Finite Group Databasebeta

← Group #67751

Character table — Group #67751

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order1222444422344444466612121212446612121212121212121212888824242424242424248888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-1-11-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111-1-11-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111-1-11-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111-1-11-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-1111-1-111-1-1111-1-1-1-11-11111-1-111-1-1-1-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-111-1-1111-1-1-1-11-11111-1-111-1-1-1-1i−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-1111-1-111-1-1111-1-1-1-11-11111-1-111-1-1-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-111-1-1111-1-1-1-11-11111-1-111-1-1-1-1−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222222-2-2-2-2222222222-2-222-2-2-2-2-2-222-2-20000000000000000000000000000
χ182222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ202222222222-1-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1111111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ212222222222-1-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1111111-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2222222222-2-222222-2-22222222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-12222-2-2-1-1-1-1-1-1-1-2-2111111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2422222222-2-2-12222-2-2-1-1-1-1-1-1-1-2-2111111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2522222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211-1-1-1-111111122-2-2-1-1-1-111110000000000000000
χ2622222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211-1-1-1-1111111-2-2221111-1-1-1-10000000000000000
χ272222-2-2-2-222222-2-2-2-2222-2-2-2-2-2222-2-222-2-2-2-2220000000000000000000000000000
χ282222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-111-1-11111-1-100003−3−333−3−330000000000000000
χ292222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-111-1-11111-1-10000−333−3−333−30000000000000000
χ302222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-1-1-111-1-111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ312222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-1-1-111-1-11111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ322222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-2-2-2222222-2-20000000000000000000000000000
χ332222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-11111-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ342222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-11111-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ352222-2-2-2-2-2-2-1-2-22222-1-1-11111-221111-1-1-1-1-1-11100003−3−33−333−30000000000000000
χ362222-2-2-2-2-2-2-1-2-22222-1-1-11111-221111-1-1-1-1-1-1110000−333−33−3−330000000000000000
χ3722-2-222-2-20022i−2i2i−2i002-2-222-2-2000000002i−2i002i−2i000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ3822-2-222-2-20022i−2i2i−2i002-2-222-2-2000000002i−2i002i−2i00000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ3922-2-222-2-2002−2i2i−2i2i002-2-222-2-200000000−2i2i00−2i2i000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ4022-2-222-2-2002−2i2i−2i2i002-2-222-2-200000000−2i2i00−2i2i00000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ4122-2-2-2-2220022i−2i−2i2i002-2-2-2-22200000000−2i2i002i−2i000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ4222-2-2-2-2220022i−2i−2i2i002-2-2-2-22200000000−2i2i002i−2i00000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ4322-2-2-2-222002−2i2i2i−2i002-2-2-2-222000000002i−2i00−2i2i000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ4422-2-2-2-222002−2i2i2i−2i002-2-2-2-222000000002i−2i00−2i2i00000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ452-22-22i−2i2i−2i2-2200002i−2i-22-22i−2i2i−2i002-20000002i−2i000000000000002−2−i2i22−2−i2i200000000
χ462-22-22i−2i2i−2i2-2200002i−2i-22-22i−2i2i−2i002-20000002i−2i00000000000000−22i2−i2−22i2−i200000000
χ472-22-22i−2i2i−2i-2220000−2i2i-22-22i−2i2i−2i00-22000000−2i2i00000000000000−i2i2−22i2−i22−200000000
χ482-22-22i−2i2i−2i-2220000−2i2i-22-22i−2i2i−2i00-22000000−2i2i00000000000000i2−i22−2−i2i2−2200000000
χ492-22-2−2i2i−2i2i2-220000−2i2i-22-2−2i2i−2i2i002-2000000−2i2i000000000000002−2i2−i22−2i2−i200000000
χ502-22-2−2i2i−2i2i2-220000−2i2i-22-2−2i2i−2i2i002-2000000−2i2i00000000000000−22−i2i2−22−i2i200000000
χ512-22-2−2i2i−2i2i-22200002i−2i-22-2−2i2i−2i2i00-220000002i−2i00000000000000−i2i22−2i2−i2−2200000000
χ522-22-2−2i2i−2i2i-22200002i−2i-22-2−2i2i−2i2i00-220000002i−2i00000000000000i2−i2−22−i2i22−200000000
χ5344-4-444-4-400-24i−4i4i−4i00-222-2-22200000000−2i2i00−2i2i0000000000000000000000000000
χ5444-4-444-4-400-2−4i4i−4i4i00-222-2-222000000002i−2i002i−2i0000000000000000000000000000
χ5544-4-4-4-44400-24i−4i−4i4i00-22222-2-2000000002i−2i00−2i2i0000000000000000000000000000
χ5644-4-4-4-44400-2−4i4i4i−4i00-22222-2-200000000−2i2i002i−2i0000000000000000000000000000
χ574-44-44i−4i4i−4i4-4-200004i−4i2-22−2i2i−2i2i00-22000000−2i2i000000000000000000000000000000
χ584-44-44i−4i4i−4i-44-20000−4i4i2-22−2i2i−2i2i002-20000002i−2i000000000000000000000000000000
χ594-44-4−4i4i−4i4i4-4-20000−4i4i2-222i−2i2i−2i00-220000002i−2i000000000000000000000000000000
χ604-44-4−4i4i−4i4i-44-200004i−4i2-222i−2i2i−2i002-2000000−2i2i000000000000000000000000000000
χ614-4-444i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000000000000000000000000000
χ624-4-444i−4i−4i4i00-200000022-2−2i2i2i−2i0000−2i32i323−230000000000000000000000000000000000
χ634-4-444i−4i−4i4i00-200000022-2−2i2i2i−2i00002i3−2i3−23230000000000000000000000000000000000
χ644-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i0000−2i32i3−23230000000000000000000000000000000000
χ664-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i00002i3−2i323−230000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).