Finite Group Databasebeta

← Group #10691924

Character table — Group #10691924

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order122222344446661212121244444444661212441212121212121212121212122466881212242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1111-1-1111-1-1-1-11-1ii−i−i1-1-1-111i−i11-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101111-1-1111-1-1111-1-1-1-11-1ii−i−i1-1-1-111i−i11-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ111111-1-1111-1-1111-1-1-1-11-1ii−i−i1-1-1-111i−i11-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii11-1-1ii−i−i-1-111−i−iii
χ121111-1-1111-1-1111-1-1-1-11-1ii−i−i1-1-1-111i−i11-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii-1-111−i−iii11-1-1ii−i−i
χ131111-1-1111-1-1111-1-1-1-11-1−i−iii1-1-1-111−ii11-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ141111-1-1111-1-1111-1-1-1-11-1−i−iii1-1-1-111−ii11-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ151111-1-1111-1-1111-1-1-1-11-1−i−iii1-1-1-111−ii11-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i11-1-1−i−iii-1-111ii−i−i
χ161111-1-1111-1-1111-1-1-1-11-1−i−iii1-1-1-111−ii11-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-22222-2-22222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-22-20000-2222-2-2002-22-20000000000000000000000002-22-200000000
χ202222222-2-2-2-2222-2-2-2-22-20000-2222-2-2002-22-2000000000000000000000000-22-2200000000
χ212222222-2-2-2-2222-2-2-2-2-2200002-222-2-200-22-22000000000000000000002-22-2000000000000
χ222222222-2-2-2-2222-2-2-2-2-2200002-222-2-200-22-2200000000000000000000-22-22000000000000
χ23222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000000000
χ24222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000000000
χ25222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-2-1-1-1-11111111122-1-1-2-2-1-111110000000000000000
χ26222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-2-1-1-1-111111111-2-2112211-1-1-1-10000000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-21111-1-111-1-11100−i3i300−i3i3−i3i3−i3i30000000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-21111-1-111-1-11100i3−i300i3−i3i3−i3i3−i30000000000000000
χ29222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122111111-1-111-1-100−i3i300−i3i3i3−i3i3−i30000000000000000
χ30222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122111111-1-111-1-100i3−i300i3−i3−i3i3−i3i30000000000000000
χ312222-2-2222-2-2222-2-2-2-2-222i2i−2i−2i-22-2-222−2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ322222-2-2222-2-2222-2-2-2-2-22−2i−2i2i2i-22-2-2222i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ332222-2-22-2-2222222222220000-2-2-2-2-2-2002-2-220000000000000000000000002i−2i−2i2i00000000
χ342222-2-22-2-2222222222220000-2-2-2-2-2-2002-2-22000000000000000000000000−2i2i2i−2i00000000
χ352222-2-22-2-2222222222-2-2000022-2-2-2-200-222-2000000000000000000002-2-22000000000000
χ362222-2-22-2-2222222222-2-2000022-2-2-2-200-222-200000000000000000000-222-2000000000000
χ372222-2-2-122-2-2-1-1-111112-22i2i−2i−2i2-211-1-12i−2i-1-111−i−i−i−iiiii2-2-1-12i−2i11−i−iii0000000000000000
χ382222-2-2-122-2-2-1-1-111112-22i2i−2i−2i2-211-1-12i−2i-1-111−i−i−i−iiiii-2211−2i2i-1-1ii−i−i0000000000000000
