Finite Group Databasebeta

← Group #10695582

Character table — Group #10695582

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222222344666244466661212121212124444612121212121212121244881212121224242424222244444488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1
χ9222222222-2-22222-2-2-22222-2-2-2-2-2-200002-2000000000000000000002200-2-2000000
χ10222222222-2-22222-2-2-22222-2-2-2-2-2-200002-200000000000000000000-2-20022000000
χ1122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ1422222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ15222222-2-2222222-22-2-222-2-22222-2-222-2-2-2-22222-2-2-2-2000000000000000000000000
χ16222222-2-2222222-22-2-222-2-22222-2-2-2-222-2-2-2-2-2-22222000000000000000000000000
χ17222222-2-22-2-2222-2-22222-2-2-2-2-2-2220000-2200000000000000000000000000002-200
χ18222222-2-22-2-2222-2-22222-2-2-2-2-2-2220000-220000000000000000000000000000-2200
χ19222222-2-2-122-1-1-1-22-2-2-1-111-1-1-1-11122-2-211-1-1-1-11111000033−3−333−3−3000000000000
χ20222222-2-2-122-1-1-1-22-2-2-1-111-1-1-1-11122-2-211-1-1-1-111110000−3−333−3−333000000000000
χ21222222-2-2-122-1-1-1-22-2-2-1-111-1-1-1-111-2-222111111-1-1-1-1000033−3−3−3−333000000000000
χ22222222-2-2-122-1-1-1-22-2-2-1-111-1-1-1-111-2-222111111-1-1-1-10000−3−33333−3−3000000000000
χ232222-2-222222222-2-22-2-2-22222-2-2-2-20000-22000000002-2002-22-20000000000000000
χ242222-2-222222222-2-22-2-2-22222-2-2-2-20000-2200000000-2200-22-220000000000000000
χ252222-2-2222-2-2222-22-22-2-222-2-222220000-2-200000000000000000000002200-2-20000
χ262222-2-2222-2-2222-22-22-2-222-2-222220000-2-20000000000000000000000-2-200220000
χ272222-2-222-122-1-1-1-2-22-211-1-1-1-1111100001-133−3−333−3−32-200-11-113−33−3000000000000
χ282222-2-222-122-1-1-1-2-22-211-1-1-1-1111100001-133−3−333−3−3-22001-11-1−33−33000000000000
χ292222-2-222-122-1-1-1-2-22-211-1-1-1-1111100001-1−3−333−3−3332-200-11-11−33−33000000000000
χ302222-2-222-122-1-1-1-2-22-211-1-1-1-1111100001-1−3−333−3−333-22001-11-13−33−3000000000000
χ312222-2-2-2-22222222-2-22-2-2-2-222-2-22200002-200000000002-200002-2-22000000000000
χ322222-2-2-2-22222222-2-22-2-2-2-222-2-22200002-20000000000-220000-222-2000000000000
χ332222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-20000220000000000000000000000000000002i−2i
χ342222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-2000022000000000000000000000000000000−2i2i
χ352222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-1133−3−3−3−333002-2−333−3-111-1000000000000
χ362222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-1133−3−3−3−33300-223−3−331-1-11000000000000
χ372222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-11−3−33333−3−3002-23−3−33-111-1000000000000
χ382222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-11−3−33333−3−300-22−333−31-1-11000000000000
χ3944444444-2-4-4-2-2-24-4-4-4-2-2-2-22222220000-2200000000000000000000000000000000
χ40444444-4-4-2-4-4-2-2-2-4-444-2-2222222-2-200002-200000000000000000000000000000000
χ414444-4-444-2-4-4-2-2-2-44-4422-2-222-2-2-2-200002200000000000000000000000000000000
χ424444-4-4-4-4-2-4-4-2-2-2444-4222222-2-2220000-2-200000000000000000000000000000000
χ4344-4-4000044i−4i4-4-4000000004i−4i0000000000000000000000000000002-2002i−2i000000
χ4444-4-4000044i−4i4-4-4000000004i−4i000000000000000000000000000000-2200−2i2i000000
χ4544-4-400004−4i4i4-4-400000000−4i4i0000000000000000000000000000002-200−2i2i000000
χ4644-4-400004−4i4i4-4-400000000−4i4i000000000000000000000000000000-22002i−2i000000
χ474-44-4004-4400-44-40000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ484-44-4004-4400-44-40000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ494-44-4004-4-2002-22000000-220023−2323−232i−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−ζ11000000000000000000000000
χ504-44-4004-4-2002-22000000-220023−2323−23−2i2i−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+ζ11000000000000000000000000
χ514-44-4004-4-2002-22000000-2200−2323−23232i−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−ζ11000000000000000000000000
χ524-44-4004-4-2002-22000000-2200−2323−2323−2i2i−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+ζ11000000000000000000000000
χ534-44-400-44400-44-4000000-440000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ544-44-400-44400-44-4000000-44000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ554-44-400-44-2002-220000002-20023−23−23232i−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+ζ11000000000000000000000000
χ564-44-400-44-2002-220000002-20023−23−2323−2i2i2i−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−ζ11000000000000000000000000
χ574-44-400-44-2002-220000002-200−232323−232i−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+ζ11000000000000000000000000
χ584-44-400-44-2002-220000002-200−232323−23−2i2i2i−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−ζ11000000000000000000000000
χ594-4-444-400400-4-4400004-40000000000000000000000000000000000002-2002-20000
χ604-4-444-400400-4-4400004-4000000000000000000000000000000000000-2200-220000
χ614-4-44-4400400-4-440000-440000000000000000000000000000000000002-200-220000
χ624-4-44-4400400-4-440000-44000000000000000000000000000000000000-22002-20000
χ6388-8-80000-48i−8i-44400000000−4i4i000000000000000000000000000000000000000000
χ6488-8-80000-4−8i8i-444000000004i−4i000000000000000000000000000000000000000000
χ658-8-888-800-40044-40000-440000000000000000000000000000000000000000000000
χ668-8-88-8800-40044-400004-40000000000000000000000000000000000000000000000

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