Finite Group Databasebeta

← Group #68238

Character table — Group #68238

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222222224444444444444444444466668888888888121212121212121212122424
order122244443444466612121212444488881212121224242424242424244444881212121224242424222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1111111-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i11-1-1i−i11-1-1ii−i−i111-1-1-1ii−i−ii−i
χ101111-1-1-1-1111-1-1111-1-1-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-1-111i−i11-1-1ii−i−i-1-1-1111−i−iii−ii
χ111111-1-1-1-1111-1-1111-1-1-1-111-1-1−i−iii11-1-1−i−i−i−iiiii11-1-1−ii11-1-1−i−iii111-1-1-1−i−iii−ii
χ121111-1-1-1-1111-1-1111-1-1-1-111-1-1−i−iii11-1-1−i−i−i−iiiii-1-111−ii11-1-1−i−iii-1-1-1111ii−i−ii−i
χ131111-1-1-1-1111-1-1111-1-1-1-1-1-111ii−i−i11-1-1iiii−i−i−i−i11-1-1−ii-1-111−i−iii1-1-1-111ii−i−i−ii
χ141111-1-1-1-1111-1-1111-1-1-1-1-1-111ii−i−i11-1-1iiii−i−i−i−i-1-111−ii-1-111−i−iii-1111-1-1−i−iiii−i
χ151111-1-1-1-1111-1-1111-1-1-1-1-1-111−i−iii11-1-1−i−i−i−iiiii11-1-1i−i-1-111ii−i−i1-1-1-111−i−iiii−i
χ161111-1-1-1-1111-1-1111-1-1-1-1-1-111−i−iii11-1-1−i−i−i−iiiii-1-111i−i-1-111ii−i−i-1111-1-1ii−i−i−ii
χ17222222222-2-2-2-2222222200000000-2-2-2-20000000022220000000000-200-200000000
χ18222222222-2-2-2-2222222200000000-2-2-2-200000000-2-2-2-20000000000200200000000
χ1922222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111110000-2-2-1-1-1-11111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000221111-1-1-1-1000000000000
χ232222-2-2-2-22-2-222222-2-2-2-200000000-2-2220000000022-2-20000000000-200200000000
χ242222-2-2-2-22-2-222222-2-2-2-200000000-2-22200000000-2-2220000000000200-200000000
χ252222-2-2-2-2-122-2-2-1-1-1111122-2-22i2i−2i−2i-1-111−i−i−i−iiiii00002i−2i-1-111−i−iii000000000000
χ262222-2-2-2-2-122-2-2-1-1-1111122-2-2−2i−2i2i2i-1-111iiii−i−i−i−i0000−2i2i-1-111ii−i−i000000000000
χ272222-2-2-2-2-122-2-2-1-1-11111-2-2222i2i−2i−2i-1-111−i−i−i−iiiii0000−2i2i11-1-1ii−i−i000000000000
χ282222-2-2-2-2-122-2-2-1-1-11111-2-222−2i−2i2i2i-1-111iiii−i−i−i−i00002i−2i11-1-1−i−iii000000000000
χ2922-2-22i−2i2i−2i20000-22-22i−2i2i−2i00001+i−1−i1−i−1+i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2-200000000000000001−i−1+i1+i−1−i00
χ3022-2-22i−2i2i−2i20000-22-22i−2i2i−2i00001+i−1−i1−i−1+i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2i2i-220000000000000000−1+i1−i−1−i1+i00
χ3122-2-22i−2i2i−2i20000-22-22i−2i2i−2i0000−1−i1+i−1+i1−i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2-20000000000000000−1+i1−i−1−i1+i00
χ3222-2-22i−2i2i−2i20000-22-22i−2i2i−2i0000−1−i1+i−1+i1−i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2i2i-2200000000000000001−i−1+i1+i−1−i00
χ3322-2-2−2i2i−2i2i20000-22-2−2i2i−2i2i00001−i−1+i1+i−1−i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i2i−2i-220000000000000000−1−i1+i−1+i1−i00
χ3422-2-2−2i2i−2i2i20000-22-2−2i2i−2i2i00001−i−1+i1+i−1−i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i2-200000000000000001+i−1−i1−i−1+i00
χ3522-2-2−2i2i−2i2i20000-22-2−2i2i−2i2i0000−1+i1−i−1−i1+i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2i−2i-2200000000000000001+i−1−i1−i−1+i00
χ3622-2-2−2i2i−2i2i20000-22-2−2i2i−2i2i0000−1+i1−i−1−i1+i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i2-20000000000000000−1−i1+i−1+i1−i00
χ372-22-22i−2i−2i2i22-22i−2i-2-222i−2i−2i2i000000002-22i−2i000000000000000000000002-202i−2i000000
