Finite Group Databasebeta

← Group #8047

Character table — Group #8047

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111111122222222444444444444444444888811111111222222224444444444444444448888
order1222444422224444244444444444444444888822224444222244442444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91111-1-1-1-111-1-111-1-1-1111-1-111-1-1ii−i−iii−i−ii−ii−i1111-1-1-1-111-1-111-1-1-1111-1-111-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1-1-111-1-111-1-1-1111-1-111-1-1−i−iii−i−iii−ii−ii1111-1-1-1-111-1-111-1-1-1111-1-111-1-1−i−iii−i−iii−ii−ii
χ111111-1-1-1-111-1-111-1-1-11-1-111-1-111ii−i−iii−i−i−ii−ii1111-1-1-1-111-1-111-1-1-11-1-111-1-111ii−i−iii−i−i−ii−ii
χ121111-1-1-1-111-1-111-1-1-11-1-111-1-111−i−iii−i−iiii−ii−i1111-1-1-1-111-1-111-1-1-11-1-111-1-111−i−iii−i−iiii−ii−i
χ131111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii11-1-1-1-111−iii−i1111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii11-1-1-1-111−iii−i
χ141111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii-1-11111-1-1i−i−ii1111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii-1-11111-1-1i−i−ii
χ151111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i11-1-1-1-111i−i−ii1111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i11-1-1-1-111i−i−ii
χ161111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i-1-11111-1-1−iii−i1111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i-1-11111-1-1−iii−i
χ172222222222-2-2-2-222-2-2000000000000000000002222222222-2-2-2-222-2-200000000000000000000
χ1822222222-2-22222-2-2-2-20000000000000000000022222222-2-22222-2-2-2-200000000000000000000
χ192222-2-2-2-22222-2-2-2-22-2000000000000000000002222-2-2-2-22222-2-2-2-22-200000000000000000000
χ202222-2-2-2-2-2-2-2-222222-2000000000000000000002222-2-2-2-2-2-2-2-222222-200000000000000000000
χ2122-2-22i2i−2i−2i002-22i−2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000000022-2-22i2i−2i−2i002-22i−2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ2222-2-22i2i−2i−2i002-22i−2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000000022-2-22i2i−2i−2i002-22i−2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ2322-2-22i2i−2i−2i00-22−2i2i00001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000000022-2-22i2i−2i−2i00-22−2i2i00001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000
χ2422-2-22i2i−2i−2i00-22−2i2i0000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000000022-2-22i2i−2i−2i00-22−2i2i0000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000
χ2522-2-2−2i−2i2i2i002-2−2i2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000000022-2-2−2i−2i2i2i002-2−2i2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ2622-2-2−2i−2i2i2i002-2−2i2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000000022-2-2−2i−2i2i2i002-2−2i2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ2722-2-2−2i−2i2i2i00-222i−2i00001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000000022-2-2−2i−2i2i2i00-222i−2i00001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000
χ2822-2-2−2i−2i2i2i00-222i−2i0000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000000022-2-2−2i−2i2i2i00-222i−2i0000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000
χ292-22-22i−2i2i−2i2-200002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00002-22-22i−2i2i−2i2-200002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ302-22-22i−2i2i−2i2-200002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00002-22-22i−2i2i−2i2-200002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ312-22-22i−2i2i−2i-220000−2i2i00000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00002-22-22i−2i2i−2i-220000−2i2i00000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ322-22-22i−2i2i−2i-220000−2i2i0000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00002-22-22i−2i2i−2i-220000−2i2i0000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ332-22-2−2i2i−2i2i2-20000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00002-22-2−2i2i−2i2i2-20000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ342-22-2−2i2i−2i2i2-20000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00002-22-2−2i2i−2i2i2-20000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ352-22-2−2i2i−2i2i-2200002i−2i00000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00002-22-2−2i2i−2i2i-2200002i−2i00000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ362-22-2−2i2i−2i2i-2200002i−2i0000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00002-22-2−2i2i−2i2i-2200002i−2i0000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ374-4-444-4-440000000000000000000000000000004-4-444-4-44000000000000000000000000000000
χ384-4-44-444-40000000000000000000000000000004-4-44-444-4000000000000000000000000000000
