79)(69,71)(75,85,84,83)(81,82);(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)(54,55,57,62,58,64,69,77,59,63,68,78,70,60,71,73)(56,61,66,75,67,76,81,85,65,74,79,84,80,72,82,83)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,e^2=g,g^2=h,b^a=bg,f^a=fh,i^a=i^52,e^b=eh,d^c=dh1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322230);