Finite Group Databasebeta

← Group #10696754

Character table — Group #10696754

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122234444666244446612121212121212128888121224242424242424242466881212242424248888224488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-11-11-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-11-111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ9222222222222-22-2-2-2-2-2222222-2-20000-2-200000000000000000000000000002-2
χ10222222222222-22-2-2-2-2-2222222-2-20000-2-20000000000000000000000000000-22
χ112222222-2-22222-2-22-222-2-2-2-222220000-2-20000000000002-20022-2-20000000000
χ122222222-2-22222-2-22-222-2-2-2-222220000-2-2000000000000-2200-2-2220000000000
χ132222222-2-2222-2-22-22-2-2-2-2-2-222-2-20000220000000000000000000022-2-2000000
χ142222222-2-2222-2-22-22-2-2-2-2-2-222-2-200002200000000000000000000-2-222000000
χ1522222-2-2222222-2-2-2222-2-222-2-2-2-20000-22000000002-22200-2-200000000000000
χ1622222-2-2222222-2-2-2222-2-222-2-2-2-20000-2200000000-22-2-2002200000000000000
χ1722222-2-222222-2-222-2-2-2-2-222-2-22200002-200000000000000000000000020-2000
χ1822222-2-222222-2-222-2-2-2-2-222-2-22200002-2000000000000000000000000-202000
χ1922222-2-2-2-2222222-2-22222-2-2-2-2-2-22i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ2022222-2-2-2-2222222-2-22222-2-2-2-2-2-2−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ2122222-2-2-2-2222-22-222-2-222-2-2-2-2220000-22000000000000000000000000020-200
χ2222222-2-2-2-2222-22-222-2-222-2-2-2-2220000-220000000000000000000000000-20200
χ232222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000
χ242222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-111110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-10000000000
χ272222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300−i3i32-2−i3i3-1-1110000000000
χ282222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300i3−i3-22i3−i311-1-10000000000
χ292222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300−i3i3-22−i3i311-1-10000000000
χ302222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300i3−i32-2i3−i3-1-1110000000000
χ312222-1-2-222-1-1-12-2-2-22-1-111-1-1111100001-133−3−3−3−3332-2-1-100113−33−30000000000
χ322222-1-2-222-1-1-12-2-2-22-1-111-1-1111100001-133−3−3−3−333-221100-1-1−33−330000000000
χ332222-1-2-222-1-1-12-2-2-22-1-111-1-1111100001-1−3−33333−3−32-2-1-10011−33−330000000000
χ342222-1-2-222-1-1-12-2-2-22-1-111-1-1111100001-1−3−33333−3−3-221100-1-13−33−30000000000
χ352222-1-2-2-2-2-1-1-1222-2-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii00−i3i300i3−i33−3−330000000000
χ362222-1-2-2-2-2-1-1-1222-2-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii00i3−i300−i3i3−333−30000000000
χ372222-1-2-2-2-2-1-1-1222-2-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i00−i3i300i3−i3−333−30000000000
χ382222-1-2-2-2-2-1-1-1222-2-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i00i3−i300−i3i33−3−330000000000
χ394444-24444-2-2-2-44-4-4-422-2-2-2-2-2-222000022000000000000000000000000000000
χ404444-244-4-4-2-2-2-4-44-44222222-2-2220000-2-2000000000000000000000000000000
χ414444-2-4-444-2-2-2-4-444-42222-2-222-2-20000-22000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2-44-44422-2-22222-2-200002-2000000000000000000000000000000
χ4344-4-444i−4i004-4-4000000000004i−4i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ4444-4-444i−4i004-4-4000000000004i−4i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ4544-4-44−4i4i004-4-400000000000−4i4i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ4644-4-44−4i4i004-4-400000000000−4i4i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ4744-4-4-24i−4i00-22200000−2i32i30000−2i2i23−232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ50000000000000000000000
χ4844-4-4-24i−4i00-22200000−2i32i30000−2i2i23−23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ50000000000000000000000
χ4944-4-4-24i−4i00-222000002i3−2i30000−2i2i−23232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ130000000000000000000000
χ5044-4-4-24i−4i00-222000002i3−2i30000−2i2i−2323−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ130000000000000000000000
χ5144-4-4-2−4i4i00-22200000−2i32i300002i−2i−2323−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000
χ5244-4-4-2−4i4i00-22200000−2i32i300002i−2i−23232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000
χ5344-4-4-2−4i4i00-222000002i3−2i300002i−2i23−23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000
χ5444-4-4-2−4i4i00-222000002i3−2i300002i−2i23−232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000
χ554-4-444004-4-4-440000000004-40000000000000000000000000000002-22-2000000
χ564-4-444004-4-4-440000000004-4000000000000000000000000000000-22-22000000
χ574-4-44400-44-4-44000000000-440000000000000000000000000000002-2-22000000
χ584-4-44400-44-4-44000000000-44000000000000000000000000000000-222-2000000
χ598-88-880000-88-8000000000000000000000000000000000000000000000000000
χ608-88-8-400004-44000000043−43000000000000000000000000000000000000000000
χ618-88-8-400004-440000000−4343000000000000000000000000000000000000000000
χ628-8-88-4008-844-4000000000-440000000000000000000000000000000000000000
χ638-8-88-400-8844-40000000004-40000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.