Finite Group Databasebeta

← Group #10697675

Character table — Group #10697675

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212446688888888121212121212121212122424242424242424242424242424242444881212121224242424444488882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ922222222-2-222-22-2222-2-2-2-2-2-22200000000-2-222-2-2-2-2220000000000000000000000000000000022-2-20000
χ1022222222-2-222-22-2222-2-2-2-2-2-22200000000-2-222-2-2-2-22200000000000000000000000000000000-2-2220000
χ112222222-222-2-22-222222222-2-2220000000022-2-2-2-2-2-2-2-2000000000000000000000000000022-2-200000000
χ122222222-222-2-22-222222222-2-2220000000022-2-2-2-2-2-2-2-20000000000000000000000000000-2-22200000000
χ132222222-2-2-2-2-2-2-2-2222-2-2-2-222222i2i2i2i−2i−2i−2i−2i-2-2-2-22222-2-22i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000
χ142222222-2-2-2-2-2-2-2-2222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i-2-2-2-22222-2-2−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i000000000000000000000000
χ15222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-12i2i2i2i−2i−2i−2i−2i1111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii0000−i3−i3i3i333−3−3000000000000
χ20222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-12i2i2i2i−2i−2i−2i−2i1111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii0000i3i3−i3−i3−3−333000000000000
χ21222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-1−2i−2i−2i−2i2i2i2i2i1111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i0000−i3−i3i3i3−3−333000000000000
χ22222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-1−2i−2i−2i−2i2i2i2i2i1111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i0000i3i3−i3−i333−3−3000000000000
χ232222-2-2222-2-2-222-222222222-2-2-200000000-2-22222-2-2-2-20000000000000000000000000000000000002-200
χ242222-2-2222-2-2-222-222222222-2-2-200000000-2-22222-2-2-2-2000000000000000000000000000000000000-2200
χ252222-2-222-22-2-2-222222-2-2-2-2-22-2-2000000002222-2-222-2-200000000000000002-2002-22-20000000000000000
χ262222-2-222-22-2-2-222222-2-2-2-2-22-2-2000000002222-2-222-2-20000000000000000-2200-22-220000000000000000
χ272222-2-22-22-2222-2-22222222-22-2-200000000-2-2-2-2-2-222220000000000000000002-200002-22-2000000000000
χ282222-2-22-22-2222-2-22222222-22-2-200000000-2-2-2-2-2-22222000000000000000000-220000-22-22000000000000
χ292222-2-22-2-2222-2-22222-2-2-2-22-2-2-20000000022-2-222-2-222000000000000000000000000000000000000002-2
χ302222-2-22-2-2222-2-22222-2-2-2-22-2-2-20000000022-2-222-2-22200000000000000000000000000000000000000-22
χ312222-2-2-12-22-2-2-222-1-1-11111-221100000000-1-1-1-111-1-1113333−3−3−3−33333−3−3−3−32-200-11-113−3−33000000000000
χ322222-2-2-12-22-2-2-222-1-1-11111-221100000000-1-1-1-111-1-1113333−3−3−3−33333−3−3−3−3-22001-11-1−333−3000000000000
χ332222-2-2-12-22-2-2-222-1-1-11111-221100000000-1-1-1-111-1-111−3−3−3−33333−3−3−3−333332-200-11-11−333−3000000000000
χ342222-2-2-12-22-2-2-222-1-1-11111-221100000000-1-1-1-111-1-111−3−3−3−33333−3−3−3−33333-22001-11-13−3−33000000000000
χ352222-2-2-1-22-2222-2-2-1-1-1-1-1-1-1-221100000000111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3002-2−i3i3i3−i3-11-11000000000000
χ362222-2-2-1-22-2222-2-2-1-1-1-1-1-1-1-221100000000111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300-22i3−i3−i3i31-11-1000000000000
χ372222-2-2-1-22-2222-2-2-1-1-1-1-1-1-1-221100000000111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3002-2i3−i3−i3i3-11-11000000000000
χ382222-2-2-1-22-2222-2-2-1-1-1-1-1-1-1-221100000000111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300-22−i3i3i3−i31-11-1000000000000
χ392-2-222-2202-200-2022-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−20000000000002i−2i00−i2i2−i2i20000
χ402-2-222-2202-200-2022-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−2000000000000−2i2i00i2−i2i2−i20000
χ412-2-222-2202-200-2022-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−2220000000000002i−2i00i2−i2i2−i20000
χ422-2-222-2202-200-2022-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−222000000000000−2i2i00−i2i2−i2i20000
χ432-2-222-220-220020-22-2-2-2-222002-2−i2−i2i2i2i2i2−i2−i2-2200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000002-2−i2i2i2−i20000
χ442-2-222-220-220020-22-2-2-2-222002-2−i2−i2i2i2i2i2−i2−i2-2200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000-22i2−i2−i2i20000
χ452-2-222-220-220020-22-2-2-2-222002-2i2i2−i2−i2−i2−i2i2i2-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000002-2i2−i2−i2i20000
χ462-2-222-220-220020-22-2-2-2-222002-2i2i2−i2−i2−i2−i2i2i2-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000-22−i2i2i2−i20000
χ47444444-24-4-444-44-4-2-2-22222-4-4-2-20000000022-2-22222-2-20000000000000000000000000000000000000000
χ48444444-2-444-4-44-44-2-2-2-2-2-2-2-4-4-2-200000000-2-2222222220000000000000000000000000000000000000000
χ494444-4-4-244-4-4-444-4-2-2-2-2-2-2-24-4220000000022-2-2-2-222220000000000000000000000000000000000000000
