Finite Group Databasebeta

← Group #72084

Character table — Group #72084

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order122244442234466688888888121212126612122424242424242424444444448888888822446666121212128888
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
χ51111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-11111-1-1
χ91111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1i−ii−i
χ101111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111−ii−ii
χ111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1−ii−ii
χ121111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111i−ii−i
χ131111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ172222222222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ182222222222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ192222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ202222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ2122222222-2-22-2-2222000000002222-2-2-2-2000000000000000022-2-222-2-20000000000000000
χ2222222222-2-22-2-2222000000002222-2-2-2-20000000000000000-2-222-2-2220000000000000000
χ232222-2-2-2-2222-2-222200000000-2-2-2-222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ242222-2-2-2-2222-2-222200000000-2-2-2-222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ252222-2-2-2-2-2-2-122-1-1-12222-2-2-2-2111111-1-1-1-1-1-11111000000000000000022-2-2-1-1-1-111110000
χ262222-2-2-2-2-2-2-122-1-1-12222-2-2-2-2111111-1-1-1-1-1-111110000000000000000-2-2221111-1-1-1-10000
χ272222-2-2-2-2-2-2-122-1-1-1-2-2-2-22222111111-1-11111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ282222-2-2-2-2-2-2-122-1-1-1-2-2-2-22222111111-1-11111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ2922-2-22i−2i2i−2i002002-2-222−2−2−i2−i2i2i22i2i−2i−2i000022−2−2−i2−i2i2i21+i1+i−1−i−1−i1−i1−i−1+i−1+i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ3022-2-22i−2i2i−2i002002-2-222−2−2−i2−i2i2i22i2i−2i−2i000022−2−2−i2−i2i2i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ3122-2-22i−2i2i−2i002002-2-2−2−222i2i2−i2−i22i2i−2i−2i0000−2−222i2i2−i2−i21+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ3222-2-22i−2i2i−2i002002-2-2−2−222i2i2−i2−i22i2i−2i−2i0000−2−222i2i2−i2−i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ3322-2-2−2i2i−2i2i002002-2-222−2−2i2i2−i2−i2−2i−2i2i2i000022−2−2i2i2−i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ3422-2-2−2i2i−2i2i002002-2-222−2−2i2i2−i2−i2−2i−2i2i2i000022−2−2i2i2−i2−i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ3522-2-2−2i2i−2i2i002002-2-2−2−222−i2−i2i2i2−2i−2i2i2i0000−2−222−i2−i2i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ3622-2-2−2i2i−2i2i002002-2-2−2−222−i2−i2i2i2−2i−2i2i2i0000−2−222−i2−i2i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ372-22-22i−2i−2i2i00200-22-22−22−2−i2i2−i2i22i−2i2i−2i00002−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ382-22-22i−2i−2i2i00200-22-22−22−2−i2i2−i2i22i−2i2i−2i00002−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ392-22-22i−2i−2i2i00200-22-2−22−22i2−i2i2−i22i−2i2i−2i0000−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ402-22-22i−2i−2i2i00200-22-2−22−22i2−i2i2−i22i−2i2i−2i0000−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ412-22-2−2i2i2i−2i00200-22-22−22−2i2−i2i2−i2−2i2i−2i2i00002−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ422-22-2−2i2i2i−2i00200-22-22−22−2i2−i2i2−i2−2i2i−2i2i00002−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ432-22-2−2i2i2i−2i00200-22-2−22−22−i2i2−i2i2−2i2i−2i2i0000−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ442-22-2−2i2i2i−2i00200-22-2−22−22−i2i2−i2i2−2i2i−2i2i0000−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ452-2-2222-2-22-222-2-2-22000000002-2-222-22-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ462-2-2222-2-22-222-2-2-22000000002-2-222-22-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ472-2-2222-2-2-222-22-2-222-2-222-2-222-2-22-22-222-2-222-2-2200000000000000000000000000000000
χ482-2-2222-2-2-222-22-2-22-222-2-222-22-2-22-22-22-222-2-222-200000000000000000000000000000000
χ492-2-2222-2-2-22-1-2211-12-2-222-2-22-111-11-11-1-111-1-111-100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ502-2-2222-2-2-22-1-2211-12-2-222-2-22-111-11-11-1-111-1-111-100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ512-2-2222-2-2-22-1-2211-1-222-2-222-2-111-11-11-11-1-111-1-1100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ522-2-2222-2-2-22-1-2211-1-222-2-222-2-111-11-11-11-1-111-1-1100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ532-2-22-2-2222-22-22-2-222-2-22-222-2-222-22-2-222-2-22-222-200000000000000000000000000000000
χ542-2-22-2-2222-22-22-2-22-222-22-2-22-222-22-2-22-222-22-2-2200000000000000000000000000000000
χ552-2-22-2-2222-2-1-2211-12-2-22-222-21-1-11-111-1-111-11-1-1100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ562-2-22-2-2222-2-1-2211-12-2-22-222-21-1-11-111-1-111-11-1-1100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ572-2-22-2-2222-2-1-2211-1-222-22-2-221-1-11-111-11-1-11-111-100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ582-2-22-2-2222-2-1-2211-1-222-22-2-221-1-11-111-11-1-11-111-100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ592-2-22-2-222-2222-2-2-2200000000-222-2-222-2000000002-2-222-2-22000000000000000000000000
χ602-2-22-2-222-2222-2-2-2200000000-222-2-222-200000000-222-2-222-2000000000000000000000000
χ6144444444-4-4-2-4-4-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000
χ624444-4-4-4-444-2-4-4-2-2-2000000002222-2-2220000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i00-200-2222222−22−22−2i2−2i22i22i2−2i−2i2i2i0000−2−222i2i2−i2−i200000000000000000000000000000000
χ6444-4-44i−4i4i−4i00-200-222−22−2222222i22i2−2i2−2i2−2i−2i2i2i000022−2−2−i2−i2i2i200000000000000000000000000000000
χ6544-4-4−4i4i−4i4i00-200-2222222−22−222i22i2−2i2−2i22i2i−2i−2i0000−2−222−i2−i2i2i200000000000000000000000000000000
χ6644-4-4−4i4i−4i4i00-200-222−22−222222−2i2−2i22i22i22i2i−2i−2i000022−2−2i2i2−i2−i200000000000000000000000000000000
χ674-44-44i−4i−4i4i00-2002-2222−2222−22−2i22i2−2i22i2−2i2i−2i2i0000−22−22i2−i2i2−i200000000000000000000000000000000
χ684-44-44i−4i−4i4i00-2002-22−2222−22222i2−2i22i2−2i2−2i2i−2i2i00002−22−2−i2i2−i2i200000000000000000000000000000000
χ694-44-4−4i4i4i−4i00-2002-2222−2222−222i2−2i22i2−2i22i−2i2i−2i0000−22−22−i2i2−i2i200000000000000000000000000000000
χ704-44-4−4i4i4i−4i00-2002-22−2222−2222−2i22i2−2i22i22i−2i2i−2i00002−22−2i2−i2i2−i200000000000000000000000000000000
χ714-4-4444-4-44-4-24-422-200000000-222-2-22-220000000000000000000000000000000000000000
χ724-4-44-4-444-44-24-422-2000000002-2-222-2-220000000000000000000000000000000000000000

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