Finite Group Databasebeta

← Group #70535

Character table — Group #70535

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order1222444422344666888888881212121266121224242424242424244444444488888888448812121212242424242488
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
χ51111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
χ61111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1
χ81111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111
χ91111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1i−i11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11−ii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1−ii11-1-1−i−iii-11i−i
χ141111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11i−i-1-111ii−i−i1-1−ii
χ151111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii1-1−ii
χ161111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−i-11i−i
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
χ192222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ202222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2122222222-2-22-2-222222-2-222-2-22222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ2222222222-2-22-2-2222-2-222-2-2222222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2322222222-2-2-1-2-2-1-1-122-2-222-2-2-1-1-1-11111-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2422222222-2-2-1-2-2-1-1-122-2-222-2-2-1-1-1-11111-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2522222222-2-2-1-2-2-1-1-1-2-222-2-222-1-1-1-1111111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ2622222222-2-2-1-2-2-1-1-1-2-222-2-222-1-1-1-1111111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ272222-2-2-2-2222-2-22222i2i−2i−2i−2i−2i2i2i-2-2-2-222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ282222-2-2-2-2222-2-2222−2i−2i2i2i2i2i−2i−2i-2-2-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ292222-2-2-2-222-1-2-2-1-1-12i2i−2i−2i−2i−2i2i2i1111-1-111−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−330000
χ302222-2-2-2-222-1-2-2-1-1-12i2i−2i−2i−2i−2i2i2i1111-1-111−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−30000
χ312222-2-2-2-222-1-2-2-1-1-1−2i−2i2i2i2i2i−2i−2i1111-1-111ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−30000
χ322222-2-2-2-222-1-2-2-1-1-1−2i−2i2i2i2i2i−2i−2i1111-1-111ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−330000
χ332222-2-2-2-2-2-2-122-1-1-12i2i2i2i−2i−2i−2i−2i111111-1-1−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii0000
χ342222-2-2-2-2-2-2-122-1-1-12i2i2i2i−2i−2i−2i−2i111111-1-1−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ352222-2-2-2-2-2-2-122-1-1-1−2i−2i−2i−2i2i2i2i2i111111-1-1iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ362222-2-2-2-2-2-2-122-1-1-1−2i−2i−2i−2i2i2i2i2i111111-1-1iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ3722-2-22i−2i2i−2i002002-2-200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232i−2i2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ231+i1+i−1−i−1−i1−i1−i−1+i−1+i−i2−i2i2i222−2−20000000000000000
χ3822-2-22i−2i2i−2i002002-2-200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232i−2i2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−1−i−1−i1+i1+i−1+i−1+i1−i1−ii2i2−i2−i2−2−2220000000000000000
χ3922-2-22i−2i2i−2i002002-2-2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232i−2i2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ231+i1+i−1−i−1−i1−i1−i−1+i−1+ii2i2−i2−i2−2−2220000000000000000
χ4022-2-22i−2i2i−2i002002-2-2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232i−2i2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−1−i−1−i1+i1+i−1+i−1+i1−i1−i−i2−i2i2i222−2−20000000000000000
χ4122-2-2−2i2i−2i2i002002-2-2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2i2i−2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ131−i1−i−1+i−1+i1+i1+i−1−i−1−ii2i2−i2−i222−2−20000000000000000
χ4222-2-2−2i2i−2i2i002002-2-2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2i2i−2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−1+i−1+i1−i1−i−1−i−1−i1+i1+i−i2−i2i2i2−2−2220000000000000000
