Finite Group Databasebeta

← Group #10696087

Character table — Group #10696087

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12222234466644444661212121212121212888812122424242424242424448812121212242424244444244488
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
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-111-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-1111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-111
χ92222222222222-2-2-2-22222-2-2-2-2-2-200002-2000000002-20022-2-200000000000000
χ102222222222222-2-2-2-22222-2-2-2-2-2-200002-200000000-2200-2-22200000000000000
χ112222222-2-2222-22-22-222-2-22222-2-20000-2-20000000000000000000022-2-2000000
χ122222222-2-2222-22-22-222-2-22222-2-20000-2-200000000000000000000-2-222000000
χ132222222-2-2222-2-22-2222-2-2-2-2-2-2220000-2200000000000000000000000002-2000
χ142222222-2-2222-2-22-2222-2-2-2-2-2-2220000-220000000000000000000000000-22000
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
χ19222222-122-1-1-12-2-2-2-2-1-1-1-11111110000-113333−3−3−3−32-200-1-11133−3−30000000000
χ20222222-122-1-1-12-2-2-2-2-1-1-1-11111110000-113333−3−3−3−3-220011-1-1−3−3330000000000
χ21222222-122-1-1-12-2-2-2-2-1-1-1-11111110000-11−3−3−3−333332-200-1-111−3−3330000000000
χ22222222-122-1-1-12-2-2-2-2-1-1-1-11111110000-11−3−3−3−33333-220011-1-133−3−30000000000
χ232222-2-2222222-22-2-22-2-22222-2-22222-2-2-2-222-2-222-2-20000000000000000000000
χ242222-2-2222222-22-2-22-2-22222-2-222-2-222-2-2-2-222-2-2220000000000000000000000
χ252222-2-2222222-2-222-2-2-222-2-222-2-20000-2200000000002-200002-22-20000000000
χ262222-2-2222222-2-222-2-2-222-2-222-2-20000-220000000000-220000-22-220000000000
χ272222-2-22-2-2222222-2-2-2-2-2-222-2-2-2-200002200000000000000000000000000002i−2i
χ282222-2-22-2-2222222-2-2-2-2-2-222-2-2-2-20000220000000000000000000000000000−2i2i
χ292222-2-22-2-22222-2-222-2-2-2-2-2-2222200002-2000000000000000000000000200-200
χ302222-2-22-2-22222-2-222-2-2-2-2-2-2222200002-2000000000000000000000000-200200
χ312222-2-2-122-1-1-1-22-2-2211-1-1-1-111-1-122-2-211-1-111-1-11100003−33−33−3−330000000000
χ322222-2-2-122-1-1-1-22-2-2211-1-1-1-111-1-122-2-211-1-111-1-1110000−33−33−333−30000000000
χ332222-2-2-122-1-1-1-22-2-2211-1-1-1-111-1-1-2-2221111-1-111-1-100003−33−3−333−30000000000
χ342222-2-2-122-1-1-1-22-2-2211-1-1-1-111-1-1-2-2221111-1-111-1-10000−33−333−3−330000000000
χ352222-2-2-122-1-1-1-2-222-211-1-111-1-11100001-133−3−3−3−333002-2−333−3-11-110000000000
χ362222-2-2-122-1-1-1-2-222-211-1-111-1-11100001-133−3−3−3−33300-223−3−331-11-10000000000
χ372222-2-2-122-1-1-1-2-222-211-1-111-1-11100001-1−3−33333−3−3002-23−3−33-11-110000000000
χ382222-2-2-122-1-1-1-2-222-211-1-111-1-11100001-1−3−33333−3−300-22−333−31-11-10000000000
χ39444444-2-4-4-2-2-2-44-44-4-2-222-2-2-2-222000022000000000000000000000000000000
χ40444444-2-4-4-2-2-2-4-44-44-2-2222222-2-200002-2000000000000000000000000000000
χ414444-4-4-2-4-4-2-2-2444-4-42222-2-222220000-2-2000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-24-4-444222222-2-2-2-20000-22000000000000000000000000000000
χ434-44-40044i−4i4-4-400000004i−4i000000000000000000000000000000002-22i−2i000000
χ444-44-40044i−4i4-4-400000004i−4i00000000000000000000000000000000-22−2i2i000000
χ454-44-4004−4i4i4-4-40000000−4i4i000000000000000000000000000000002-2−2i2i000000
χ464-44-4004−4i4i4-4-40000000−4i4i00000000000000000000000000000000-222i−2i000000
χ474-4-444-4400-44-4000004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ484-4-444-4400-44-4000004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ494-4-444-4-2002-2200000-220023−2323−23002i−2i2i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ504-4-444-4-2002-2200000-220023−2323−2300−2i2i−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ514-4-444-4-2002-2200000-2200−2323−2323002i−2i2i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ524-4-444-4-2002-2200000-2200−2323−232300−2i2i−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ534-4-44-44400-44-400000-44000000002i−2i−2i2i002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ544-4-44-44400-44-400000-4400000000−2i2i2i−2i00−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ554-4-44-44-2002-22000002-20023−23−2323002i−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
χ564-4-44-44-2002-22000002-20023−23−232300−2i2i2i−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
χ574-4-44-44-2002-22000002-200−232323−23002i−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
χ584-4-44-44-2002-22000002-200−232323−2300−2i2i2i−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
χ5988-8-800800-8-88000000000000000000000000000000000000000000000000000
χ6088-8-800-40044-4000000000000043−43000000000000000000000000000000000000
χ6188-8-800-40044-40000000000000−4343000000000000000000000000000000000000
χ628-88-800-48i−8i-4440000000−4i4i000000000000000000000000000000000000000000
χ638-88-800-4−8i8i-44400000004i−4i000000000000000000000000000000000000000000

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