Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9044 |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 81 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)(58,59,63,60)(61,65,62,64)(66,69)(67,72)(68,74)(70,77)(71,78)(73,76)(75,80)(79,81);(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)(58,60,63,59)(61,64,62,65)(66,68,70,75)(67,71,73,79)(69,74,77,80)(72,78,76,81);(54,55,57,56)(58,59,62,65,63,60,61,64)(66,67)(68,71)(69,76,77,72)(70,73)(74,78,80,81)(75,79)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=egh,d^b=dg,e^b=eh,f^b=fg,i^b=i^52,d^c=dh,e^c=eg,f^c=fh1034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64724);