Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#341 ⋊ C2 |
| Sylow | C53 ⋊ #10760 |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61)(59,66)(60,71)(62,76)(63,77)(64,78)(65,79)(67,82)(68,75)(69,83)(70,84)(72,86)(73,87)(74,88)(80,89)(81,85);(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)(54,55,56,57)(58,60,63,73,64,74,62,72)(59,65,69,81,68,80,67,70)(61,71,77,87,78,88,76,86)(66,79,83,85,75,89,82,84);(58,59,62,69,64,68,63,67)(60,70,72,65,74,81,73,80)(61,75,77,83,78,66,76,82)(71,85,87,79,88,84,86,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,f^c=fh,i^c=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74983);