Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #33427 |
524 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)(61,72)(64,79)(66,69)(67,81)(75,82)(76,77)(80,84);(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)(54,56)(55,61,60,72)(57,69)(58,67)(59,65)(62,77,73,76)(63,64,74,79)(66,68)(70,75)(71,81)(78,84,85,80)(82,83);(55,60)(57,68)(61,72)(63,74)(64,79)(66,69)(70,83)(75,82);(54,55,57,62,58,63,70,78,59,60,68,73,71,74,83,85)(56,64,66,80,67,72,82,77,65,79,69,84,81,61,75,76)Polycyclic presentation:
2^8,53|a^2=f,c^2=e,f^2=g,g^2=h,b^a=be,c^a=cg,e^a=eh,f^b=fh,d^c=dh,f^c=fh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322703);