Finite Group Databasebeta

← Group #10696598

Character table — Group #10696598

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12222234466644444661212121212121212444412121212121212121212448812121212242424248888244488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ9222222222222-22-2-2-222-2-22222-2-20000-2-20000000000000000000000002-20000
χ10222222222222-22-2-2-222-2-22222-2-20000-2-2000000000000000000000000-220000
χ112222222-2-22222-2-22-222-2-2-2-2-2-22222-2-2-222222-2-2-2-20000000000000000000000
χ122222222-2-22222-2-22-222-2-2-2-2-2-222-2-222-22-2-2-2-222220000000000000000000000
χ132222222-2-2222-2-22-222222-2-2-2-2-2-200002-2000000000000000000000000002-200
χ142222222-2-2222-2-22-222222-2-2-2-2-2-200002-200000000000000000000000000-2200
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-10000000000
χ19222222-1-2-2-1-1-12-2-22-2-1-1111111-1-122-2-21-1-1-1-1-111110000−i3−i3i3i3−i3−i3i3i30000000000
χ20222222-1-2-2-1-1-12-2-22-2-1-1111111-1-122-2-21-1-1-1-1-111110000i3i3−i3−i3i3i3−i3−i30000000000
χ21222222-1-2-2-1-1-12-2-22-2-1-1111111-1-1-2-2221-11111-1-1-1-10000−i3−i3i3i3i3i3−i3−i30000000000
χ22222222-1-2-2-1-1-12-2-22-2-1-1111111-1-1-2-2221-11111-1-1-1-10000i3i3−i3−i3−i3−i3i3i30000000000
χ232222-2-22222222-2-2-22-2-2-2-222-2-2-2-2000022000000002-2002-22-200000000000000
χ242222-2-22222222-2-2-22-2-2-2-222-2-2-2-200002200000000-2200-22-2200000000000000
χ252222-2-2222222-2-222-2-2-22222-2-2220000-2-200000000000000000000000000002-2
χ262222-2-2222222-2-222-2-2-22222-2-2220000-2-20000000000000000000000000000-22
χ272222-2-22-2-2222222-2-2-2-222-2-222-2-20000-2200000000002i−2i00002i−2i2i−2i0000000000
χ282222-2-22-2-2222222-2-2-2-222-2-222-2-20000-220000000000−2i2i0000−2i2i−2i2i0000000000
χ292222-2-22-2-2222-22-222-2-2-2-2-2-2222200002-20000000000000000000022-2-2000000
χ302222-2-22-2-2222-22-222-2-2-2-2-2-2222200002-200000000000000000000-2-222000000
χ312222-2-2-122-1-1-12-2-2-221111-1-111110000-1-133−3−333−3−32-200-11-113−3−330000000000
χ322222-2-2-122-1-1-12-2-2-221111-1-111110000-1-133−3−333−3−3-22001-11-1−333−30000000000
χ332222-2-2-122-1-1-12-2-2-221111-1-111110000-1-1−3−333−3−3332-200-11-11−333−30000000000
χ342222-2-2-122-1-1-12-2-2-221111-1-111110000-1-1−3−333−3−333-22001-11-13−3−330000000000
χ352222-2-2-1-2-2-1-1-1222-2-211-1-111-1-11100001-133−3−3−3−333002i−2i−i3i3i3−i3−ii−ii0000000000
χ362222-2-2-1-2-2-1-1-1222-2-211-1-111-1-11100001-133−3−3−3−33300−2i2ii3−i3−i3i3i−ii−i0000000000
χ372222-2-2-1-2-2-1-1-1222-2-211-1-111-1-11100001-1−3−33333−3−3002i−2ii3−i3−i3i3−ii−ii0000000000
χ382222-2-2-1-2-2-1-1-1222-2-211-1-111-1-11100001-1−3−33333−3−300−2i2i−i3i3i3−i3i−ii−i0000000000
χ39444444-244-2-2-2-44-4-4-4-2-222-2-2-2-222000022000000000000000000000000000000
χ40444444-2-4-4-2-2-2-4-44-44-2-2-2-22222220000-22000000000000000000000000000000
χ414444-4-4-244-2-2-2-4-444-422-2-2-2-222-2-2000022000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-2-44-444222222-2-2-2-20000-22000000000000000000000000000000
χ434-44-40044-4-44-40000000004-400002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ444-44-40044-4-44-40000000004-40000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ454-44-4004-44-44-4000000000-4400002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ464-44-4004-44-44-4000000000-440000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ474-44-400-24-42-22000000023−23-220023−232i−2i2i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ484-44-400-24-42-22000000023−23-220023−23−2i2i−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ494-44-400-24-42-220000000−2323-2200−23232i−2i2i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ504-44-400-24-42-220000000−2323-2200−2323−2i2i−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ514-44-400-2-442-22000000023−232-200−23232i−2i−2i2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ524-44-400-2-442-22000000023−232-200−2323−2i2i2i−2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ534-44-400-2-442-220000000−23232-20023−232i−2i−2i2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ544-44-400-2-442-220000000−23232-20023−23−2i2i2i−2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ554-4-444-44004-4-4000004-400000000000000000000000000000000002i−2i2i−2i000000
χ564-4-444-44004-4-4000004-40000000000000000000000000000000000−2i2i−2i2i000000
χ574-4-44-444004-4-400000-4400000000000000000000000000000000002i−2i−2i2i000000
χ584-4-44-444004-4-400000-440000000000000000000000000000000000−2i2i2i−2i000000
χ5988-8-800800-8-88000000000000000000000000000000000000000000000000000
χ6088-8-800-40044-40000000000043−4300000000000000000000000000000000000000
χ6188-8-800-40044-400000000000−434300000000000000000000000000000000000000
χ628-8-888-8-400-44400000-4400000000000000000000000000000000000000000000
χ638-8-88-88-400-444000004-400000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.