χ4322-2-2−2i2i−2i2i002002-2-200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2i2i−2i2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ131−i1−i−1+i−1+i1+i1+i−1−i−1−i−i2−i2i2i2−2−2220000000000000000
χ4422-2-2−2i2i−2i2i002002-2-200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2i2i−2i2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−1+i−1+i1−i1−i−1−i−1−i1+i1+ii2i2−i2−i222−2−20000000000000000
χ452-22-22i−2i−2i2i00200-22-22ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−2i2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13001+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2−i2i2−i2i20000000000000000
χ462-22-22i−2i−2i2i00200-22-22ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−2i2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22i2−i2i2−i20000000000000000
χ472-22-22i−2i−2i2i00200-22-2−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−2i2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13001+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−22i2−i2i2−i20000000000000000
χ482-22-22i−2i−2i2i00200-22-2−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−2i2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−22−2−i2i2−i2i20000000000000000
χ492-22-2−2i2i2i−2i00200-22-2−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002i−2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23001−i−1+i1−i−1+i1+i−1−i1+i−1−i2−22−2i2−i2i2−i20000000000000000
χ502-22-2−2i2i2i−2i00200-22-2−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002i−2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22−22−i2i2−i2i20000000000000000
χ512-22-2−2i2i2i−2i00200-22-22ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23002i−2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23001−i−1+i1−i−1+i1+i−1−i1+i−1−i−22−22−i2i2−i2i20000000000000000
χ522-22-2−2i2i2i−2i00200-22-22ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23002i−2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−22−2i2−i2i2−i20000000000000000
χ532-2-2222-2-22-222-2-2-2200000000-2-2222-22-200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ542-2-2222-2-22-222-2-2-2200000000-2-2222-22-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ552-2-2222-2-2-222-22-2-2200000000-2-222-22-22000000002-2-222-2-22000000000000000000000000
χ562-2-2222-2-2-222-22-2-2200000000-2-222-22-2200000000-222-2-222-2000000000000000000000000
χ572-2-22-2-2222-22-22-2-220000000022-2-22-2-22000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ582-2-22-2-2222-22-22-2-220000000022-2-22-2-2200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ592-2-22-2-222-2222-2-2-220000000022-2-2-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ602-2-22-2-222-2222-2-2-220000000022-2-2-222-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ6144-4-44i−4i4i−4i00-200-22200−4ζ5−4ζ134ζ5+4ζ13004ζ7+4ζ23−4ζ7−4ζ23−2i2i−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ6244-4-44i−4i4i−4i00-200-222004ζ5+4ζ13−4ζ5−4ζ1300−4ζ7−4ζ234ζ7+4ζ23−2i2i−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ6344-4-4−4i4i−4i4i00-200-222004ζ7+4ζ23−4ζ7−4ζ2300−4ζ5−4ζ134ζ5+4ζ132i−2i2i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ6444-4-4−4i4i−4i4i00-200-22200−4ζ7−4ζ234ζ7+4ζ23004ζ5+4ζ13−4ζ5−4ζ132i−2i2i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ654-44-44i−4i−4i4i00-2002-224ζ7+4ζ23−4ζ7−4ζ2300−4ζ5−4ζ134ζ5+4ζ13002i−2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000
χ664-44-44i−4i−4i4i00-2002-22−4ζ7−4ζ234ζ7+4ζ23004ζ5+4ζ13−4ζ5−4ζ13002i−2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000
χ674-44-4−4i4i4i−4i00-2002-22−4ζ5−4ζ134ζ5+4ζ13004ζ7+4ζ23−4ζ7−4ζ2300−2i2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000
χ684-44-4−4i4i4i−4i00-2002-224ζ5+4ζ13−4ζ5−4ζ1300−4ζ7−4ζ234ζ7+4ζ2300−2i2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000
χ694-4-4444-4-44-4-24-422-20000000022-2-2-22-220000000000000000000000000000000000000000
χ704-4-4444-4-4-44-2-4422-20000000022-2-22-22-20000000000000000000000000000000000000000
χ714-4-44-4-4444-4-2-4422-200000000-2-222-222-20000000000000000000000000000000000000000
χ724-4-44-4-444-44-24-422-200000000-2-2222-2-220000000000000000000000000000000000000000

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