Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #10741 |
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:
(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)(58,61,63,73)(59,65,67,80)(60,69,71,86)(62,75,76,72)(64,77,78,89)(66,81,74,79)(68,82,83,84)(70,87,88,85);(58,60)(59,64,67,78)(61,69)(62,70)(63,71)(65,77,80,89)(66,68,74,83)(72,85)(73,86)(75,87)(76,88)(79,84,81,82);(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)(54,55,56,57)(58,59)(60,68)(61,65)(62,74)(63,67)(64,70)(66,76)(69,84)(71,83)(72,81)(73,80)(75,79)(77,85)(78,88)(82,86)(87,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=h,d^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^52,e^b=eh,d^c=dh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74891);