Finite Group Databasebeta

← Group #307816

Character table — Group #307816

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-111-1-1-11111-1-1
χ51111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-11-1-11-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1111-1
χ12111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111111-1-1-1-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1111-111-1-1111-1
χ172222222222-2-222-2-2-2-20000222200-2-2-2-2000022-2-20000000000000000000000
χ182222222222-2-222-2-2-2-2000022-2-200-2-2220000-2-2220000000000000000000000
χ192222222222-2-222-2-2-2-20000-2-2220022-2-20000-2-2220000000000000000000000
χ202222222222-2-222-2-2-2-20000-2-2-2-2002222000022-2-20000000000000000000000
χ2122222222-2-222-2-222-2-222220000220000-2-2-2-200000000000000200-200000000
χ2222222222-2-222-2-222-2-222220000-2-2000022-2-200000000000000-200200000000
χ2322222222-2-222-2-222-2-2-2-2-2-20000220000222200000000000000-200-200000000
χ2422222222-2-222-2-222-2-2-2-2-2-20000-2-20000-2-22200000000000000200200000000
χ252-22-2-22-222222-2-2-2-2-2222-2-2002i−2i00002i−2i002-20000000000000000002i−2i000000
χ262-22-2-22-222222-2-2-2-2-2222-2-200−2i2i0000−2i2i002-2000000000000000000−2i2i000000
χ272-22-2-22-222222-2-2-2-2-22-2-222002i−2i00002i−2i00-22000000000000000000−2i2i000000
χ282-22-2-22-222222-2-2-2-2-22-2-22200−2i2i0000−2i2i00-220000000000000000002i−2i000000
χ292-22-2-22-2222-2-2-2-2222-20000002i−2i0000−2i2i0000000022-2-22i2i−2i−2i00000000000000
χ302-22-2-22-2222-2-2-2-2222-20000002i−2i0000−2i2i00000000-2-222−2i−2i2i2i00000000000000
χ312-22-2-22-2222-2-2-2-2222-2000000−2i2i00002i−2i0000000022-2-2−2i−2i2i2i00000000000000
χ322-22-2-22-2222-2-2-2-2222-2000000−2i2i00002i−2i00000000-2-2222i2i−2i−2i00000000000000
χ332-22-2-22-22-2-22222-2-22-222-2-2000000000000-220000000000002i−2i02i−2i000000000
χ342-22-2-22-22-2-22222-2-22-222-2-2000000000000-22000000000000−2i2i0−2i2i000000000
χ352-22-2-22-22-2-22222-2-22-2-2-2220000000000002-20000000000002i−2i0−2i2i000000000
χ362-22-2-22-22-2-22222-2-22-2-2-2220000000000002-2000000000000−2i2i02i−2i000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ38444-4-4-44-44-4004-40000000000000000000000000022−2222−22000000000000000000
χ39444-4-4-44-44-4004-400000000000000000000000000−2222−2222000000000000000000
χ40444-4-4-44-4-4400-44000000000000004-400000000000000000000000000000000
χ41444-4-4-44-4-4400-4400000000000000-4400000000000000000000000000000000
χ4244-44-44-4-4004-4004-400000000004-40000000000000000000000000000000000
χ4344-44-44-4-4004-4004-40000000000-440000000000000000000000000000000000
χ4444-44-44-4-400-4400-44000000000000000000000000000000000000000022−220000
χ4544-44-44-4-400-4400-440000000000000000000000000000000000000000−22220000
χ4644-4-44-4-44000000000022−2222−2200000000000000002i2−2i200002i−2i2i−2i00000000000000
χ4744-4-44-4-44000000000022−2222−220000000000000000−2i22i20000−2i2i−2i2i00000000000000
χ4844-4-44-4-440000000000−2222−222200000000000000002i2−2i20000−2i2i−2i2i00000000000000
χ4944-4-44-4-440000000000−2222−22220000000000000000−2i22i200002i−2i2i−2i00000000000000
χ504-4444-4-4-44-400-440000000000000000000000000022−22−2222000000000000000000
χ514-4444-4-4-44-400-4400000000000000000000000000−222222−22000000000000000000
χ524-4444-4-4-4-44004-4000000004-400000000000000000000000000000000000000
χ534-4444-4-4-4-44004-400000000-4400000000000000000000000000000000000000
χ544-44-4-44-44-4-4-4-44444-4400000000000000000000000000000000000000000000
χ554-4-44-4-444000000000022−22−22220000000000000022−220000002-2-2200000000000000
χ564-4-44-4-444000000000022−22−222200000000000000−2222000000-222-200000000000000
χ574-4-44-4-4440000000000−222222−220000000000000022−22000000-222-200000000000000
χ584-4-44-4-4440000000000−222222−2200000000000000−22220000002-2-2200000000000000
χ594-4-4-4444-4004-400-4400000000000000004i−4i0000000000000000000000000000
χ604-4-4-4444-4004-400-440000000000000000−4i4i0000000000000000000000000000
χ614-4-4-4444-400-44004-40000000000000000000000000000000000000000002i2−2i200
χ624-4-4-4444-400-44004-4000000000000000000000000000000000000000000−2i22i200

Here i is the imaginary unit (i² = −1).