Finite Group Databasebeta

← Group #348982

Character table — Group #348982

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442222444444444444222222444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-11
χ811111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-111111-1-1-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-111111-1-1-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-111111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-111111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ131111111111111111-1-1-1-1-1-11-1-11111-1-111111-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-11-1-11111-1-111111-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-11-1-11111-1-11-1-1-1-111-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-11-1-11111-1-11-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1722222222222-2-2-22-2222222-2-2-2-2-2-2-2-2-2-20000002220000-2-2000000000000000000000000
χ1822222222222-2-2-22-22222-2-2-222222222-2000000-2-2-20000-2-2000000000000000000000000
χ1922222222222-2-2-22-2-2-2-2-222-2-2-22222-2-2-20000002-2-2000022000000000000000000000000
χ2022222222222-2-2-22-2-2-2-2-2-2-2-222-2-2-2-222-2000000-222000022000000000000000000000000
χ2122222222-2-2-2222-22000022-2220000-2-2-2000022-200-2-2-2-200000022000000000000000000
χ2222222222-2-2-2222-22000022-2220000-2-2-20000-2-2-2002222000000-2-2000000000000000000
χ2322222222-2-2-2222-220000-2-2-2-2-2000022-2000022200-2-222000000-2-2000000000000000000
χ2422222222-2-2-2222-220000-2-2-2-2-2000022-20000-2-220022-2-200000022000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000222-2-2000022222-2-200-20000000022-2-200000000000000000000
χ2622222222-2-2-2-2-2-2-2-20000222-2-20000222-2-22200-200000000-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-22220000-2-2222-2-200200000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-22220000-2-22-2-2220020000000022-2-200000000000000000000
χ292-22-22-22-222-2000-2022-2-20002-222-2-22-20000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ302-22-22-22-222-2000-2022-2-20002-222-2-22-20000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ312-22-22-22-222-2000-2022-2-2000-22-2-222-220000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ322-22-22-22-222-2000-2022-2-2000-22-2-222-220000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ332-22-22-22-222-2000-20-2-2220002-2-2-2222-20000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ342-22-22-22-222-2000-20-2-2220002-2-2-2222-20000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ352-22-22-22-222-2000-20-2-222000-2222-2-2-220000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ362-22-22-22-222-2000-20-2-222000-2222-2-2-220000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ372-22-2-22-222-2222-2-2-2000000-2002i−2i2i−2i0022-22-20002i−2i002i−2i0000002i−2i000000000000000000
χ382-22-2-22-222-2222-2-2-2000000-2002i−2i2i−2i002-22-220002i−2i00−2i2i000000−2i2i000000000000000000
χ392-22-2-22-222-2222-2-2-2000000-200−2i2i−2i2i0022-22-2000−2i2i00−2i2i000000−2i2i000000000000000000
χ402-22-2-22-222-2222-2-2-2000000-200−2i2i−2i2i002-22-22000−2i2i002i−2i0000002i−2i000000000000000000
χ412-22-2-22-222-22-2-22-220000002002i−2i2i−2i00-200002-20−2i2i2-200002i−2i2i−2i00000000000000000000
χ422-22-2-22-222-22-2-22-220000002002i−2i2i−2i00-20000-220−2i2i-220000−2i2i−2i2i00000000000000000000
χ432-22-2-22-222-22-2-22-22000000200−2i2i−2i2i00-200002-202i−2i2-20000−2i2i−2i2i00000000000000000000
χ442-22-2-22-222-22-2-22-22000000200−2i2i−2i2i00-20000-2202i−2i-2200002i−2i2i−2i00000000000000000000
χ452-22-2-22-22-22-222-22-22-22-200200000000-2000000000002i−2i2-22i−2i−2i2i−2i2i000000000000000000
χ462-22-2-22-22-22-222-22-22-22-200200000000-200000000000−2i2i2-2−2i2i2i−2i2i−2i000000000000000000
χ472-22-2-22-22-22-222-22-2-22-2200200000000-2000000000002i−2i-22−2i2i2i−2i−2i2i000000000000000000
χ482-22-2-22-22-22-222-22-2-22-2200200000000-200000000000−2i2i-222i−2i−2i2i2i−2i000000000000000000
χ492-22-2-22-22-22-2-2-22222-22-200-20000000022-2-222-2000-2200-22000000000000000000000000
χ502-22-2-22-22-22-2-2-22222-22-200-2000000002-222-2-220002-200-22000000000000000000000000
χ512-22-2-22-22-22-2-2-2222-22-2200-20000000022-2-22-220002-2002-2000000000000000000000000
χ522-22-2-22-22-22-2-2-2222-22-2200-2000000002-222-22-2000-22002-2000000000000000000000000
χ534444-4-4-4-44-4-4000400000000004i−4i−4i4i000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-400040000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ554444-4-4-4-4-444000-404-4-44000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-444000-40-444-4000000000000000000000000000000000000000000000000000
χ5744-4-444-4-40000000000004i−4i00000000000000000000000000000002-22-22i−2i2i−2i0000000000
χ5844-4-444-4-40000000000004i−4i0000000000000000000000000000000-22-22−2i2i−2i2i0000000000
χ5944-4-444-4-4000000000000−4i4i00000000000000000000000000000002-22-2−2i2i−2i2i0000000000
χ6044-4-444-4-4000000000000−4i4i0000000000000000000000000000000-22-222i−2i2i−2i0000000000
χ6144-4-4-4-4440004-440-400000000000000000000000000000000000000000000000002i2−2i20000
χ6244-4-4-4-4440004-440-40000000000000000000000000000000000000000000000000−2i22i20000
χ6344-4-4-4-444000-44-40400000000000000000000000000000000000000000000000000022−2200
χ6444-4-4-4-444000-44-404000000000000000000000000000000000000000000000000000−222200
χ654-44-44-44-4-4-440004000000004-40000-440000000000000000000000000000000000000000
χ664-44-44-44-4-4-44000400000000-4400004-40000000000000000000000000000000000000000
χ674-4-444-4-440004-4-4040000000000000000000000000000000000000000022−22−22220000000000
χ684-4-444-4-440004-4-40400000000000000000000000000000000000000000−222222−220000000000
χ694-4-444-4-44000-4440-400000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ704-4-444-4-44000-4440-40000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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