Finite Group Databasebeta

← Group #68756

Character table — Group #68756

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order1222444422344444444446661212121266121212121212121212122222444444444444448812121212242424242488
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
χ51111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-1111iiii−i−i−i−i111-1-1-1-1-1-111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-1111iiii−i−i−i−i111-1-1-1-1-1-111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-1111iiii−i−i−i−i111-1-1-1-1-1-111iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-1111iiii−i−i−i−i111-1-1-1-1-1-111iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-1111−i−i−i−iiiii111-1-1-1-1-1-111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1-1-1111−i−i−i−iiiii111-1-1-1-1-1-111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151111-1-1-1-1-1-1111−i−i−i−iiiii111-1-1-1-1-1-111−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161111-1-1-1-1-1-1111−i−i−i−iiiii111-1-1-1-1-1-111−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ172222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ182222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ192222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ202222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2122222222-2-22-2-2000000002222222-2-2-2-20000000022-2-2-2-222000000000000000000000000
χ2222222222-2-22-2-2000000002222222-2-2-2-200000000-2-22222-2-2000000000000000000000000
χ232222-2-2-2-2222-2-200000000222-2-2-2-222-2-2000000002222-2-2-2-2000000000000000000000000
χ242222-2-2-2-2222-2-200000000222-2-2-2-222-2-200000000-2-2-2-22222000000000000000000000000
χ252222-2-2-2-2-2-2-1222i2i2i2i−2i−2i−2i−2i-1-1-1111111-1-1−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii0000
χ262222-2-2-2-2-2-2-1222i2i2i2i−2i−2i−2i−2i-1-1-1111111-1-1−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ272222-2-2-2-2-2-2-122−2i−2i−2i−2i2i2i2i2i-1-1-1111111-1-1iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ282222-2-2-2-2-2-2-122−2i−2i−2i−2i2i2i2i2i-1-1-1111111-1-1iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ2922-2-22i−2i2i−2i002001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-2-22i−2i2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i002-22i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3022-2-22i−2i2i−2i002001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-2-22i−2i2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i00-22−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3122-2-22i−2i2i−2i00200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2-22i−2i2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i002-22i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3222-2-22i−2i2i−2i00200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2-22i−2i2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00-22−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3322-2-2−2i2i−2i2i002001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2-2−2i2i−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i002-2−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ3422-2-2−2i2i−2i2i002001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2-2−2i2i−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00-222i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ3522-2-2−2i2i−2i2i00200−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2-2−2i2i−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i002-2−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ3622-2-2−2i2i−2i2i00200−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2-2−2i2i−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00-222i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ372-22-22i−2i−2i2i002001−i−1+i1−i−1+i1+i−1−i1+i−1−i-22-2−2i2i2i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ382-22-22i−2i−2i2i002001−i−1+i1−i−1+i1+i−1−i1+i−1−i-22-2−2i2i2i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i-220000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ392-22-22i−2i−2i2i00200−1+i1−i−1+i1−i−1−i1+i−1−i1+i-22-2−2i2i2i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ402-22-22i−2i−2i2i00200−1+i1−i−1+i1−i−1−i1+i−1−i1+i-22-2−2i2i2i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-220000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ412-22-2−2i2i2i−2i002001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22-22i−2i−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-20000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ422-22-2−2i2i2i−2i002001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22-22i−2i−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i-2200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ432-22-2−2i2i2i−2i00200−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22-22i−2i−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-20000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ442-22-2−2i2i2i−2i00200−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22-22i−2i−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i-2200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ452-2-2222-2-22-222-22i−2i−2i2i−2i2i2i−2i-2-22-2-2222-22-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ462-2-2222-2-22-222-2−2i2i2i−2i2i−2i−2i2i-2-22-2-2222-22-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ472-2-2222-2-22-2-12-22i−2i−2i2i−2i2i2i−2i11-111-1-1-11-11−iii−ii−i−ii000000000000000000003−33−3−i3i3−i3i30000
χ482-2-2222-2-22-2-12-22i−2i−2i2i−2i2i2i−2i11-111-1-1-11-11−iii−ii−i−ii00000000000000000000−33−33i3−i3i3−i30000
χ492-2-2222-2-22-2-12-2−2i2i2i−2i2i−2i−2i2i11-111-1-1-11-11i−i−ii−iii−i000000000000000000003−33−3i3−i3i3−i30000
χ502-2-2222-2-22-2-12-2−2i2i2i−2i2i−2i−2i2i11-111-1-1-11-11i−i−ii−iii−i00000000000000000000−33−33−i3i3−i3i30000
χ512-2-2222-2-2-222-2200000000-2-22-2-222-22-2200000000000000002-2-222-2-220000000000000000
χ522-2-2222-2-2-222-2200000000-2-22-2-222-22-220000000000000000-222-2-222-20000000000000000
χ532-2-22-2-2222-22-2200000000-2-2222-2-22-2-2200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ542-2-22-2-2222-22-2200000000-2-2222-2-22-2-220000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ552-2-22-2-222-2222-22-2-222-2-22-2-2222-2-2-222-22-2-222-2-2200000000000000000000000000000000
χ562-2-22-2-222-2222-2-222-2-222-2-2-2222-2-2-222-2-222-2-222-200000000000000000000000000000000
χ572-2-22-2-222-22-12-22-2-222-2-2211-1-1-1111-1-11-111-1-111-1000000000000000000003−3−33−333−30000
χ582-2-22-2-222-22-12-22-2-222-2-2211-1-1-1111-1-11-111-1-111-100000000000000000000−333−33−3−330000
χ592-2-22-2-222-22-12-2-222-2-222-211-1-1-1111-1-111-1-111-1-11000000000000000000003−3−333−3−330000
χ602-2-22-2-222-22-12-2-222-2-222-211-1-1-1111-1-111-1-111-1-1100000000000000000000−333−3−333−30000
χ6144444444-4-4-2-4-400000000-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ624444-4-4-4-444-2-4-400000000-2-2-22222-2-2220000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i00-2002+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i-222−2i2i−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000000000
χ6444-4-44i−4i4i−4i00-200−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i-222−2i2i−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000000000
χ6544-4-4−4i4i−4i4i00-2002−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i-2222i−2i2i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000000000
χ6644-4-4−4i4i−4i4i00-200−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i-2222i−2i2i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000000000000000
χ674-44-44i−4i−4i4i00-2002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i2-222i−2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000000000
χ684-44-44i−4i−4i4i00-200−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i2-222i−2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000000000
χ694-44-4−4i4i4i−4i00-2002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i2-22−2i2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000000000
χ704-44-4−4i4i4i−4i00-200−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i2-22−2i2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000000000
χ714-4-4444-4-4-44-2-440000000022-222-2-22-22-20000000000000000000000000000000000000000
χ724-4-44-4-4444-4-2-440000000022-2-2-222-222-20000000000000000000000000000000000000000

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