Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #21181 |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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)(58,62,64,63)(59,67,69,68)(60,72,74,73)(61,76,78,77)(65,70,80,83)(66,75,82,81)(71,86,88,87)(79,84,85,89);(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)(58,61,63,77,64,78,62,76)(59,66,67,75,69,82,68,81)(60,71,73,87,74,88,72,86)(65,79,70,84,80,85,83,89);(54,56,57,55)(58,60)(59,65)(61,71)(62,72)(63,73)(64,74)(66,79)(67,70)(68,83)(69,80)(75,84)(76,86)(77,87)(78,88)(81,89)(82,85);(54,55,57,56)(58,59)(60,70)(61,75)(62,67)(63,68)(64,69)(65,73)(66,77)(71,85)(72,80)(74,83)(76,82)(78,81)(79,88)(84,87)(86,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=f,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,e^b=eh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 173117);