Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2905 ⋊ C2 |
| Sylow | C53 ⋊ #23535 |
1352 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(57,72)(62,80)(66,81)(70,83)(71,82)(73,74)(76,84)(79,85);(54,57,58,73,60,72,59,74)(55,62,63,70,64,80,75,83)(56,66,67,82,69,81,68,71)(61,76,65,79,78,84,77,85);(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)(55,61)(57,71)(58,68)(59,67)(60,69)(62,79)(63,77)(64,78)(65,75)(66,74)(70,76)(72,82)(73,81)(80,85)(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)(56,65)(57,70)(58,75)(59,63)(60,64)(61,67)(62,73)(66,76)(68,78)(69,77)(71,79)(72,83)(74,80)(81,84)(82,85)Polycyclic presentation:
2^8,53|c^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,c^b=cg,e^b=eh,g^b=gh,i^b=i^52,d^c=dh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197491);