Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#421 ⋊ C2 |
| Sylow | C53 ⋊ #11037 |
1252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(54,57)(55,62)(56,66)(58,70)(59,71)(60,72)(61,75)(63,79)(64,81)(65,82)(67,83)(68,84)(69,74)(73,80)(76,85)(77,78);(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)(54,56)(55,61)(57,69)(58,74)(59,67)(60,68)(62,78)(63,77)(64,76)(65,73)(66,71)(70,84)(72,83)(75,80)(79,85)(81,82);(54,55,59,63,60,64,58,73)(56,65,67,61,68,77,74,76)(57,62,71,79,72,81,70,80)(66,78,83,85,84,82,69,75)Polycyclic presentation:
2^8,53|a^2=g,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,c^b=cf,d^b=dh,e^b=eh,f^b=fh,f^c=fh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76457);