Finite Group Databasebeta

← Group #68176

Character table — Group #68176

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order1222444434444666888888881212121212121212242424242424242422444444888888882466881212242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1
χ91111-1-1-1-1111-1-1111iiii−i−i−i−i-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i-11i−i
χ101111-1-1-1-1111-1-1111iiii−i−i−i−i-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii1-1−ii
χ111111-1-1-1-1111-1-1111iiii−i−i−i−i-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-111i−i-1-1ii−i−i1-1−ii
χ121111-1-1-1-1111-1-1111iiii−i−i−i−i-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1-1−ii11−i−iii-11i−i
χ131111-1-1-1-1111-1-1111−i−i−i−iiiii-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii-11−ii
χ141111-1-1-1-1111-1-1111−i−i−i−iiiii-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i1-1i−i
χ151111-1-1-1-1111-1-1111−i−i−i−iiiii-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-111−ii-1-1−i−iii1-1i−i
χ161111-1-1-1-1111-1-1111−i−i−i−iiiii-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-1-1i−i11ii−i−i-11−ii
χ17222222222-2-2-2-2222000000002222-2-2-2-20000000022-2-2-2-222000000000000000000000000
χ18222222222-2-2-2-2222000000002222-2-2-2-200000000-2-22222-2-2000000000000000000000000
χ1922222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-122-1-1-1-1-1-10000
χ2022222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-211-2-21111110000
χ2122222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000022-1-1-2-2-1-111110000
χ2222222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000-2-2112211-1-1-1-10000
χ232222-2-2-2-22-2-22222200000000-2-2-2-2-2-2220000000022-2-222-2-2000000000000000000000000
χ242222-2-2-2-22-2-22222200000000-2-2-2-2-2-22200000000-2-222-2-222000000000000000000000000
χ252222-2-2-2-2-122-2-2-1-1-12i2i2i2i−2i−2i−2i−2i1111-1-111−i−i−i−iiiii00000000000000002-2-1-12i−2i11−i−iii0000
χ262222-2-2-2-2-122-2-2-1-1-12i2i2i2i−2i−2i−2i−2i1111-1-111−i−i−i−iiiii0000000000000000-2211−2i2i-1-1ii−i−i0000
χ272222-2-2-2-2-122-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i1111-1-111iiii−i−i−i−i00000000000000002-2-1-1−2i2i11ii−i−i0000
χ282222-2-2-2-2-122-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i1111-1-111iiii−i−i−i−i0000000000000000-22112i−2i-1-1−i−iii0000
χ2922-2-22i−2i2i−2i200002-2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3022-2-22i−2i2i−2i200002-2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3122-2-22i−2i2i−2i200002-2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3222-2-22i−2i2i−2i200002-2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3322-2-2−2i2i−2i2i200002-2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ3422-2-2−2i2i−2i2i200002-2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ3522-2-2−2i2i−2i2i200002-2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ3622-2-2−2i2i−2i2i200002-2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ372-22-22i−2i−2i2i22-22i−2i-22-2000000002i−2i−2i2i2-22i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ382-22-22i−2i−2i2i22-22i−2i-22-2000000002i−2i−2i2i2-22i−2i0000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ392-22-22i−2i−2i2i2-22−2i2i-22-2−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232i−2i−2i2i-22−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ402-22-22i−2i−2i2i2-22−2i2i-22-22ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232i−2i−2i2i-22−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ412-22-22i−2i−2i2i-1-22−2i2i1-11−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−iii−i1-1i−iζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23000000000000000000−i3i3003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ422-22-22i−2i−2i2i-1-22−2i2i1-11−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−iii−i1-1i−iζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23000000000000000000i3−i300−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ432-22-22i−2i−2i2i-1-22−2i2i1-112ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−iii−i1-1i−i−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23000000000000000000−