Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1735 ⋊ C2 |
| Sylow | C53 ⋊ #10773 |
1186 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)(67,75)(68,83)(69,82)(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)(59,65,68,80,69,81,67,70)(61,71,77,87,78,88,76,86)(66,79,83,89,82,85,75,84);(58,59)(60,70)(61,75,78,83)(62,68)(63,67)(64,69)(65,72)(66,77,82,76)(71,85,88,79)(73,81)(74,80)(84,87,89,86)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,e^c=eh,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, 75036);