Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21077 |
990 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)(59,67,68,78)(60,71,72,77)(61,74,76,75)(65,80,81,69)(66,82,73,88)(70,85,86,89)(79,84,87,83);(58,61,63,75,64,76,62,74)(59,66,67,82,68,73,78,88)(60,70,71,85,72,86,77,89)(65,79,69,83,81,87,80,84);(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)(54,56,57,55)(58,60,63,71,64,72,62,77)(59,65,67,69,68,81,78,80)(61,70,75,85,76,86,74,89)(66,79,82,83,73,87,88,84);(54,55,57,56)(58,59)(60,69)(61,73)(62,67)(63,78)(64,68)(65,71)(66,76)(70,84)(72,80)(74,88)(75,82)(77,81)(79,89)(83,86)(85,87)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=e,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,d^b=dh,i^b=i^52,f^c=fh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 172131);