χ392222-2-2-122-2-2-1-1-111112-2−2i−2i2i2i2-211-1-1−2i2i-1-111iiii−i−i−i−i2-2-1-1−2i2i11ii−i−i0000000000000000
χ402222-2-2-122-2-2-1-1-111112-2−2i−2i2i2i2-211-1-1−2i2i-1-111iiii−i−i−i−i-22112i−2i-1-1−i−iii0000000000000000
χ412222-2-2-122-2-2-1-1-11111-222i2i−2i−2i-2211-1-1−2i2i11-1-1−i−iiiii−i−i00−i3i300i3−i33−3−330000000000000000
χ422222-2-2-122-2-2-1-1-11111-222i2i−2i−2i-2211-1-1−2i2i11-1-1−i−iiiii−i−i00i3−i300−i3i3−333−30000000000000000
χ432222-2-2-122-2-2-1-1-11111-22−2i−2i2i2i-2211-1-12i−2i11-1-1ii−i−i−i−iii00−i3i300i3−i3−333−30000000000000000
χ442222-2-2-122-2-2-1-1-11111-22−2i−2i2i2i-2211-1-12i−2i11-1-1ii−i−i−i−iii00i3−i300−i3i33−3−330000000000000000
χ452-2-222-222-22-2-2-2222-2-2002i−2i2i−2i002-22-20000002i−2i002i−2i00000000000000000000002−22−2−i2i2−i2i2
χ462-2-222-222-22-2-2-2222-2-2002i−2i2i−2i002-22-20000002i−2i002i−2i0000000000000000000000−22−22i2−i2i2−i2
χ472-2-222-222-22-2-2-2222-2-200−2i2i−2i2i002-22-2000000−2i2i00−2i2i00000000000000000000002−22−2i2−i2i2−i2
χ482-2-222-222-22-2-2-2222-2-200−2i2i−2i2i002-22-2000000−2i2i00−2i2i0000000000000000000000−22−22−i2i2−i2i2
χ492-2-22-2222-2-22-2-22-2-222002-2-2200-222-20000002-200-2200000000000000000000002−2−22−222−2
χ502-2-22-2222-2-22-2-22-2-222002-2-2200-222-20000002-200-220000000000000000000000−222−22−2−22
χ512-2-22-2222-2-22-2-22-2-22200-222-200-222-2000000-22002-200000000000000000000002−2−222−2−22
χ522-2-22-2222-2-22-2-22-2-22200-222-200-222-2000000-22002-20000000000000000000000−222−2−222−2
χ53444444-2-4-4-4-4-2-2-222224-40000-44-2-22200-22-22000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-22222-4400004-4-2-222002-22-2000000000000000000000000000000000000
χ554444-4-4-2-4-444-2-2-2-2-2-2-2440000-4-4222200-222-2000000000000000000000000000000000000
χ564444-4-4-2-4-444-2-2-2-2-2-2-2-4-40000442222002-2-22000000000000000000000000000000000000
χ574-4-444-44-44-44-4-44-4-444000000004-4-44000000000000000000000000000000000000000000
χ584-4-444-4-24-44-422-2-2-222004i−4i4i−4i00-22-22000000−2i2i00−2i2i000000000000000000000000000000
χ594-4-444-4-24-44-422-2-2-22200−4i4i−4i4i00-22-220000002i−2i002i−2i000000000000000000000000000000
χ604-4-444-4-2-44-4422-222-2-200000000-222-200000000−2i32i300−2i32i30000000000000000000000000000
χ614-4-444-4-2-44-4422-222-2-200000000-222-2000000002i3−2i3002i3−2i30000000000000000000000000000
χ624-4-44-444-444-4-4-4444-4-400000000-44-44000000000000000000000000000000000000000000
χ634-4-44-44-24-4-4422-222-2-2004-4-44002-2-22000000-22002-2000000000000000000000000000000
χ644-4-44-44-24-4-4422-222-2-200-444-4002-2-220000002-200-22000000000000000000000000000000
χ654-4-44-44-2-444-422-2-2-222000000002-22-20000000023−2300−23230000000000000000000000000000
χ664-4-44-44-2-444-422-2-2-222000000002-22-200000000−23230023−230000000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-44443−4343−43000000000000000000000000000000000000000000000000000000
χ6988-8-800-40000-444−4343−4343000000000000000000000000000000000000000000000000000000
χ708-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-88-800-400004-4443−43−4343000000000000000000000000000000000000000000000000000000
χ728-88-800-400004-44−434343−43000000000000000000000000000000000000000000000000000000

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