Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #17777 |
900 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 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)(70,74,76,72)(71,79,80,81)(73,82,75,83)(77,84,85,78);(70,73,76,75)(71,78,80,84)(72,82,74,83)(77,79,85,81);(54,56,58,64)(55,59,60,62)(57,65,66,63)(61,69,68,67)(70,72,76,74)(71,77,80,85)(73,82,75,83)(78,79,84,81);(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)(54,55,57,61,58,60,66,68)(56,62,63,69,64,59,65,67)(70,71)(72,81)(73,78)(74,79)(75,84)(76,80)(77,82)(83,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=h,d^2=h,e^2=h,f^2=gh,b^a=be,e^a=eg,i^a=i^52,e^b=eh,f^b=fgh,d^c=dh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 138484);