Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #12981 |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(54,56)(55,60)(57,68)(58,67)(59,65)(61,64)(62,76)(63,73)(66,70)(69,81)(71,79)(72,74)(75,78)(77,85)(80,82)(83,84);(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)(54,55,57,62,58,63,69,77,59,61,70,74,71,75,82,84)(56,60,68,76,67,73,81,85,65,64,66,72,79,78,80,83);(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)(54,55,57,62,58,63,69,77,59,61,70,74,71,75,82,84)(56,64,66,76,67,78,80,85,65,60,68,72,79,73,81,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^52,e^b=eh,i^b=i^52,d^c=dh,f^c=fh1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86453);