Finite Group Databasebeta

← Group #506408

Character table — Group #506408

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1222224444444488888888444444444488888888888822224444444488881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ9111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-111-1-111-1-111-1-1
χ10111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-1-1-111-11-1-111-1-111-1-111
χ11111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-11-11111-1-11-111-1-1-1-111-1-111
χ12111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-111111-1-1-11-1-11111-1-111-1-1
χ13111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1111-1-1-111-1-11-1-1-11111-1-1-1-111
χ14111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-111-11-1-111-1-1-1111-1-1-1-11111-1-1
χ15111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-111-1-1111-1-1-111-1-11111-1-1
χ16111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1111-1-111-1111-1-111-1-1-1-111
χ1722222222222222-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ19222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222000000000000000000000000
χ20222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222222222-2-2000000000000000000000000
χ212222-2-222-2-222-2-2220000222-200000000-2-222-2-20000000022000000-2-2000000000000
χ222222-2-222-2-222-2-2220000222-200000000-2-222-2-200000000-2-200000022000000000000
χ232222-2-222-2-222-2-2-2-20000-2-22-20000000022-2-2220000000000000000002i−2i2i−2i00000000
χ242222-2-222-2-222-2-2-2-20000-2-22-20000000022-2-222000000000000000000−2i2i−2i2i00000000
χ252222-2-222-2-2-2-22200222200-220000000000000022-2-2-2-200000000000000002−22−22−22−2
χ262222-2-222-2-2-2-22200222200-220000000000000022-2-2-2-20000000000000000−22−22−22−22
χ272222-2-222-2-2-2-22200-2-2-2-200-2200000000000000-2-2222200000000000000002−22−2−22−22
χ282222-2-222-2-2-2-22200-2-2-2-200-2200000000000000-2-222220000000000000000−22−222−22−2
χ292222-2-2-2-22222-2-222000022-2200000000-2-2-2-222000000002-2000000-22000000000000
χ302222-2-2-2-22222-2-222000022-2200000000-2-2-2-22200000000-220000002-2000000000000
χ312222-2-2-2-22222-2-2-2-20000-2-2-22000000002222-2-20000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-22222-2-2-2-20000-2-2-22000000002222-2-2000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-222-2-222002222002-200000000000000-2-222-2-200000000000000002−2−222−2−22
χ342222-2-2-2-222-2-222002222002-200000000000000-2-222-2-20000000000000000−222−2−222−2
χ352222-2-2-2-222-2-22200-2-2-2-2002-20000000000000022-2-22200000000000000002−2−22−222−2
χ362222-2-2-2-222-2-22200-2-2-2-2002-20000000000000022-2-2220000000000000000−222−22−2−22
χ372-2-222-200002-2-222222-2-2-2-20022-2-200002-2000000002-200002i−2i2i−2i0000000000000000
χ382-2-222-200002-2-222222-2-2-2-20022-2-200002-2000000002-20000−2i2i−2i2i0000000000000000
χ392-2-222-200002-2-2222-2-222-2-200-2-22200002-200000000-2200002i−2i−2i2i0000000000000000
χ402-2-222-200002-2-2222-2-222-2-200-2-22200002-200000000-220000−2i2i2i−2i0000000000000000
χ412-2-222-200002-2-22-2-222-2-22200-2-2220000-22000000002-22-20000002-200000000000000
χ422-2-222-200002-2-22-2-222-2-22200-2-2220000-22000000002-2-22000000-2200000000000000
χ432-2-222-200002-2-22-2-2-2-222220022-2-20000-2200000000-222-2000000-2200000000000000
χ442-2-222-200002-2-22-2-2-2-222220022-2-20000-2200000000-22-220000002-200000000000000
χ454444444444-4-4-4-400000000-4-400000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-4-4-4000000004400000000000000000000000000000000000000000000
χ4744-4-400004i−4i000022−222i2−2i22i2−2i222−22002i−2i2i−2i22-2-200002i2−2i20022−2200000000000000000000000000
χ4844-4-400004i−4i000022−22−2i22i2−2i22i222−2200−2i2i−2i2i-2-22200002i2−2i200−222200000000000000000000000000
χ4944-4-400004i−4i0000−22222i2−2i22i2−2i2−222200−2i2i−2i2i-2-2220000−2i22i20022−2200000000000000000000000000
χ5044-4-400004i−4i0000−2222−2i22i2−2i22i2−2222002i−2i2i−2i22-2-20000−2i22i200−222200000000000000000000000000
χ5144-4-40000−4i4i000022−222i2−2i22i2−2i222−22002i−2i2i−2i-2-2220000−2i22i200−222200000000000000000000000000
χ5244-4-40000−4i4i000022−22−2i22i2−2i22i222−2200−2i2i−2i2i22-2-20000−2i22i20022−2200000000000000000000000000
χ5344-4-40000−4i4i0000−22222i2−2i22i2−2i2−222200−2i2i−2i2i22-2-200002i2−2i200−222200000000000000000000000000
χ5444-4-40000−4i4i0000−2222−2i22i2−2i22i2−2222002i−2i2i−2i-2-22200002i2−2i20022−2200000000000000000000000000
χ554-44-4004-400000022−222i2−2i2−2i22i2−2222002i−2i−2i2i2i−2i2i−2i0022−22002i2−2i20000000000000000000000000000
χ564-44-4004-400000022−22−2i22i22i2−2i2−222200−2i2i2i−2i−2i2i−2i2i0022−2200−2i22i20000000000000000000000000000
χ574-44-4004-4000000−22222i2−2i2−2i22i222−2200−2i2i2i−2i−2i2i−2i2i00−2222002i2−2i20000000000000000000000000000
χ584-44-4004-4000000−2222−2i22i22i2−2i222−22002i−2i−2i2i2i−2i2i−2i00−222200−2i22i20000000000000000000000000000
χ594-44-400-4400000022−222i2−2i2−2i22i2−2222002i−2i−2i2i−2i2i−2i2i00−222200−2i22i20000000000000000000000000000
χ604-44-400-4400000022−22−2i22i22i2−2i2−222200−2i2i2i−2i2i−2i2i−2i00−2222002i2−2i20000000000000000000000000000
χ614-44-400-44000000−22222i2−2i2−2i22i222−2200−2i2i2i−2i2i−2i2i−2i0022−2200−2i22i20000000000000000000000000000
χ624-44-400-44000000−2222−2i22i22i2−2i222−22002i−2i−2i2i−2i2i−2i2i0022−22002i2−2i20000000000000000000000000000
χ634-4-444-40000-444-4000000000000004i−4i−4i4i000000000000000000000000000000000000
χ644-4-444-40000-444-400000000000000−4i4i4i−4i000000000000000000000000000000000000
χ654-4-44-4400004-44-4440000-4-40000000000-440000000000000000000000000000000000
χ664-4-44-4400004-44-4-4-400004400000000004-40000000000000000000000000000000000
χ674-4-44-440000-44-440044-4-40000000000000000000000-44000000000000000000000000
χ684-4-44-440000-44-4400-4-44400000000000000000000004-4000000000000000000000000

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