Finite Group Databasebeta

← Group #10696024

Character table — Group #10696024

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222234444666444466121212121212121288881212242424242424242444881212121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
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
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ9222222222-2-2222-22-2-222-2-2-2-222-2-20000-2200000000000000000000000022-2-20000
χ10222222222-2-2222-22-2-222-2-2-2-222-2-20000-22000000000000000000000000-2-2220000
χ112222222-2-2222222-2-2-22222-2-2-2-2-2-200002-2000000002-20022-2-20000000000000000
χ122222222-2-2222222-2-2-22222-2-2-2-2-2-200002-200000000-2200-2-2220000000000000000
χ132222222-2-2-2-2222-2-22222-2-222-2-2220000-2-20000000000000000000022-2-200000000
χ142222222-2-2-2-2222-2-22222-2-222-2-2220000-2-200000000000000000000-2-22200000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-222-1-1-12-2-2-2-1-1-1-11111110000-113333−3−3−3−32-200-1-11133−3−3000000000000
χ20222222-1-2-222-1-1-12-2-2-2-1-1-1-11111110000-113333−3−3−3−3-220011-1-1−3−333000000000000
χ21222222-1-2-222-1-1-12-2-2-2-1-1-1-11111110000-11−3−3−3−333332-200-1-111−3−333000000000000
χ22222222-1-2-222-1-1-12-2-2-2-1-1-1-11111110000-11−3−3−3−33333-220011-1-133−3−3000000000000
χ232222-2-222222222-2-22-2-2-2222222-2-20000-2-20000000000000000000000000000002-2
χ242222-2-222222222-2-22-2-2-2222222-2-20000-2-2000000000000000000000000000000-22
χ252222-2-2222-2-22222-2-22-2-2-2-2-2-2222200002-200000000002-200002-22-2000000000000
χ262222-2-2222-2-22222-2-22-2-2-2-2-2-2222200002-20000000000-220000-22-22000000000000
χ272222-2-22-2-222222-22-22-2-222-2-2-2-2220000-2200000000000000000000000000002-200
χ282222-2-22-2-222222-22-22-2-222-2-2-2-2220000-220000000000000000000000000000-2200
χ292222-2-22-2-2-2-2222222-2-2-2-2-222-2-2-2-22i2i−2i−2i222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302222-2-22-2-2-2-2222222-2-2-2-2-222-2-2-2-2−2i−2i2i2i22−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312222-2-2-122-2-2-1-1-12-2-22111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i3002-2−i3i3−i3i3-11-11000000000000
χ322222-2-2-122-2-2-1-1-12-2-22111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i300-22i3−i3i3−i31-11-1000000000000
χ332222-2-2-122-2-2-1-1-12-2-22111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i3002-2i3−i3i3−i3-11-11000000000000
χ342222-2-2-122-2-2-1-1-12-2-22111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i300-22−i3i3−i3i31-11-1000000000000
χ352222-2-2-1-2-2-2-2-1-1-1222-21111-1-111112i2i−2i−2i-1-1−i−iii−i−iii0000−i3i3i3−i33−3−33000000000000
χ362222-2-2-1-2-2-2-2-1-1-1222-21111-1-111112i2i−2i−2i-1-1−i−iii−i−iii0000i3−i3−i3i3−333−3000000000000
χ372222-2-2-1-2-2-2-2-1-1-1222-21111-1-11111−2i−2i2i2i-1-1ii−i−iii−i−i0000−i3i3i3−i3−333−3000000000000
χ382222-2-2-1-2-2-2-2-1-1-1222-21111-1-11111−2i−2i2i2i-1-1ii−i−iii−i−i0000i3−i3−i3i33−3−33000000000000
χ39444444-244-4-4-2-2-2-44-4-4-2-22222-2-22200002-200000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-2-4-444-2-222-2-222-2-200002200000000000000000000000000000000
χ414444-4-4-24444-2-2-2-4-44-422-2-2-2-2-2-22200002200000000000000000000000000000000
χ424444-4-4-2-4-444-2-2-2-44-4422-2-22222-2-200002-200000000000000000000000000000000
χ4344-4-4004004-44-4-40000004-40000000000000000000000000000000000002-22-20000
χ4444-4-4004004-44-4-40000004-4000000000000000000000000000000000000-22-220000
χ4544-4-400400-444-4-4000000-440000000000000000000000000000000000002-2-220000
χ4644-4-400400-444-4-4000000-44000000000000000000000000000000000000-222-20000
χ474-44-44-440000-44-400004-4000000002-22-2002-22-22-22-2000000000000000000000000
χ484-44-44-440000-44-400004-400000000-22-2200-22-22-22-22000000000000000000000000
χ494-44-44-4-200002-220000-220023−230023−232-22-200−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000
χ504-44-44-4-200002-220000-220023−230023−23-22-22001−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000
χ514-44-44-4-200002-220000-2200−232300−23232-22-200−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000
χ524-44-44-4-200002-220000-2200−232300−2323-22-22001+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000
χ534-44-4-4440000-44-40000-44000000002i−2i−2i2i002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ544-44-4-4440000-44-40000-4400000000−2i2i2i−2i00−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ554-44-4-44-200002-2200002-20023−2300−23232i−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+ζ11000000000000000000000000
χ564-44-4-44-200002-2200002-20023−2300−2323−2i2i2i−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−ζ11000000000000000000000000
χ574-44-4-44-200002-2200002-200−23230023−232i−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+ζ11000000000000000000000000
χ584-44-4-44-200002-2200002-200−23230023−23−2i2i2i−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−ζ11000000000000000000000000
χ594-4-440044i−4i00-4-4400000000004i−4i00000000000000000000000000002i−2i2-200000000
χ604-4-440044i−4i00-4-4400000000004i−4i0000000000000000000000000000−2i2i-2200000000
χ614-4-44004−4i4i00-4-440000000000−4i4i00000000000000000000000000002i−2i-2200000000
χ624-4-44004−4i4i00-4-440000000000−4i4i0000000000000000000000000000−2i2i2-200000000
χ6388-8-800-4008-8-444000000-4400000000000000000000000000000000000000000000
χ6488-8-800-400-88-4440000004-400000000000000000000000000000000000000000000
χ658-8-8800-48i−8i0044-40000000000−4i4i0000000000000000000000000000000000000000
χ668-8-8800-4−8i8i0044-400000000004i−4i0000000000000000000000000000000000000000

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