Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #20460 |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(59,67)(61,74)(65,79)(68,69)(70,83)(71,85)(75,76)(86,87);(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)(54,56,57,55)(58,61,64,74)(59,66,67,82)(60,71,73,85)(62,75,63,76)(65,78,79,88)(68,80,69,81)(70,84,83,89)(72,86,77,87);(58,60,63,72,64,73,62,77)(59,65,69,70,67,79,68,83)(61,71,76,86,74,85,75,87)(66,78,81,84,82,88,80,89);(54,55,57,56)(58,59,62,68,64,67,63,69)(60,70,72,79,73,83,77,65)(61,66,75,80,74,82,76,81)(71,84,86,88,85,89,87,78)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=ef,e^2=h,f^2=h,g^2=h,b^a=be,d^a=dh,e^b=eh,f^b=fh,d^c=dh,i^c=i^521232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 167685);