Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2956 ⋊ C2 |
| Sylow | C53 ⋊ #33690 |
526 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)(57,68,69,65)(58,74)(62,76,77,78)(63,81)(66,72)(67,80,84,82)(70,73,83,85)(71,79);(54,57)(55,62)(56,65)(58,73)(59,68)(60,69)(61,76)(63,80)(64,77)(66,83)(67,71)(70,72)(74,85)(75,78)(79,84)(81,82);(54,56,60,59)(55,61,64,75)(57,65,69,68)(58,72,74,66)(62,76,77,78)(63,79,81,71)(67,80,84,82)(70,85,83,73);(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)(56,61)(57,67)(58,71)(59,75)(60,64)(62,70)(63,72)(65,82)(66,81)(68,80)(69,84)(73,76)(74,79)(77,83)(78,85)Polycyclic presentation:
2^8,53|b^2=h,d^2=e,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^52,f^b=fh,d^c=dg,e^c=eh,f^c=fg,g^c=gh,f^d=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324816);