Finite Group Databasebeta

← Group #506224

Character table — Group #506224

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1222222222444488888888444444444488888888888824444444444488881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111
χ811111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111-1-1-1-11111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11-1-111-1-1111-1-1-1-11111-1-111-1-1
χ1011111-1-1-1-11111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1111-1-111-1-111-1-111-1-111
χ1111111-1-1-1-11111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1-111-1-111-1-1-1-111-1-111
χ1211111-1-1-1-11111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-111-1-111-1-1-11111-1-111-1-111-1-1
χ1311111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-111-1-11-1-11111-1-111-1-1-1-111
χ1411111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-111111-1-111-1-1-1-11111-1-1
χ1511111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-11111-1-1-1-1-111-1-111-1-11111-1-1
χ1611111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-111-1-111-111-1-1-1-11111-1-1-1-111
χ17222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1922222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2000000000000000000000000
χ2022222-2-2-2-222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-22222000000000000000000000000
χ212222-222-2-2-222-2-2000022222-200000000-2-222-2-200000022-20000-20000000000000000
χ222222-222-2-2-222-2-2000022222-200000000-2-222-2-2000000-2-22000020000000000000000
χ232222-222-2-2-222-2-20000-2-2-2-22-20000000022-2-2220000000000000000002i−2i2i−2i00000000
χ242222-222-2-2-222-2-20000-2-2-2-22-20000000022-2-222000000000000000000−2i2i−2i2i00000000
χ252222-222-2-2-2-2-22222220000-2200000000000000-2-222-2-200000000000000002−22−22−22−2
χ262222-222-2-2-2-2-22222220000-2200000000000000-2-222-2-20000000000000000−22−22−22−22
χ272222-222-2-2-2-2-222-2-2-2-20000-220000000000000022-2-22200000000000000002−22−2−22−22
χ282222-222-2-2-2-2-222-2-2-2-20000-220000000000000022-2-2220000000000000000−22−222−22−2
χ292222-2-2-222-222-2-200002222-2200000000-2-2-2-2220000002-220000-20000000000000000
χ302222-2-2-222-222-2-200002222-2200000000-2-2-2-222000000-22-2000020000000000000000
χ312222-2-2-222-222-2-20000-2-2-2-2-22000000002222-2-20000000000000000002i−2i−2i2i00000000
χ322222-2-2-222-222-2-20000-2-2-2-2-22000000002222-2-2000000000000000000−2i2i2i−2i00000000
χ332222-2-2-222-2-2-222222200002-200000000000000-2-2-2-22200000000000000002−2−222−2−22
χ342222-2-2-222-2-2-222222200002-200000000000000-2-2-2-2220000000000000000−222−2−222−2
χ352222-2-2-222-2-2-222-2-2-2-200002-2000000000000002222-2-200000000000000002−2−22−222−2
χ362222-2-2-222-2-2-222-2-2-2-200002-2000000000000002222-2-20000000000000000−222−22−2−22
χ372-2-2220000-2-222-22i2i−2i−2i22-2-2002i2i−2i−2i00002-200002i−2i0000000002i−2i0002-2000000000000
χ382-2-2220000-2-222-22i2i−2i−2i22-2-2002i2i−2i−2i00002-200002i−2i000000000−2i2i000-22000000000000
χ392-2-2220000-2-222-22i2i−2i−2i-2-22200−2i−2i2i2i0000-2200002i−2i00000002i−2i0002-200000000000000
χ402-2-2220000-2-222-22i2i−2i−2i-2-22200−2i−2i2i2i0000-2200002i−2i0000000−2i2i000-2200000000000000
χ412-2-2220000-2-222-2−2i−2i2i2i22-2-200−2i−2i2i2i00002-20000−2i2i0000000002i−2i000-22000000000000
χ422-2-2220000-2-222-2−2i−2i2i2i22-2-200−2i−2i2i2i00002-20000−2i2i000000000−2i2i0002-2000000000000
χ432-2-2220000-2-222-2−2i−2i2i2i-2-222002i2i−2i−2i0000-220000−2i2i00000002i−2i000-2200000000000000
χ442-2-2220000-2-222-2−2i−2i2i2i-2-222002i2i−2i−2i0000-220000−2i2i0000000−2i2i0002-200000000000000
χ454444444444-4-4-4-400000000-4-400000000000000000000000000000000000000000000
χ4644444-4-4-4-44-4-4-4-4000000004400000000000000000000000000000000000000000000
χ4744-4-404-4000000022−2222−2222−2222−22002-22-222-2-20022−22000022−2200000000000000000000000000
χ4844-4-404-4000000022−2222−22−2222−222200-22-22-2-22200−2222000022−2200000000000000000000000000
χ4944-4-404-40000000−2222−222222−2222−2200-22-22-2-2220022−220000−222200000000000000000000000000
χ5044-4-404-40000000−2222−2222−2222−2222002-22-222-2-200−22220000−222200000000000000000000000000
χ5144-4-40-44000000022−2222−2222−2222−22002-22-2-2-22200−22220000−222200000000000000000000000000
χ5244-4-40-44000000022−2222−22−2222−222200-22-2222-2-20022−220000−222200000000000000000000000000
χ5344-4-40-440000000−2222−222222−2222−2200-22-2222-2-200−2222000022−2200000000000000000000000000
χ5444-4-40-440000000−2222−2222−2222−2222002-22-2-2-2220022−22000022−2200000000000000000000000000
χ554-44-40004-4000002i2−2i2−2i22i222−22−2222002i−2i−2i2i2i−2i2i−2i000022−2200002i2−2i2000000000000000000000000
χ564-44-40004-4000002i2−2i2−2i22i2−222222−2200−2i2i2i−2i−2i2i−2i2i0000−222200002i2−2i2000000000000000000000000
χ574-44-40004-400000−2i22i22i2−2i222−22−222200−2i2i2i−2i−2i2i−2i2i000022−220000−2i22i2000000000000000000000000
χ584-44-40004-400000−2i22i22i2−2i2−222222−22002i−2i−2i2i2i−2i2i−2i0000−22220000−2i22i2000000000000000000000000
χ594-44-4000-44000002i2−2i2−2i22i222−22−2222002i−2i−2i2i−2i2i−2i2i0000−22220000−2i22i2000000000000000000000000
χ604-44-4000-44000002i2−2i2−2i22i2−222222−2200−2i2i2i−2i2i−2i2i−2i000022−220000−2i22i2000000000000000000000000
χ614-44-4000-4400000−2i22i22i2−2i222−22−222200−2i2i2i−2i2i−2i2i−2i0000−222200002i2−2i2000000000000000000000000
χ624-44-4000-4400000−2i22i22i2−2i2−222222−22002i−2i−2i2i−2i2i−2i2i000022−2200002i2−2i2000000000000000000000000
χ634-4-4440000-44-4-44000000000000004i−4i−4i4i000000000000000000000000000000000000
χ644-4-4440000-44-4-4400000000000000−4i4i4i−4i000000000000000000000000000000000000
χ654-4-44-4000044-44-44i4i−4i−4i00000000000000000000−4i4i0000000000000000000000000000
χ664-4-44-4000044-44-4−4i−4i4i4i000000000000000000004i−4i0000000000000000000000000000
χ674-4-44-400004-44-44000044-4-40000000000-440000000000000000000000000000000000
χ684-4-44-400004-44-440000-4-44400000000004-40000000000000000000000000000000000

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