Finite Group Databasebeta

← Group #68774

Character table — Group #68774

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222222224444444444444444444466668888888888121212121212121212122424
order1222444422344666121212124444668888121212121212121212128888441212121224242424224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ411111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ91111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1ii−i−i11iiii−i−i−i−iii−i−i1-111-1-1ii−i−i11-1-1i−i11-1-1i−i
χ101111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1ii−i−i11iiii−i−i−i−i−i−iii1-111-1-1ii−i−i-1-111−ii-1-111−ii
χ111111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1−i−iii11iiii−i−i−i−iii−i−i-11-1-111−i−iii-1-111i−i11-1-1−ii
χ121111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1−i−iii11iiii−i−i−i−i−i−iii-11-1-111−i−iii11-1-1−ii-1-111i−i
χ131111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1ii−i−i11−i−i−i−iiiiiii−i−i-11-1-111ii−i−i11-1-1i−i-1-111−ii
χ141111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1ii−i−i11−i−i−i−iiiii−i−iii-11-1-111ii−i−i-1-111−ii11-1-1i−i
χ151111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1−i−iii11−i−i−i−iiiiiii−i−i1-111-1-1−i−iii-1-111i−i-1-111i−i
χ161111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1−i−iii11−i−i−i−iiiii−i−iii1-111-1-1−i−iii11-1-1−ii11-1-1−ii
χ172222222222-122-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ182222222222-122-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ192222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1111111110000-2-21111-1-1-1-1000000000000
χ202222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-111111111000022-1-1-1-11111000000000000
χ2122222222-2-22-2-222222220000-2-20000-2-200000000222200000000000000-2-2000000
χ2222222222-2-22-2-222222220000-2-20000-2-200000000-2-2-2-20000000000000022000000
χ232222-2-2-2-2222-2-2222-2-2-2-20000220000-2-2000000002i2i−2i−2i00000000000000−2i2i000000
χ242222-2-2-2-2222-2-2222-2-2-2-20000220000-2-200000000−2i−2i2i2i000000000000002i−2i000000
χ252222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i112i2i−2i−2i-1-1−i−i−i−iiiii00002-2-1-111−i−iii000000000000
χ262222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i11−2i−2i2i2i-1-1−i−i−i−iiiii0000-2211-1-1ii−i−i000000000000
χ272222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i112i2i−2i−2i-1-1iiii−i−i−i−i0000-2211-1-1−i−iii000000000000
χ282222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i11−2i−2i2i2i-1-1iiii−i−i−i−i00002-2-1-111ii−i−i000000000000
χ2922-2-22i−2i2i−2i002002-2-22i−2i2i−2i1+i−1−i1−i−1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002−2−i2i200
χ3022-2-22i−2i2i−2i002002-2-22i−2i2i−2i1+i−1−i1−i−1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−22i2−i200
χ3122-2-22i−2i2i−2i002002-2-22i−2i2i−2i−1−i1+i−1+i1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−22i2−i200
χ3222-2-22i−2i2i−2i002002-2-22i−2i2i−2i−1−i1+i−1+i1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000002−2−i2i200
χ3322-2-2−2i2i−2i2i002002-2-2−2i2i−2i2i1−i−1+i1+i−1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000002−2i2−i200
χ3422-2-2−2i2i−2i2i002002-2-2−2i2i−2i2i1−i−1+i1+i−1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−22−i2i200
χ3522-2-2−2i2i−2i2i002002-2-2−2i2i−2i2i−1+i1−i−1−i1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−22−i2i200
χ3622-2-2−2i2i−2i2i002002-2-2−2i2i−2i2i−1+i1−i−1−i1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002−2i2−i200
χ372-2-2222-2-22-222-2-22-222-2-200002-200002-200000000000000000000002-22-200000000
χ382-2-2222-2-22-222-2-22-222-2-200002-200002-20000000000000000000000-22-2200000000
χ392-2-2222-2-2-222-22-22-222-2-20000-222i−2i2i−2i-220000000000000000002i−2i2i−2i000000000000
χ402-2-2222-2-2-222-22-22-222-2-20000-22−2i2i−2i2i-22000000000000000000−2i2i−2i2i000000000000
χ412-2-2222-2-2-22-1-221-11-1-11100001-12i−2i2i−2i1-1−i3i3−i3i3−i3i3−i3i30000003−33−3−ii−ii000000000000
χ422-2-2222-2-2-22-1-221-11-1-11100001-12i−2i2i−2i1-1i3−i3i3−i3i3−i3i3−i3000000−33−33−ii−ii000000000000
χ432-2-2222-2-2-22-1-221-11-1-11100001-1−2i2i−2i2i1-1−i3i3−i3i3−i3i3−i3i3000000−33−33i−ii−i000000000000
χ442-2-2222-2-2-22-1-221-11-1-11100001-1−2i2i−2i2i1-1i3−i3i3−i3i3−i3i3−i30000003−33−3i−ii−i000000000000
χ452-2-22-2-2222-22-22-22-2-2-22200002-22-2-22-220000000000000000002-2-22000000000000
χ462-2-22-2-2222-22-22-22-2-2-22200002-2-222-2-22000000000000000000-222-2000000000000
χ472-2-22-2-2222-2-1-221-1111-1-10000-112-2-221-13−33−3−33−33000000−333−3-111-1000000000000
χ482-2-22-2-2222-2-1-221-1111-1-10000-112-2-221-1−33−333−33−30000003−3−33-111-1000000000000
χ492-2-22-2-2222-2-1-221-1111-1-10000-11-222-21-13−33−3−33−330000003−3−331-1-11000000000000
χ502-2-22-2-2222-2-1-221-1111-1-10000-11-222-21-1−33−333−33−3000000−333−31-1-11000000000000
χ512-2-22-2-222-2222-2-22-2-2-2220000-2200002-200000000000000000000002-2-2200000000
χ522-2-22-2-222-2222-2-22-2-2-2220000-2200002-20000000000000000000000-222-200000000
χ5344444444-4-4-2-4-4-2-2-2-2-2-2-20000220000220000000000000000000000000000000000
χ544444-4-4-4-444-2-4-4-2-2-222220000-2-20000220000000000000000000000000000000000
χ5544-4-44i−4i4i−4i00-200-222−2i2i−2i2i2+2i−2−2i2−2i−2+2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000
χ5644-4-44i−4i4i−4i00-200-222−2i2i−2i2i−2−2i2+2i−2+2i2−2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000
χ5744-4-4−4i4i−4i4i00-200-2222i−2i2i−2i2−2i−2+2i2+2i−2−2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000
χ5844-4-4−4i4i−4i4i00-200-2222i−2i2i−2i−2+2i2−2i−2−2i2+2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000000000
χ594-44-44i−4i−4i4i00400-4-444i−4i−4i4i0000000000000000000000000000000000000000000000
χ604-44-44i−4i−4i4i00-20022-2−2i2i2i−2i000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000
χ614-44-44i−4i−4i4i00-20022-2−2i2i2i−2i000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000
χ624-44-4−4i4i4i−4i00400-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-4−4i4i4i−4i00-20022-22i−2i−2i2i000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000
χ644-44-4−4i4i4i−4i00-20022-22i−2i−2i2i000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000
χ654-4-4444-4-44-4-24-42-22-2-2220000-220000-220000000000000000000000000000000000
χ664-4-44-4-444-44-24-42-2222-2-200002-20000-220000000000000000000000000000000000

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