Finite Group Databasebeta

← Group #255487

Character table — Group #255487

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422224444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ91111111111111-1-1-1-1111-1-1-1-1111111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11-111-1-11111-1-1
χ101111111111111-1-1-1-1111-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-11111-1-111
χ111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1-1-111
χ121111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-11-1-111-1-111-1-1
χ131111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-111
χ141111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-111-1-1-1-111-1-1
χ151111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1-1111111-1-1
χ161111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1111-1-111-1-111
χ172222222222-2-2-2222222-2-2-2220000-2-20022-2000022000000000000000000-2-20000000000
χ182222222222-2-2-2222222-2-2-2220000-2-200-2-2-20000-2-2000000000000000000220000000000
χ192222222222-2-2-2-2-2-2-222-222-2-20000-2-2002220000-2-2000000000000000000-220000000000
χ202222222222-2-2-2-2-2-2-222-222-2-20000-2-200-2-220000220000000000000000002-20000000000
χ2122222222-2-22222222-2-2222-2-22222-2-2-2-200-222-2-200000000000000000000000000000000
χ2222222222-2-22222222-2-2222-2-2-2-2-2-2-2-22200-2-2-22200000000000000000000000000000000
χ2322222222-2-2222-2-2-2-2-2-22-2-2222222-2-222002-2-2-2-200000000000000000000000000000000
χ2422222222-2-2222-2-2-2-2-2-22-2-222-2-2-2-2-2-2-2-2002222200000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-20000220000200000000000000000000002-20000002-20000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-2000022000020000000000000000000000-22000000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-200000000000000000000002-2000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-20000000000000000000000-220000002-20000
χ292-2222-2-2-22-20002i2i−2i−2i2-20002i−2i000000002-2000002i−2ii2i2−i2−i222−2−2i2i2−i2−i222−2−200000000000000
χ302-2222-2-2-22-20002i2i−2i−2i2-20002i−2i000000002-2000002i−2i−i2−i2i2i2−2−222−i2−i2i2i2−2−22200000000000000
χ312-2222-2-2-22-20002i2i−2i−2i2-20002i−2i00000000-2200000−2i2ii2i2−i2−i222−2−2−i2−i2i2i2−2−22200000000000000
χ322-2222-2-2-22-20002i2i−2i−2i2-20002i−2i00000000-2200000−2i2i−i2−i2i2i2−2−222i2i2−i2−i222−2−200000000000000
χ332-2222-2-2-22-2000−2i−2i2i2i2-2000−2i2i000000002-200000−2i2ii2i2−i2−i2−2−222i2i2−i2−i2−2−22200000000000000
χ342-2222-2-2-22-2000−2i−2i2i2i2-2000−2i2i000000002-200000−2i2i−i2−i2i2i222−2−2−i2−i2i2i222−2−200000000000000
χ352-2222-2-2-22-2000−2i−2i2i2i2-2000−2i2i00000000-22000002i−2ii2i2−i2−i2−2−222−i2−i2i2i222−2−200000000000000
χ362-2222-2-2-22-2000−2i−2i2i2i2-2000−2i2i00000000-22000002i−2i−i2−i2i2i222−2−2i2i2−i2−i2−2−22200000000000000
χ372-22-2-22-222-222-20000-22-2000022-2-22-200000002-2002i−2i2i−2i00000000000000002i−2i00000000
χ382-22-2-22-222-222-20000-22-2000022-2-22-200000002-200−2i2i−2i2i0000000000000000−2i2i00000000
χ392-22-2-22-222-222-20000-22-20000-2-2222-20000000-22002i−2i2i−2i0000000000000000−2i2i00000000
χ402-22-2-22-222-222-20000-22-20000-2-2222-20000000-2200−2i2i−2i2i00000000000000002i−2i00000000
χ412-22-2-22-22-2222-200002-2-2000022-2-2-220000000-220000002i−2i2i−2i000000000000002i−2i000000
χ422-22-2-22-22-2222-200002-2-2000022-2-2-220000000-22000000−2i2i−2i2i00000000000000−2i2i000000
χ432-22-2-22-22-2222-200002-2-20000-2-222-2200000002-20000002i−2i2i−2i00000000000000−2i2i000000
χ442-22-2-22-22-2222-200002-2-20000-2-222-2200000002-2000000−2i2i−2i2i000000000000002i−2i000000
χ452-2-2-2222-2002-222-22-200-22-2002i−2i2i−2i00000002i−2i000000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ462-2-2-2222-2002-222-22-200-22-2002i−2i2i−2i00000002i−2i000000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ472-2-2-2222-2002-222-22-200-22-200−2i2i−2i2i0000000−2i2i000000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ482-2-2-2222-2002-222-22-200-22-200−2i2i−2i2i0000000−2i2i000000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ492-2-2-2222-2002-22-22-2200-2-22002i−2i2i−2i0000000−2i2i000000000000i2−i2i2−i2−i2i2−i2i200000000002−2−22
χ502-2-2-2222-2002-22-22-2200-2-22002i−2i2i−2i0000000−2i2i000000000000−i2i2−i2i2i2−i2i2−i20000000000−222−2
χ512-2-2-2222-2002-22-22-2200-2-2200−2i2i−2i2i00000002i−2i000000000000i2−i2i2−i2−i2i2−i2i20000000000−222−2
χ522-2-2-2222-2002-22-22-2200-2-2200−2i2i−2i2i00000002i−2i000000000000−i2i2−i2i2i2−i2i2−i200000000002−2−22
χ53444-4-4-44-4440000000-4-4000000000000000000000022−22−222200000000000000000000000000
χ54444-4-4-44-4440000000-4-40000000000000000000000−222222−2200000000000000000000000000
χ55444-4-4-44-4-4-4000000044000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ56444-4-4-44-4-4-400000004400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5744-44-44-4-4004-4-4000000400004i−4i−4i4i0000000000000000000000000000000000000000000
χ5844-44-44-4-4004-4-400000040000−4i4i4i−4i0000000000000000000000000000000000000000000
χ5944-44-44-4-400-444000000-400000000004-4000000000000000000000000000000000000000
χ6044-44-44-4-400-444000000-40000000000-44000000000000000000000000000000000000000
χ6144-4-44-4-44000004i−4i−4i4i000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ6244-4-44-4-44000004i−4i−4i4i00000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ6344-4-44-4-4400000−4i4i4i−4i000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ6444-4-44-4-4400000−4i4i4i−4i00000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ654-4444-4-4-4-440004i4i−4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ664-4444-4-4-4-44000−4i−4i4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ674-44-4-44-444-4-4-440000-44400000000-4400000000000000000000000000000000000000000
χ684-44-4-44-44-44-4-4400004-44000000004-400000000000000000000000000000000000000000
χ694-4-4-4444-400-44-44-44-4004-440000000000000000000000000000000000000000000000000
χ704-4-4-4444-400-44-4-44-440044-40000000000000000000000000000000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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