Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12667 |
296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(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)(54,57,71,80,60,55,62,79,58,65,59,72,73,63,74,64)(56,66,67,81,68,70,82,84,69,61,75,76,83,77,78,85);(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)(54,56)(55,61,63,66)(57,70,65,77)(58,69)(59,67)(60,68)(62,78)(64,76,79,81)(71,75)(72,84,80,85)(73,83)(74,82);(54,55,59,64,60,65,74,80,58,63,71,79,73,57,62,72)(56,61,67,76,68,77,82,85,69,66,75,81,83,70,78,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=de,e^2=g,g^2=h,b^a=bd,f^a=fh,c^b=cg,d^b=dh,f^c=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84941);