χ3911111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ41111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ42111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ4311111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111
χ4411111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ4511111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1
χ4611111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111
χ471111-1-1-1-111-1-111-1-1-1111-1-111-1-1ii−i−iii−i−ii−ii−i-1-1-1-11111-1-111-1-1111-1-1-111-1-111−i−iii−i−iii−ii−ii
χ481111-1-1-1-111-1-111-1-1-1111-1-111-1-1−i−iii−i−iii−ii−ii-1-1-1-11111-1-111-1-1111-1-1-111-1-111ii−i−iii−i−ii−ii−i
χ491111-1-1-1-111-1-111-1-1-11-1-111-1-111ii−i−iii−i−i−ii−ii-1-1-1-11111-1-111-1-1111-111-1-111-1-1−i−iii−i−iiii−ii−i
χ501111-1-1-1-111-1-111-1-1-11-1-111-1-111−i−iii−i−iiii−ii−i-1-1-1-11111-1-111-1-1111-111-1-111-1-1ii−i−iii−i−i−ii−ii
χ511111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii11-1-1-1-111−iii−i-1-1-1-1111111-1-111-1-11-1−i−iiiii−i−i-1-11111-1-1i−i−ii
χ521111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii-1-11111-1-1i−i−ii-1-1-1-1111111-1-111-1-11-1−i−iiiii−i−i11-1-1-1-111−iii−i
χ531111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i11-1-1-1-111i−i−ii-1-1-1-1111111-1-111-1-11-1ii−i−i−i−iii-1-11111-1-1−iii−i
χ541111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i-1-11111-1-1−iii−i-1-1-1-1111111-1-111-1-11-1ii−i−i−i−iii11-1-1-1-111i−i−ii
χ552222222222-2-2-2-222-2-200000000000000000000-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000
χ5622222222-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000
χ572222-2-2-2-22222-2-2-2-22-200000000000000000000-2-2-2-22222-2-2-2-22222-2200000000000000000000
χ582222-2-2-2-2-2-2-2-222222-200000000000000000000-2-2-2-222222222-2-2-2-2-2200000000000000000000
χ5922-2-22i2i−2i−2i002-22i−2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000-2-222−2i−2i2i2i00-22−2i2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ6022-2-22i2i−2i−2i002-22i−2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000-2-222−2i−2i2i2i00-22−2i2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ6122-2-22i2i−2i−2i00-22−2i2i00001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000-2-222−2i−2i2i2i002-22i−2i0000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000
χ6222-2-22i2i−2i−2i00-22−2i2i0000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000-2-222−2i−2i2i2i002-22i−2i00001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000
χ6322-2-2−2i−2i2i2i002-2−2i2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000-2-2222i2i−2i−2i00-222i−2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ6422-2-2−2i−2i2i2i002-2−2i2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000-2-2222i2i−2i−2i00-222i−2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ6522-2-2−2i−2i2i2i00-222i−2i00001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000-2-2222i2i−2i−2i002-2−2i2i0000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000
χ6622-2-2−2i−2i2i2i00-222i−2i0000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000-2-2222i2i−2i−2i002-2−2i2i00001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000
χ672-22-22i−2i2i−2i2-200002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000-22-22−2i2i−2i2i-220000−2i2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ682-22-22i−2i2i−2i2-200002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000-22-22−2i2i−2i2i-220000−2i2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ692-22-22i−2i2i−2i-220000−2i2i00000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000-22-22−2i2i−2i2i2-200002i−2i0000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ702-22-22i−2i2i−2i-220000−2i2i0000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000-22-22−2i2i−2i2i2-200002i−2i00000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ712-22-2−2i2i−2i2i2-20000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000-22-222i−2i2i−2i-2200002i−2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ722-22-2−2i2i−2i2i2-20000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000-22-222i−2i2i−2i-2200002i−2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ732-22-2−2i2i−2i2i-2200002i−2i00000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000-22-222i−2i2i−2i2-20000−2i2i0000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ742-22-2−2i2i−2i2i-2200002i−2i0000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000-22-222i−2i2i−2i2-20000−2i2i00000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ754-4-444-4-44000000000000000000000000000000-444-4-444-4000000000000000000000000000000
χ764-4-44-444-4000000000000000000000000000000-444-44-4-44000000000000000000000000000000

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