Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #10955 |
900 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)(54,57,60,70)(55,62)(56,66,67,82)(58,71,59,72)(61,74)(63,79)(64,69)(65,78)(68,81,73,84)(75,80)(76,83)(77,85);(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)(54,56,59,68,60,67,58,73)(55,61,65,75,63,77,64,76)(57,66,72,81,70,82,71,84)(62,74,78,80,79,85,69,83);(54,55,58,65,60,63,59,64)(56,61,68,76,67,77,73,75)(57,69,71,62,70,78,72,79)(66,80,81,74,82,83,84,85)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=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76004);