Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3328 ⋊ C2 |
| Sylow | C53 ⋊ #19834 |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
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)(70,74,76,71)(72,79,81,85)(73,82,75,78)(77,84,83,80);(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)(54,57,59,65)(55,61,62,69)(56,63,58,67)(60,68,66,64)(70,73,76,75)(71,78,74,82)(72,80,81,84)(77,85,83,79);(54,56,59,58)(55,60,62,66)(57,63,65,67)(61,68,69,64)(70,72,76,81)(71,77,74,83)(73,80,75,84)(78,85,82,79);(54,55)(56,60)(57,64)(58,66)(59,62)(61,63)(65,68)(67,69)(70,71,76,74)(72,79,81,85)(73,78,75,82)(77,84,83,80)Polycyclic presentation:
2^8,53|a^2=g,b^2=gh,c^2=gh,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,d^b=de,e^b=eg,f^c=fh,i^c=i^52,e^d=eg794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 160094);