Finite Group Databasebeta

← Group #10823707

Character table — Group #10823707

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444666666668888888888888888881616161616161616161616162424242424242424242424242424
order1222222222366666666644444444444444444444441212121212121212121212121212121222222444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1111-1-111-1-1-1-111111-1-11-1-111-1-1-1-11-1-1111-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11-1-11-1-1-1-111111-1-1-1-11-1-1-1-11111
χ51111111111111111111111111111-11-111-11-1-1-111-1-11111-11-1-11-1-1-111-1-1-11-111-11-1-1-111-1-1
χ61111111111111111111111111111-11-1-1-1-11-111-1-111-1-1-1-1-11-1-11-111-1-111-11-1-1-1-11-111-1-111
χ71111111111111111111111111111-1-1111-1-11-1-1-1-1111111-1-11-1-11-1-1-1-111-1-1111-1-11-1-1-1-111
χ81111111111111111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11-1-1-1-111111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1111111
χ1111111111111111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111111-1-11-1-111-1-1-1-1-111-1-1-111-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-11-1-11-1-1-1-11111-11111-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-11-111-11-1-1-111-1-11111-11-1-11-1-1-111-1-11-11-1-11-1111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11-111-1-111-1-1-1-1-11-1-11-111-1-1111-11111-11-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111111-1-11-1-11-1-1-1-11111-1-1-111-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-11-1-111111-1-111-11111-1-1-1-1-111
χ172222222222-1-1-1-1-1-1-1-1-1-10000000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ182222222222-1-1-1-1-1-1-1-1-1-100000000222-2-2222-2-2-2-2-2-21111-1-1-1-1-1-111111100000000000000
χ192222222222-1-1-1-1-1-1-1-1-1-1000000002-2-2222-2-222-2-2-2-2-1-1-1-1-111-111-1-1111100000000000000
χ202222222222-1-1-1-1-1-1-1-1-1-1000000002-2-2-2-22-2-2-2-222221111-111-11111-1-1-1-100000000000000
χ212222222222-1-1-1-1-1-1-1-1-1-100000000-22-222-22-2-2-222-2-2-1-1-1-11-111-1111-1-11100000000000000
χ222222222222-1-1-1-1-1-1-1-1-1-100000000-22-2-2-2-22-222-2-22211111-111-11-1-111-1-100000000000000
χ232222222222-1-1-1-1-1-1-1-1-1-100000000-2-2222-2-22-2-2-2-222-1-1-1-111-111-11111-1-100000000000000
χ242222222222-1-1-1-1-1-1-1-1-1-100000000-2-22-2-2-2-222222-2-2111111-111-1-1-1-1-11100000000000000
χ2522222-2-22-2-222222-2-22-2-22222-2-2-2-20020000-2000000000000-20020000000020000-2000000
χ2622222-2-22-2-222222-2-22-2-22222-2-2-2-200-200002000000000000200-200000000-200002000000
χ2722222-2-22-2-222222-2-22-2-2-2-2-2-222220020000-2000000000000-200200000000-200002000000
χ2822222-2-22-2-222222-2-22-2-2-2-2-2-2222200-200002000000000000200-20000000020000-2000000
χ292222-22-2-22-22222-22-2-22-222-2-222-2-2020000-2000000000000-20020000000020000-20000000
χ302222-22-2-22-22222-22-2-22-222-2-222-2-20-200002000000000000200-200000000-2000020000000
χ312222-22-2-22-22222-22-2-22-2-2-222-2-222020000-2000000000000-200200000000-2000020000000
χ322222-22-2-22-22222-22-2-22-2-2-222-2-2220-200002000000000000200-20000000020000-20000000
χ332222-2-22-2-222222-2-22-2-2222-2-2-2-22220000-2000000000000-200200000000-20000200000000
χ342222-2-22-2-222222-2-22-2-2222-2-2-2-222-200002000000000000200-20000000020000-200000000
χ352222-2-22-2-222222-2-22-2-22-2-22222-2-220000-2000000000000-20020000000020000-200000000
χ362222-2-22-2-222222-2-22-2-22-2-22222-2-2-200002000000000000200-200000000-20000200000000