χ504444-4-4-2-4-4444-4-44-2-2-222224-42200000000-2-222-2-222-2-20000000000000000000000000000000000000000
χ5144-4-4004400000-40-44-4000000002-22-22-22-2004-40000002-22-22-22-22-22-22-22-2000000000000000000000000
χ5244-4-4004400000-40-44-400000000-22-22-22-22004-4000000-22-22-22-22-22-22-22-22000000000000000000000000
χ5344-4-4004-40000040-44-4000000002i−2i2i−2i−2i2i−2i2i00-440000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5444-4-4004-40000040-44-400000000−2i2i−2i2i2i−2i2i−2i00-44000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5544-4-400-2400000-402-2223−2323−2300002-22-22-22-200-2223−230000−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000
χ5644-4-400-2400000-402-2223−2323−230000-22-22-22-2200-2223−2300001−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000
χ5744-4-400-2400000-402-22−2323−232300002-22-22-22-200-22−23230000−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000
χ5844-4-400-2400000-402-22−2323−23230000-22-22-22-2200-22−232300001+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000
χ5944-4-400-2-400000402-2223−2323−2300002i−2i2i−2i−2i2i−2i2i002-2−23230000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ6044-4-400-2-400000402-2223−2323−230000−2i2i−2i2i2i−2i2i−2i002-2−23230000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ6144-4-400-2-400000402-22−2323−232300002i−2i2i−2i−2i2i−2i2i002-223−230000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ6244-4-400-2-400000402-22−2323−23230000−2i2i−2i2i2i−2i2i−2i002-223−230000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ634-44-40040004i−4i000-4-44000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000004i−4i2ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ644-44-40040004i−4i000-4-4400000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000004i−4i−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ654-44-4004000−4i4i000-4-4400000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000−4i4i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ664-44-4004000−4i4i000-4-44000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000−4i4i2ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ674-44-400-20004i−4i00022-223−23−232300002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000−2i32i3−2i2i−2ζ72ζ72ζ7−2ζ7−2ζ232ζ232ζ23−2ζ232ζ5−2ζ5−2ζ52ζ52ζ13−2ζ13−2ζ132ζ13000000000000000000000000
χ684-44-400-20004i−4i00022-223−23−23230000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000−2i32i3−2i2i2ζ7−2ζ7−2ζ72ζ72ζ23−2ζ23−2ζ232ζ23−2ζ52ζ52ζ5−2ζ5−2ζ132ζ132ζ13−2ζ13000000000000000000000000
χ694-44-400-20004i−4i00022-2−232323−2300002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000002i3−2i3−2i2i−2ζ232ζ232ζ23−2ζ23−2ζ72ζ72ζ7−2ζ72ζ13−2ζ13−2ζ132ζ132ζ5−2ζ5−2ζ52ζ5000000000000000000000000
χ704-44-400-20004i−4i00022-2−232323−230000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000002i3−2i3−2i2i2ζ23−2ζ23−2ζ232ζ232ζ7−2ζ7−2ζ72ζ7−2ζ132ζ132ζ13−2ζ13−2ζ52ζ52ζ5−2ζ5000000000000000000000000
χ714-44-400-2000−4i4i00022-223−23−23230000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000002i3−2i32i−2i2ζ5−2ζ5−2ζ52ζ52ζ13−2ζ13−2ζ132ζ13−2ζ72ζ72ζ7−2ζ7−2ζ232ζ232ζ23−2ζ23000000000000000000000000
χ724-44-400-2000−4i4i00022-223−23−232300002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ230000002i3−2i32i−2i−2ζ52ζ52ζ5−2ζ5−2ζ132ζ132ζ13−2ζ132ζ7−2ζ7−2ζ72ζ72ζ23−2ζ23−2ζ232ζ23000000000000000000000000
χ734-44-400-2000−4i4i00022-2−232323−230000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000−2i32i32i−2i2ζ13−2ζ13−2ζ132ζ132ζ5−2ζ5−2ζ52ζ5−2ζ232ζ232ζ23−2ζ23−2ζ72ζ72ζ7−2ζ7000000000000000000000000
χ744-44-400-2000−4i4i00022-2−232323−2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000−2i32i32i−2i−2ζ132ζ132ζ13−2ζ13−2ζ52ζ52ζ5−2ζ52ζ23−2ζ23−2ζ232ζ232ζ7−2ζ7−2ζ72ζ7000000000000000000000000
χ754-4-444-4-204-400-404-222-2-22200-222222−22−222222−22−22-2200000000−2−222−2−222−2−222−2−222000000000000000000000000
χ764-4-444-4-204-400-404-222-2-22200-22−22−222222−22−222222-220000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ774-4-444-4-20-440040-4-22222-2-200-22−2i2−2i22i22i22i22i2−2i2−2i22-200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ784-4-444-4-20-440040-4-22222-2-200-222i22i2−2i2−2i2−2i2−2i22i22i22-200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ794-4-44-44404400-40-44-4-444-4-400-4400000000-44000000000000000000000000000000000000000000000000
χ804-4-44-4440-4-4004044-4-4-4-44400-44000000004-4000000000000000000000000000000000000000000000000
χ814-4-44-44-204400-40-4-222-2-222002-2000000002-200000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ824-4-44-44-204400-40-4-222-2-222002-2000000002-200000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ834-4-44-44-20-4-400404-22222-2-2002-200000000-220000000066−6−6−6−66666−6−6−6−666000000000000000000000000
χ844-4-44-44-20-4-400404-22222-2-2002-200000000-2200000000−6−66666−6−6−6−66666−6−6000000000000000000000000

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