Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #10699 |
842 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)(54,55,56,57)(58,61,63,76,64,77,62,75)(59,66,69,83,68,82,67,81)(60,71,74,87,73,86,72,85)(65,78,80,89,79,88,70,84);(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)(58,60)(59,65,68,79)(61,71)(62,72)(63,74)(64,73)(66,78,82,88)(67,70,69,80)(75,85)(76,87)(77,86)(81,84,83,89);(58,59)(60,70,73,80)(61,66)(62,67)(63,69)(64,68)(65,72,79,74)(71,84,86,89)(75,81)(76,83)(77,82)(78,85,88,87)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=g,d^2=h,g^2=h,b^a=bd,f^a=fh,e^b=eh,i^b=i^522168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74737);