χ372-22-2222-2-2-222-2-2-2-2-22222i−2i2i−2i2i−2i2i−2i0002i−2i0000000002i2i−2i−2i0000000000000002-2000000000
χ382-22-2222-2-2-222-2-2-2-2-22222i−2i2i−2i2i−2i2i−2i000−2i2i000000000−2i−2i2i2i000000000000000-22000000000
χ392-22-2222-2-2-222-2-2-2-2-2222−2i2i−2i2i−2i2i−2i2i0002i−2i0000000002i2i−2i−2i000000000000000-22000000000
χ402-22-2222-2-2-222-2-2-2-2-2222−2i2i−2i2i−2i2i−2i2i000−2i2i000000000−2i−2i2i2i0000000000000002-2000000000
χ412-22-22-2-2-22222-2-2-2222-2-22i−2i2i−2i−2i2i−2i2i0000000000002-2000000000000002-20000000000002i−2i
χ422-22-22-2-2-22222-2-2-2222-2-22i−2i2i−2i−2i2i−2i2i000000000000-2200000000000000-22000000000000−2i2i
χ432-22-22-2-2-22222-2-2-2222-2-2−2i2i−2i2i2i−2i2i−2i0000000000002-2000000000000002-2000000000000−2i2i
χ442-22-22-2-2-22222-2-2-2222-2-2−2i2i−2i2i2i−2i2i−2i000000000000-2200000000000000-220000000000002i−2i
χ452-22-2-22-22-2222-2-22-22-22-22i−2i−2i2i2i−2i−2i2i00000000002-2000000000000002-20000000000002i−2i00
χ462-22-2-22-22-2222-2-22-22-22-22i−2i−2i2i2i−2i−2i2i0000000000-2200000000000000-22000000000000−2i2i00
χ472-22-2-22-22-2222-2-22-22-22-2−2i2i2i−2i−2i2i2i−2i00000000002-2000000000000002-2000000000000−2i2i00
χ482-22-2-22-22-2222-2-22-22-22-2−2i2i2i−2i−2i2i2i−2i0000000000-2200000000000000-220000000000002i−2i00
χ492-22-2-2-2222-222-2-222-2-2-222i−2i−2i2i−2i2i2i−2i000000002-2000000000000002-20000000000002i−2i0000
χ502-22-2-2-2222-222-2-222-2-2-222i−2i−2i2i−2i2i2i−2i00000000-2200000000000000-22000000000000−2i2i0000
χ512-22-2-2-2222-222-2-222-2-2-22−2i2i2i−2i2i−2i−2i2i000000002-2000000000000002-2000000000000−2i2i0000
χ522-22-2-2-2222-222-2-222-2-2-22−2i2i2i−2i2i−2i−2i2i00000000-2200000000000000-220000000000002i−2i0000
χ5344444-4-44-4-4-2-2-2-2-222-222000000000040000-4000000000000200-200000000000000000000
χ5444444-4-44-4-4-2-2-2-2-222-2220000000000-400004000000000000-200200000000000000000000
χ554444-44-4-44-4-2-2-2-22-222-2200000000040000-4000000000000200-2000000000000000000000
χ564444-44-4-44-4-2-2-2-22-222-22000000000-400004000000000000-2002000000000000000000000
χ574444-4-44-4-44-2-2-2-222-222-20000000040000-4000000000000200-20000000000000000000000
χ584444-4-44-4-44-2-2-2-222-222-200000000-400004000000000000-20020000000000000000000000
χ594-44-4444-4-4-4-2-222222-2-2-2000000000004i−4i000000000−2i−2i2i2i00000000000000000000000000
χ604-44-4444-4-4-4-2-222222-2-2-200000000000−4i4i0000000002i2i−2i−2i00000000000000000000000000
χ614-44-44-4-4-444-2-2222-2-2-222000000000000000000004-400000000000000-2200000000000000
χ624-44-44-4-4-444-2-2222-2-2-22200000000000000000000-44000000000000002-200000000000000
χ634-44-4-44-44-44-2-222-22-22-220000000000000000004-400000000000000-220000000000000000
χ644-44-4-44-44-44-2-222-22-22-22000000000000000000-44000000000000002-20000000000000000
χ654-44-4-4-4444-4-2-222-2-2222-200000000000000004-400000000000000-22000000000000000000
χ664-44-4-4-4444-4-2-222-2-2222-20000000000000000-44000000000000002-2000000000000000000
χ6788-8-80000008-8-880000000000000000000000000000000000000000000000000000000000
χ6888-8-8000000-444-40000000000000000000000000000−2i32i3−2i32i300000000000000000000000000
χ6988-8-8000000-444-400000000000000000000000000002i3−2i32i3−2i300000000000000000000000000
χ708-8-880000008-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-88000000-44-44000000000000000000000000000023−23−232300000000000000000000000000
χ728-8-88000000-44-440000000000000000000000000000−232323−2300000000000000000000000000

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