Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2984 ⋊ C2 |
| Sylow | C53 ⋊ #17601 |
882 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 85 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)(70,73,75,81)(71,77,78,85)(72,79,74,80)(76,83,82,84);(55,60)(59,67)(61,68)(62,69)(70,72,75,74)(71,76,78,82)(73,80,81,79)(77,84,85,83);(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)(55,59)(57,65)(58,64)(60,67)(61,69)(62,68)(63,66)(70,71)(72,76)(73,77)(74,82)(75,78)(79,83)(80,84)(81,85);(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)(56,62,64,69)(57,61)(58,60)(59,63,67,65)(66,68)(71,76)(72,74)(77,83)(78,82)(79,80)(84,85)Polycyclic presentation:
2^8,53|a^2=f,c^2=g,d^2=g,e^2=h,b^a=be,c^a=ch,e^a=eg,i^a=i^52,e^b=eh,f^b=fgh,i^b=i^52,d^c=dg1349 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 137146);