Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7457 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 2 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)(54,55,56,60,57,62,64,71,58,61,66,73,67,74,79,76,59,63,65,72,68,77,78,85,69,75,80,70,82,83,81,84);(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)(55,60,61,70,63,72,75,73)(56,64,65,78)(57,67)(58,69)(62,76,74,71,77,84,83,85)(66,81,80,79)(68,82)Polycyclic presentation:
2^8,53|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,d^b=dgh,f^b=fh,i^b=i^52,d^c=dh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57237);