Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C53 ⋊ #20340 |
1956 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)(57,70)(62,77)(66,80)(71,72)(74,84)(78,83)(79,85)(81,82);(54,57)(55,62)(56,66)(58,71)(59,72)(60,70)(61,74)(63,78)(64,77)(65,79)(67,81)(68,82)(69,80)(73,83)(75,85)(76,84);(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)(54,56,59,68,60,69,58,67)(55,61,63,65,64,76,73,75)(57,66,72,82,70,80,71,81)(62,74,78,79,77,84,83,85);(54,55,58,63,60,64,59,73)(56,65,68,61,69,75,67,76)(57,62,71,78,70,77,72,83)(66,79,82,74,80,85,81,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,e^2=h,f^2=h,g^2=h,b^a=be,g^a=gh,f^b=fh,i^b=i^52,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, 166947);