Finite Group Databasebeta

← Group #71802

Character table — Group #71802

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order122244442234444444444666121212126612121212121212121212888888888888888822446666121212128888
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
χ511111111-1-1111-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ611111111-1-1111-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ711111111-1-1111-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-111
χ811111111-1-1111-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-11111-1-1
χ91111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1111-1-1-1-111i−ii−i
χ101111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-1-11111-1-1−ii−ii
χ111111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1111-1-1-1-111−ii−ii
χ121111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-1-11111-1-1i−ii−i
χ131111-1-1-1-1-1-1111-1-11111-1-1111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-11111-1-1-1-1i−i−ii
χ141111-1-1-1-1-1-1111-1-11111-1-1111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-11111−iii−i
χ151111-1-1-1-1-1-1111-1-11111-1-1111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-11111-1-1-1-1−iii−i
χ161111-1-1-1-1-1-1111-1-11111-1-1111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-11111i−i−ii
χ1722222222222-2-2-2-2-2-222-2-2222222222-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ182222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ192222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ202222222222-1-2-2-2-2-2-222-2-2-1-1-1-1-1-1-1-1-111111111-1-100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ212222222222-1-2-2-2-2-2-222-2-2-1-1-1-1-1-1-1-1-111111111-1-100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2222222222-2-22-2-22222-2-2-2-22222222-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ2322222222-2-2-122-2-2-2-2-2-222-1-1-1-1-1-1-111-1-1-1-111111100000000000000002-22-2-1-111-1-1110000
χ2422222222-2-2-122-2-2-2-2-2-222-1-1-1-1-1-1-111-1-1-1-11111110000000000000000-22-2211-1-111-1-10000
χ2522222222-2-2-1-2-22222-2-2-2-2-1-1-1-1-1-1-1111111-1-1-1-11100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ2622222222-2-2-1-2-22222-2-2-2-2-1-1-1-1-1-1-1111111-1-1-1-11100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ272222-2-2-2-2222-2-2-2-222-2-222222-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000
χ282222-2-2-2-222-12222-2-2-2-2-2-2-1-1-11111-1-1-1-111-1-1111100000000000000002-2-22-1-11111-1-10000
χ292222-2-2-2-222-12222-2-2-2-2-2-2-1-1-11111-1-1-1-111-1-111110000000000000000-222-211-1-1-1-1110000
χ302222-2-2-2-222-1-2-2-2-222-2-222-1-1-11111-1-111-1-111-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ312222-2-2-2-222-1-2-2-2-222-2-222-1-1-11111-1-111-1-111-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ322222-2-2-2-2-2-22-2-222-2-22222222-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000000000
χ332222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-11111-1-1-1-1000000000000000022-2-2-1-1-1-111110000
χ342222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-11111-1-1-1-10000000000000000-2-2221111-1-1-1-10000
χ352222-2-2-2-2-2-2-1-2-222-2-22222-1-1-111111111-1-1-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ362222-2-2-2-2-2-2-1-2-222-2-22222-1-1-111111111-1-1-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ3722-2-22i−2i2i−2i002002i−2i2-200002-2-22i2i−2i−2i0000002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3822-2-22i−2i2i−2i002002i−2i2-200002-2-22i2i−2i−2i0000002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3922-2-22i−2i2i−2i00200−2i2i-2200002-2-22i2i−2i−2i000000−2i2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ4022-2-22i−2i2i−2i00200−2i2i-2200002-2-22i2i−2i−2i000000−2i2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ4122-2-2−2i2i−2i2i002002i−2i-2200002-2-2−2i−2i2i2i0000002i−2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ4222-2-2−2i2i−2i2i002002i−2i-2200002-2-2−2i−2i2i2i0000002i−2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ4322-2-2−2i2i−2i2i00200−2i2i2-200002-2-2−2i−2i2i2i000000−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ4422-2-2−2i2i−2i2i00200−2i2i2-200002-2-2−2i−2i2i2i000000−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ452-22-22i−2i−2i2i0022-20000002i−2i-22-22i−2i2i−2i002-22i−2i000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ462-22-22i−2i−2i2i0022-20000002i−2i-22-22i−2i2i−2i002-22i−2i00000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ472-22-22i−2i−2i2i002-22000000−2i2i-22-22i−2i2i−2i00-22−2i2i000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ482-22-22i−2i−2i2i002-22000000−2i2i-22-22i−2i2i−2i00-22−2i2i0000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ492-22-2−2i2i2i−2i0022-2000000−2i2i-22-2−2i2i−2i2i002-2−2i2i00000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ502-22-2−2i2i2i−2i0022-2000000−2i2i-22-2−2i2i−2i2i002-2−2i2i000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ512-22-2−2i2i2i−2i002-220000002i−2i-22-2−2i2i−2i2i00-222i−2i0000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ522-22-2−2i2i2i−2i002-220000002i−2i-22-2−2i2i−2i2i00-222i−2i000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ532-2-2222-2-22-220000002-200-2-222-2-222-2000000002-2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ542-2-2222-2-22-220000002-200-2-222-2-222-2000000002-2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ552-2-2222-2-2-222000000-2200-2-222-2-22-2200000000-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ562-2-2222-2-2-222000000-2200-2-222-2-22-2200000000-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ572-2-22-2-2222-22000000-2200-2-22-222-22-200000000-222−2−222−2−222−2−222−2−220000000000000000
χ582-2-22-2-2222-22000000-2200-2-22-222-22-200000000-22−222−2−222−2−222−2−222−20000000000000000
χ592-2-22-2-222-2220000002-200-2-22-222-2-22000000002-22−2−222−2−22−222−2−222−20000000000000000
χ602-2-22-2-222-2220000002-200-2-22-222-2-22000000002-2−222−2−222−22−2−222−2−220000000000000000
χ6144-4-44i−4i4i−4i00-2004i−4i4-40000-222−2i−2i2i2i000000−2i2i-220000000000000000000000000000000000
χ6244-4-44i−4i4i−4i00-200−4i4i-440000-222−2i−2i2i2i0000002i−2i2-20000000000000000000000000000000000
χ6344-4-4−4i4i−4i4i00-2004i−4i-440000-2222i2i−2i−2i000000−2i2i2-20000000000000000000000000000000000
χ6444-4-4−4i4i−4i4i00-200−4i4i4-40000-2222i2i−2i−2i0000002i−2i-220000000000000000000000000000000000
χ654-44-44i−4i−4i4i00-24-40000004i−4i2-22−2i2i−2i2i00-22−2i2i00000000000000000000000000000000000000
χ664-44-44i−4i−4i4i00-2-44000000−4i4i2-22−2i2i−2i2i002-22i−2i00000000000000000000000000000000000000
χ674-44-4−4i4i4i−4i00-24-4000000−4i4i2-222i−2i2i−2i00-222i−2i00000000000000000000000000000000000000
χ684-44-4−4i4i4i−4i00-2-440000004i−4i2-222i−2i2i−2i002-2−2i2i00000000000000000000000000000000000000
χ694-4-4444-4-44-4-20000004-40022-2-222-2-2200000000-2200000000000000000000000000000000
χ704-4-4444-4-4-44-2000000-440022-2-222-22-2000000002-200000000000000000000000000000000
χ714-4-44-4-4444-4-2000000-440022-22-2-22-22000000002-200000000000000000000000000000000
χ724-4-44-4-444-44-20000004-40022-22-2-222-200000000-2200000000000000000000000000000000

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