χ382-22-22i−2i−2i2i22-22i−2i-2-222i−2i−2i2i000000002-22i−2i00000000000000000000000-220−2i2i000000
χ392-22-22i−2i−2i2i2-22−2i2i-2-222i−2i−2i2i2-22i−2i0000-22−2i2i000000000000002-22i−2i0000000000000000
χ402-22-22i−2i−2i2i2-22−2i2i-2-222i−2i−2i2i-22−2i2i0000-22−2i2i00000000000000-22−2i2i0000000000000000
χ412-22-22i−2i−2i2i-1-22−2i2i11-1−iii−i2-22i−2i00001-1i−i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000-11−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ422-22-22i−2i−2i2i-1-22−2i2i11-1−iii−i2-22i−2i00001-1i−iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000-11−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ432-22-22i−2i−2i2i-1-22−2i2i11-1−iii−i-22−2i2i00001-1i−i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000001-1i−iζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ442-22-22i−2i−2i2i-1-22−2i2i11-1−iii−i-22−2i2i00001-1i−iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000001-1i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ452-22-2−2i2i2i−2i22-2−2i2i-2-22−2i2i2i−2i000000002-2−2i2i000000000000000000000002-20−2i2i000000
χ462-22-2−2i2i2i−2i22-2−2i2i-2-22−2i2i2i−2i000000002-2−2i2i00000000000000000000000-2202i−2i000000
χ472-22-2−2i2i2i−2i2-222i−2i-2-22−2i2i2i−2i2-2−2i2i0000-222i−2i000000000000002-2−2i2i0000000000000000
χ482-22-2−2i2i2i−2i2-222i−2i-2-22−2i2i2i−2i-222i−2i0000-222i−2i00000000000000-222i−2i0000000000000000
χ492-22-2−2i2i2i−2i-1-222i−2i11-1i−i−ii2-2−2i2i00001-1−iiζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000-11i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ502-22-2−2i2i2i−2i-1-222i−2i11-1i−i−ii2-2−2i2i00001-1−ii−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000-11i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ512-22-2−2i2i2i−2i-1-222i−2i11-1i−i−ii-222i−2i00001-1−iiζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000001-1−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ522-22-2−2i2i2i−2i-1-222i−2i11-1i−i−ii-222i−2i00001-1−ii−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000001-1−iiζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000
χ544444-4-4-4-4-2-4-444-2-2-222220000000022-2-20000000000000000000000000000000000
χ5544-4-44i−4i4i−4i-200002-22−2i2i−2i2i00002+2i−2−2i2−2i−2+2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000
χ5644-4-44i−4i4i−4i-200002-22−2i2i−2i2i0000−2−2i2+2i−2+2i2−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000
χ5744-4-4−4i4i−4i4i-200002-222i−2i2i−2i00002−2i−2+2i2+2i−2−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000
χ5844-4-4−4i4i−4i4i-200002-222i−2i2i−2i0000−2+2i2−2i−2−2i2+2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000000000
χ594-44-44i−4i−4i4i-24-44i−4i22-2−2i2i2i−2i00000000-22−2i2i0000000000000000000000000000000000
χ604-44-4−4i4i4i−4i-24-4−4i4i22-22i−2i−2i2i00000000-222i−2i0000000000000000000000000000000000
χ614-4-4444-4-4400004-4-444-4-40000000000000000000000000000000000000000000000
χ624-4-4444-4-4-20000-222-2-222000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ634-4-4444-4-4-20000-222-2-222000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ644-4-44-4-444400004-4-4-4-4440000000000000000000000000000000000000000000000
χ654-4-44-4-444-20000-22222-2-20000000000006−6−666−6−6600000000000000000000000000
χ664-4-44-4-444-20000-22222-2-2000000000000−666−6−666−600000000000000000000000000

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