Finite Group Databasebeta

← Group #69207

Character table — Group #69207

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222222222223333444444444444446666666666666688881616161624242424
order1222344666888816161616161616164444121224242424484848484848484844888816161616161616164444121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ611111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91-11-111-1-1-11-1-111iiii−i−i−i−iii−i−i-1111-1-1iiii−i−i−i−ii−iii−i−i1111-1-1-1-11-1i−ii−i1-11-1i−i
χ101-11-111-1-1-11-1-111iiii−i−i−i−iii−i−i-1111-1-1iiii−i−i−i−ii−iii−i−i1111-1-1-1-1-11−ii−ii-11-11−ii
χ111-11-111-1-1-11-1-111iiii−i−i−i−i−i−iii-1111-1-1iiii−i−i−i−i−ii−i−iii-1-1-1-111111-1i−ii−i1-1-11−ii
χ121-11-111-1-1-11-1-111iiii−i−i−i−i−i−iii-1111-1-1iiii−i−i−i−i−ii−i−iii-1-1-1-11111-11−ii−ii-111-1i−i
χ131-11-111-1-1-11-1-111−i−i−i−iiiiiii−i−i-1111-1-1−i−i−i−iiiiii−iii−i−i-1-1-1-111111-1−ii−ii1-1-11i−i
χ141-11-111-1-1-11-1-111−i−i−i−iiiiiii−i−i-1111-1-1−i−i−i−iiiiii−iii−i−i-1-1-1-11111-11i−ii−i-111-1−ii
χ151-11-111-1-1-11-1-111−i−i−i−iiiii−i−iii-1111-1-1−i−i−i−iiiii−ii−i−iii1111-1-1-1-11-1−ii−ii1-11-1−ii
χ161-11-111-1-1-11-1-111−i−i−i−iiiii−i−iii-1111-1-1−i−i−i−iiiii−ii−i−iii1111-1-1-1-1-11i−ii−i-11-11i−i
χ172222222222-2-2-2-200000000222222-2-2-2-20000000022-2-2-2-200000000000000000000
χ182222222222-2-2-2-200000000-2-2-2-222-2-2-2-200000000-2-2222200000000000000000000
χ1922222-2-2222000022−2−222−2−22222-2-2000022−2−222−2−2-2-2000022−2−222−2−2000000000000
χ2022222-2-2222000022−2−222−2−2-2-2-2-2-2-2000022−2−222−2−2220000−2−222−2−222000000000000
χ2122222-2-22220000−2−222−2−2222222-2-20000−2−222−2−222-2-20000−2−222−2−222000000000000
χ2222222-2-22220000−2−222−2−222-2-2-2-2-2-20000−2−222−2−22222000022−2−222−2−2000000000000
χ232222-122-1-1-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000002222-1-1-1-10000
χ242222-122-1-1-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-2-2-211110000
χ252222-122-1-1-12222-2-2-2-2-2-2-2-20000-1-1-1-1-1-1111111110000000000000022-2-211-1-10000
χ262222-122-1-1-12222-2-2-2-2-2-2-2-20000-1-1-1-1-1-11111111100000000000000-2-222-1-1110000
χ2722-2-22002-2-22−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ52-22-2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ2822-2-22002-2-22−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5-22-22002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ2922-2-22002-2-22−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ52-22-2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3022-2-22002-2-22−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5-22-22002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3122-2-22002-2-2−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ72-22-200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ3222-2-22002-2-2−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7-22-2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3322-2-22002-2-2−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ72-22-200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3422-2-22002-2-2−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7-22-2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ352-22-222-2-2-2222-2-2000000002i2i−2i−2i-22-2-222000000002i−2i−2i−2i2i2i00000000000000000000
χ362-22-222-2-2-2222-2-200000000−2i−2i2i2i-22-2-22200000000−2i2i2i2i−2i−2i00000000000000000000
χ372-22-22-22-2-220000i2i2−i2−i2−i2−i2i2i22i2i−2i−2i2-20000i2i2−i2−i2−i2−i2i2i2−2i2i000022−2−2−2−222000000000000
χ382-22-22-22-2-220000i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i2-20000i2i2−i2−i2−i2−i2i2i22i−2i0000−2−22222−2−2000000000000
χ392-22-22-22-2-220000−i2−i2i2i2i2i2−i2−i22i2i−2i−2i2-20000−i2−i2i2i2i2i2−i2−i2−2i2i0000−2−22222−2−2000000000000
χ402-22-22-22-2-220000−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i2-20000−i2−i2i2i2i2i2−i2−i22i−2i000022−2−2−2−222000000000000
χ412-22-2-12-211-1-2-2222i2i2i2i−2i−2i−2i−2i00001-1-1-111−i−i−i−iiiii000000000000002-22i−2i−ii-110000
χ422-22-2-12-211-1-2-2222i2i2i2i−2i−2i−2i−2i00001-1-1-111−i−i−i−iiiii00000000000000-22−2i2ii−i1-10000
χ432-22-2-12-211-1-2-222−2i−2i−2i−2i2i2i2i2i00001-1-1-111iiii−i−i−i−i000000000000002-2−2i2ii−i-110000
χ442-22-2-12-211-1-2-222−2i−2i−2i−2i2i2i2i2i00001-1-1-111iiii−i−i−i−i00000000000000-222i−2i−ii1-10000
χ452-2-22200-22-22−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ52i−2i−2i2i00−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ462-2-22200-22-22−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−2i2i2i−2i00−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ472-2-22200-22-22−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ52i−2i−2i2i00−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ482-2-22200-22-22−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−2i2i2i−2i00−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ492-2-22200-22-2−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ72i−2i−2i2i002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ502-2-22200-22-2−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−2i2i2i−2i002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ512-2-22200-22-2−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ72i−2i−2i2i002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ522-2-22200-22-2−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−2i2i2i−2i002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ534444-244-2-2-2-4-4-4-4000000000000-2-222220000000000000000000000000000000000
χ544444-2-4-4-2-2-200002222−22−222222−22−220000220000−2−222−2−22200000000000000000000000000
χ554444-2-4-4-2-2-20000−22−222222−22−222222000022000022−2−222−2−200000000000000000000000000
χ5644-4-4-200-22222−2222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000000000000000
χ5744-4-4-200-22222−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000000000000000
χ5844-4-4-200-222−2222−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000000000000000
χ5944-4-4-200-222−2222−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000000000000000
χ604-44-4-24-422-244-4-40000000000002-222-2-20000000000000000000000000000000000
χ614-44-4-2-4422-200002i22i2−2i2−2i2−2i2−2i22i22i20000-220000−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ624-44-4-2-4422-20000−2i2−2i22i22i22i22i2−2i2−2i20000-220000i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ634-4-44-2002-2222−22−22222ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ50000002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000000000000000
χ644-4-44-2002-2222−22−2222−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ50000002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000000000000000
χ654-4-44-2002-22−222222−222ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000000000000000
χ664-4-44-2002-22−222222−22−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.