Finite Group Databasebeta

← Group #350169

Character table — Group #350169

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442244444444444444444444444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-11111-1-1-1-1-1-111-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-11111-1-1-1-1-1-111-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11111-1-111-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-11111-1-111-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222-2-222-2-2222222222222-2-2-2-2-200000000-2-2-2-200000000000000000000000000
χ182222222222-2-222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-22222-2-2-2-222-2-2200000000-2-22200000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2-2-2222222-2-220000000022-2-200000000000000000000000000
χ2122222222-2-222-2-22222-2-20000000022-2-2-200000000000022-2-222-2-2000000000000000000
χ2222222222-2-222-2-22222-2-20000000022-2-2-2000000000000-2-222-2-222000000000000000000
χ2322222222-2-222-2-222-2-22200000000-2-2-2-2200000000000022-2-2-2-222000000000000000000
χ2422222222-2-222-2-222-2-22200000000-2-2-2-22000000000000-2-22222-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-200000000-2-222222-2-222-2-2000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-200000000-2-2222-2-222-2-222000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222000000002222-222-2-2-2-222000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222000000002222-2-2-22222-2-2000000000000000000000000000000
χ292-22-222-2-22-22-22-22-2000000002i2i−2i−2i002-2000002-22-2002i−2i2i−2i2i−2i0000000000000000000000
χ302-22-222-2-22-22-22-22-2000000002i2i−2i−2i002-200000-22-22002i−2i−2i2i−2i2i0000000000000000000000
χ312-22-222-2-22-22-22-22-200000000−2i−2i2i2i002-2000002-22-200−2i2i−2i2i−2i2i0000000000000000000000
χ322-22-222-2-22-22-22-22-200000000−2i−2i2i2i002-200000-22-2200−2i2i2i−2i2i−2i0000000000000000000000
χ332-22-222-2-22-2-222-2-22000000002i2i−2i−2i00-2202-22-2000000−2i2i00002i−2i2i−2i000000000000000000
χ342-22-222-2-22-2-222-2-22000000002i2i−2i−2i00-220-22-22000000−2i2i0000−2i2i−2i2i000000000000000000
χ352-22-222-2-22-2-222-2-2200000000−2i−2i2i2i00-2202-22-20000002i−2i0000−2i2i−2i2i000000000000000000
χ362-22-222-2-22-2-222-2-2200000000−2i−2i2i2i00-220-22-220000002i−2i00002i−2i2i−2i000000000000000000
χ372-22-222-2-2-222-2-222-200002i2i−2i−2i000000-2202-2-2200002i−2i002i−2i−2i2i0000000000000000000000
χ382-22-222-2-2-222-2-222-200002i2i−2i−2i000000-220-222-200002i−2i00−2i2i2i−2i0000000000000000000000
χ392-22-222-2-2-222-2-222-20000−2i−2i2i2i000000-2202-2-220000−2i2i00−2i2i2i−2i0000000000000000000000
χ402-22-222-2-2-222-2-222-20000−2i−2i2i2i000000-220-222-20000−2i2i002i−2i−2i2i0000000000000000000000
χ412-22-222-2-2-22-22-22-2200002i2i−2i−2i0000002-2000002-2-22−2i2i0000002i−2i−2i2i000000000000000000
χ422-22-222-2-2-22-22-22-2200002i2i−2i−2i0000002-200000-222-2−2i2i000000−2i2i2i−2i000000000000000000
χ432-22-222-2-2-22-22-22-220000−2i−2i2i2i0000002-2000002-2-222i−2i000000−2i2i2i−2i000000000000000000
χ442-22-222-2-2-22-22-22-220000−2i−2i2i2i0000002-200000-222-22i−2i0000002i−2i−2i2i000000000000000000
χ452-22-2-2-2222200-2-2002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ462-22-2-2-2222200-2-2002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ472-22-2-2-2222200-2-2002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ482-22-2-2-2222200-2-2002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ492-22-2-2-2222200-2-200-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ502-22-2-2-2222200-2-200-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ512-22-2-2-2222200-2-200-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ522-22-2-2-2222200-2-200-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ534444-4-4-4-44-400-4400000000004-4-440000000000000000000000000000000000000000000
χ544444-4-4-4-44-400-440000000000-444-40000000000000000000000000000000000000000000
χ554444-4-4-4-4-44004-40000004-4-4400000000000000000000000000000000000000000000000
χ564444-4-4-4-4-44004-4000000-444-400000000000000000000000000000000000000000000000
χ5744-4-44-44-4000000000000000000004i−4i000000000000000000000002-22-22i−2i2i−2i0000000000
χ5844-4-44-44-4000000000000000000004i−4i00000000000000000000000-22-22−2i2i−2i2i0000000000
χ5944-4-44-44-400000000000000000000−4i4i000000000000000000000002-22-2−2i2i−2i2i0000000000
χ6044-4-44-44-400000000000000000000−4i4i00000000000000000000000-22-222i−2i2i−2i0000000000
χ6144-4-4-44-44004-400-4400000000000000000000000000000000000000000000000002i2−2i20000
χ6244-4-4-44-44004-400-440000000000000000000000000000000000000000000000000−2i22i20000
χ6344-4-4-44-4400-44004-40000000000000000000000000000000000000000000000000002i2−2i200
χ6444-4-4-44-4400-44004-4000000000000000000000000000000000000000000000000000−2i22i200
χ654-44-4-4-444-4-40044004-4-44000000000000000000000000000000000000000000000000000
χ664-44-4-4-444-4-4004400-444-4000000000000000000000000000000000000000000000000000
χ674-4-44-444-4004400-4-400000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ684-4-44-444-4004400-4-40000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ694-4-44-444-400-4-400440000000000000000000000000000000000000000022−22−22220000000000
χ704-4-44-444-400-4-4004400000000000000000000000000000000000000000−222222−220000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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