i3i3003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ442-22-22i−2i−2i2i-1-22−2i2i1-112ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−iii−i1-1i−i−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23000000000000000000i3−i300−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ452-22-2−2i2i2i−2i22-2−2i2i-22-200000000−2i2i2i−2i2-2−2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ462-22-2−2i2i2i−2i22-2−2i2i-22-200000000−2i2i2i−2i2-2−2i2i00000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ472-22-2−2i2i2i−2i2-222i−2i-22-22ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2i2i2i−2i-222i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ482-22-2−2i2i2i−2i2-222i−2i-22-2−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2i2i2i−2i-222i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ492-22-2−2i2i2i−2i-1-222i−2i1-112ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13i−i−ii1-1−ii−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13000000000000000000−i3i300−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ502-22-2−2i2i2i−2i-1-222i−2i1-112ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13i−i−ii1-1−ii−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13000000000000000000i3−i3003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ512-22-2−2i2i2i−2i-1-222i−2i1-11−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13i−i−ii1-1−iiζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13000000000000000000−i3i300−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ522-22-2−2i2i2i−2i-1-222i−2i1-11−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13i−i−ii1-1−iiζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13000000000000000000i3−i3003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ532-2-2222-2-220000-2-22−i2i2i2−i2i2−i2−i2i222-2-20000−i2i2i2−i2i2−i2−i2i22-200002-2−i2i2i2−i2i2−i2−i2i20000000000000000
χ542-2-2222-2-220000-2-22−i2i2i2−i2i2−i2−i2i222-2-20000−i2i2i2−i2i2−i2−i2i2-220000-22i2−i2−i2i2−i2i2i2−i20000000000000000
χ552-2-2222-2-220000-2-22i2−i2−i2i2−i2i2i2−i222-2-20000i2−i2−i2i2−i2i2i2−i22-200002-2i2−i2−i2i2−i2i2i2−i20000000000000000
χ562-2-2222-2-220000-2-22i2−i2−i2i2−i2i2i2−i222-2-20000i2−i2−i2i2−i2i2i2−i2-220000-22−i2i2i2−i2i2−i2−i2i20000000000000000
χ572-2-22-2-22220000-2-222−2−222−2−22-2-22200002−2−222−2−222-20000-222−2−222−2−220000000000000000
χ582-2-22-2-22220000-2-222−2−222−2−22-2-22200002−2−222−2−22-2200002-2−222−2−222−20000000000000000
χ592-2-22-2-22220000-2-22−222−2−222−2-2-2220000−222−2−222−22-20000-22−222−2−222−20000000000000000
χ602-2-22-2-22220000-2-22−222−2−222−2-2-2220000−222−2−222−2-2200002-22−2−222−2−220000000000000000
χ6144444444-2-4-4-4-4-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000
χ624444-4-4-4-4-2-4-444-2-2-200000000222222-2-20000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i-20000-2222+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i−2i2i−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000000000
χ6444-4-44i−4i4i−4i-20000-222−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i−2i2i−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000000000
χ6544-4-4−4i4i−4i4i-20000-2222−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i2i−2i2i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000000000
χ6644-4-4−4i4i−4i4i-20000-222−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i2i−2i2i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000000000000000
χ674-44-44i−4i−4i4i-24-44i−4i2-2200000000−2i2i2i−2i-22−2i2i0000000000000000000000000000000000000000
χ684-44-4−4i4i4i−4i-24-4−4i4i2-22000000002i−2i−2i2i-222i−2i0000000000000000000000000000000000000000
χ694-4-4444-4-4-2000022-2−2i22i22i2−2i22i2−2i2−2i22i2-2-2220000i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000
χ704-4-4444-4-4-2000022-22i2−2i2−2i22i2−2i22i22i2−2i2-2-2220000−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000
χ714-4-44-4-444-2000022-222−22−222222−22−222222-2-20000−222−2−222−200000000000000000000000000000000
χ724-4-44-4-444-2000022-2−222222−22−222222−2222-2-200002−2−222−2−2200000000000000000000000000000000

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