Finite Group Databasebeta

← Group #349684

Character table — Group #349684

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1-1-111111-1-1-1-11-1-1111111-1-1-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-111111-1-1-1-11-1-1111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ121111111111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1
χ131111111111111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111-11
χ141111111111111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-2-222-2222222-222-2-22222-2-2-20000000000-2-2-2000000000000000000000000
χ182222222222-2-2-222-222-2-2-2-2-222-2-2-2-2-2-2-2220000000000-222000000000000000000000000
χ192222222222-2-2-222-2-2-22222-2-2-222-2-2-2-2-2-2-20000000000222000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-2-2222222-22200000000002-2-2000000000000000000000000
χ2122222222-2-2222-2-22220000-2-2-2220000-20022-2-2220000-200-2-20000000000000000000000
χ2222222222-2-2222-2-22220000-2-2-2220000-200-2-222-2-20000-200220000000000000000000000
χ2322222222-2-2222-2-22-2-20000-222-2-20000-20022-2-2-2-20000200220000000000000000000000
χ2422222222-2-2222-2-22-2-20000-222-2-20000-200-2-222220000200-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22200002-2-2-2-2000020000000022-2-22000022-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-22200002-2-2-2-20000200000000-2-22220000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2000022222000020000000022-2-2-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-20000222220000200000000-2-222-2000022-2-2000000000000000000
χ292-2222-2-2-22222-2-2-2-20022-2-2200000000-22-22-22-2002-22-2000000000000000000000000000
χ302-2222-2-2-22222-2-2-2-20022-2-2200000000-22-2-22-2200-22-22000000000000000000000000000
χ312-2222-2-2-22222-2-2-2-200-2-222200000000-2-222-22-200-22-22000000000000000000000000000
χ322-2222-2-2-22222-2-2-2-200-2-222200000000-2-22-22-22002-22-2000000000000000000000000000
χ332-2222-2-2-222-2-22-2-220022-2-2-2000000002-2200002i−2i00000002i−2i2i−2i2i−2i000000000000000000
χ342-2222-2-2-222-2-22-2-220022-2-2-2000000002-220000−2i2i0000000−2i2i−2i2i−2i2i000000000000000000
χ352-2222-2-2-222-2-22-2-2200-2-222-20000000022-200002i−2i00000002i−2i−2i2i−2i2i000000000000000000
χ362-2222-2-2-222-2-22-2-2200-2-222-20000000022-20000−2i2i0000000−2i2i2i−2i2i−2i000000000000000000
χ372-2222-2-2-2-2-222-222-2000000-200002i2i−2i−2i2002-2-2200000002i−2i002i−2i−2i2i000000000000000000
χ382-2222-2-2-2-2-222-222-2000000-200002i2i−2i−2i200-222-200000002i−2i00−2i2i2i−2i000000000000000000
χ392-2222-2-2-2-2-222-222-2000000-20000−2i−2i2i2i2002-2-220000000−2i2i00−2i2i2i−2i000000000000000000
χ402-2222-2-2-2-2-222-222-2000000-20000−2i−2i2i2i200-222-20000000−2i2i002i−2i−2i2i000000000000000000
χ412-2222-2-2-2-2-2-2-22222000000200002i2i−2i−2i-20000002i−2i2-2-220−2i2i−2i2i0000000000000000000000
χ422-2222-2-2-2-2-2-2-22222000000200002i2i−2i−2i-2000000−2i2i-222-20−2i2i2i−2i0000000000000000000000
χ432-2222-2-2-2-2-2-2-2222200000020000−2i−2i2i2i-20000002i−2i-222-202i−2i−2i2i0000000000000000000000
χ442-2222-2-2-2-2-2-2-2222200000020000−2i−2i2i2i-2000000−2i2i2-2-2202i−2i2i−2i0000000000000000000000
χ452-22-2-22-222-20002-202i−2i2-22-202i−2i002i−2i2i−2i0000000000000000000000i2i2−i2−i222−2−20000i2−i22−200
χ462-22-2-22-222-20002-202i−2i2-22-202i−2i002i−2i2i−2i0000000000000000000000−i2−i2i2i2−2−2220000−i2i2−2200
χ472-22-2-22-222-20002-202i−2i-22-2202i−2i00−2i2i−2i2i0000000000000000000000i2i2−i2−i222−2−20000−i2i2−2200
χ482-22-2-22-222-20002-202i−2i-22-2202i−2i00−2i2i−2i2i0000000000000000000000−i2−i2i2i2−2−2220000i2−i22−200
χ492-22-2-22-222-20002-20−2i2i2-22-20−2i2i00−2i2i−2i2i0000000000000000000000i2i2−i2−i2−2−2220000i2−i2−2200
χ502-22-2-22-222-20002-20−2i2i2-22-20−2i2i00−2i2i−2i2i0000000000000000000000−i2−i2i2i222−2−20000−i2i22−200
χ512-22-2-22-222-20002-20−2i2i-22-220−2i2i002i−2i2i−2i0000000000000000000000i2i2−i2−i2−2−2220000−i2i22−200
χ522-22-2-22-222-20002-20−2i2i-22-220−2i2i002i−2i2i−2i0000000000000000000000−i2−i2i2i222−2−20000i2−i2−2200
χ53444-4-4-44-44-4000-440004-4-440000000000000000000000000000000000000000000000000
χ54444-4-4-44-44-4000-44000-444-40000000000000000000000000000000000000000000000000
χ55444-4-4-44-4-440004-40000000000004-4-440000000000000000000000000000000000000000
χ56444-4-4-44-4-440004-4000000000000-444-40000000000000000000000000000000000000000
χ5744-4-444-4-4004-4400-4000000000000000000000000000000000000022−2222−2200000000000000
χ5844-4-444-4-4004-4400-40000000000000000000000000000000000000−2222−222200000000000000
χ5944-4-444-4-400-44-4004000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ6044-4-444-4-400-44-400400000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ614-44-4-44-44-44000-4404i−4i00000−4i4i0000000000000000000000000000000000000000000000
χ624-44-4-44-44-44000-440−4i4i000004i−4i0000000000000000000000000000000000000000000000
χ634-4-44-444-4000000000000000004-4000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ644-4-44-444-4000000000000000004-400000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ654-4-44-444-400000000000000000-44000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ664-4-44-444-400000000000000000-4400000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ674-4-4-44-444004-4-400400000000000000000000000000000000000000000000022−2200000000
χ684-4-4-44-444004-4-4004000000000000000000000000000000000000000000000−222200000000
χ694-4-4-44-44400-44400-4000000000000000000000000000000000000000000000002i2−2i2000000
χ704-4-4-44-44400-44400-400000000000000000000000000000000000000000000000−2i22i2000000
χ7188-88-8-8-88000000000000000000000000000000000000000000000000000000000000000

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