Finite Group Databasebeta

← Group #142172

Character table — Group #142172

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222222222-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ2122-22-22-2-222-2-2000000002-222002-2-2-22-20000000022-2-222-2-200000000000000000000
χ2222-22-22-2-222-2-2000000002-222002-2-2-22-200000000-2-222-2-22200000000000000000000
χ2322-22-22-2-222-2-2000000002-2-2-2002-222-2200002i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ2422-22-22-2-222-2-2000000002-2-2-2002-222-220000−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ2522-22-22-2-222-2-200000000-222200-22-2-2-22000022-2-200000000-2-2220000000000000000
χ2622-22-22-2-222-2-200000000-222200-22-2-2-220000-2-2220000000022-2-20000000000000000
χ2722-22-22-2-222-2-200000000-22-2-200-22222-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2822-22-22-2-222-2-200000000-22-2-200-22222-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292-222-2-22-22-2-2200002i2i−2i−2i002i−2i00002i−2i002-2001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ302-222-2-22-22-2-2200002i2i−2i−2i002i−2i00002i−2i002-200−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ312-222-2-22-22-2-2200002i2i−2i−2i00−2i2i0000−2i2i00-22001−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000000000
χ322-222-2-22-22-2-2200002i2i−2i−2i00−2i2i0000−2i2i00-2200−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000000000
χ332-222-2-22-22-2-220000−2i−2i2i2i002i−2i00002i−2i00-22001+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000000000
χ342-222-2-22-22-2-220000−2i−2i2i2i002i−2i00002i−2i00-2200−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0000000000000000
χ352-222-2-22-22-2-220000−2i−2i2i2i00−2i2i0000−2i2i002-2001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ362-222-2-22-22-2-220000−2i−2i2i2i00−2i2i0000−2i2i002-200−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ372-2-222-2-222-22-222-2-20000002i−2i2-200−2i2i00002i−2i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ382-2-222-2-222-22-222-2-20000002i−2i2-200−2i2i00002i−2i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ392-2-222-2-222-22-222-2-2000000−2i2i2-2002i−2i0000−2i2i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ402-2-222-2-222-22-222-2-2000000−2i2i2-2002i−2i0000−2i2i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
χ412-2-222-2-222-22-2-2-2220000002i−2i-2200−2i2i0000−2i2i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ422-2-222-2-222-22-2-2-2220000002i−2i-2200−2i2i0000−2i2i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ432-2-222-2-222-22-2-2-222000000−2i2i-22002i−2i00002i−2i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ442-2-222-2-222-22-2-2-222000000−2i2i-22002i−2i00002i−2i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ452-2-222-2-22-22-2222-2-22-22-22200-22-2-200000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ462-2-222-2-22-22-2222-2-22-22-22200-22-2-200000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ472-2-222-2-22-22-2222-2-2-22-22-2-200-2222000000000000000000000000000000002−22−2−22−22
χ482-2-222-2-22-22-2222-2-2-22-22-2-200-222200000000000000000000000000000000−22−222−22−2
χ492-2-222-2-22-22-22-2-2222-22-2-2-2002-222000000000000000000000000000000002−2−222−2−22
χ502-2-222-2-22-22-22-2-2222-22-2-2-2002-22200000000000000000000000000000000−222−2−222−2
χ512-2-222-2-22-22-22-2-222-22-2222002-2-2-200000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ522-2-222-2-22-22-22-2-222-22-2222002-2-2-200000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ5344444444-4-4-4-4444400000000-4-4000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000
χ55444-4-4-4-4400004-44-400000000000000000000000000000000000000002i−2i2i−2i00000000
χ56444-4-4-4-4400004-44-40000000000000000000000000000000000000000−2i2i−2i2i00000000
χ57444-4-4-4-440000-44-4400000000000000000000000000000000000000002i−2i−2i2i00000000
χ58444-4-4-4-440000-44-440000000000000000000000000000000000000000−2i2i2i−2i00000000
χ5944-44-44-4-4-4-44400004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6044-44-44-4-4-4-4440000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ614-444-4-44-4-444-4000000004-40000-440000000000000000000000000000000000000000
χ624-444-4-44-4-444-400000000-4400004-40000000000000000000000000000000000000000
χ634-4-4-4-444400004-4-440000000000000000000000000000000000002-22-2000000000000
χ644-4-4-4-444400004-4-44000000000000000000000000000000000000-22-22000000000000
χ654-4-4-4-44440000-444-40000000000000000000000000000000000002-2-22000000000000
χ664-4-4-4-44440000-444-4000000000000000000000000000000000000-222-2000000000000
χ6788-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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