Finite Group Databasebeta

← Group #134535

Character table — Group #134535

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-222-2-2-222-2-2-2-2-2220000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2222-2-2222-2-2-2-20000000000000000000000000000
χ19222222222222-2-2-2-2222222-2-2-222-222-2-2-2-20000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2222-2-22-2-2-2-2220000000000000000000000000000
χ2122-2-22-2-222-22-2000000002222-2-2-2-2002-200000022-2-2002-20000000000000000
χ2222-2-22-2-222-22-2000000002222-2-2-2-2002-2000000-2-22200-220000000000000000
χ2322-2-22-2-222-22-20000000022-2-22-2-2200-22002i2i−2i−2i00002i−2i000000000000000000
χ2422-2-22-2-222-22-20000000022-2-22-2-2200-2200−2i−2i2i2i0000−2i2i000000000000000000
χ2522-2-22-2-222-22-200000000-2-222-222-200-22002i2i−2i−2i0000−2i2i000000000000000000
χ2622-2-22-2-222-22-200000000-2-222-222-200-2200−2i−2i2i2i00002i−2i000000000000000000
χ2722-2-22-2-222-22-200000000-2-2-2-22222002-200000022-2-200-220000000000000000
χ2822-2-22-2-222-22-200000000-2-2-2-22222002-2000000-2-222002-20000000000000000
χ292-222-2-2-222-2-2200002i2i−2i−2i2i−2i0002i−2i02-20000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ302-222-2-2-222-2-2200002i2i−2i−2i2i−2i0002i−2i02-2000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ312-222-2-2-222-2-2200002i2i−2i−2i−2i2i000−2i2i0-220000000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ322-222-2-2-222-2-2200002i2i−2i−2i−2i2i000−2i2i0-22000000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ332-222-2-2-222-2-220000−2i−2i2i2i2i−2i0002i−2i0-220000000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ342-222-2-2-222-2-220000−2i−2i2i2i2i−2i0002i−2i0-22000000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ352-222-2-2-222-2-220000−2i−2i2i2i−2i2i000−2i2i02-20000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ362-222-2-2-222-2-220000−2i−2i2i2i−2i2i000−2i2i02-2000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ372-2-2-2-2222-2-22200002-22-2002-2200-200002-2000000000000i2−i2i2−i2i2−i2i2−i200000000
χ382-2-2-2-2222-2-22200002-22-2002-2200-200002-2000000000000−i2i2−i2i2−i2i2−i2i200000000
χ392-2-2-2-2222-2-22200002-22-200-22-20020000-220000000000002−22−2−22−2200000000
χ402-2-2-2-2222-2-22200002-22-200-22-20020000-22000000000000−22−222−22−200000000
χ412-2-2-2-2222-2-2220000-22-22002-2200-20000-22000000000000i2−i2−i2i2i2−i2−i2i200000000
χ422-2-2-2-2222-2-2220000-22-22002-2200-20000-22000000000000−i2i2i2−i2−i2i2i2−i200000000
χ432-2-2-2-2222-2-2220000-22-2200-22-200200002-20000000000002−2−22−222−200000000
χ442-2-2-2-2222-2-2220000-22-2200-22-200200002-2000000000000−222−22−2−2200000000
χ4544444444-4-4-4-444-4-40000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-4-4440000000000000000000000000000000000000000000000
χ4744-4-44-4-44-44-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ4844-4-44-4-44-44-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ494-444-4-4-44-444-400000000004-4-40040000000000000000000000000000000000
χ504-444-4-4-44-444-40000000000-44400-40000000000000000000000000000000000
χ514-44-444-4-40000004-40000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ524-44-444-4-40000004-4000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ534-44-444-4-4000000-440000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ544-44-444-4-4000000-44000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ554-4-444-44-400004i−4i000000000000000000002-2-222i−2i−2i2i00000000000000000000
χ564-4-444-44-400004i−4i00000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ574-4-444-44-40000−4i4i000000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ584-4-444-44-40000−4i4i00000000000000000000-222-22i−2i−2i2i00000000000000000000
χ594-4-4-4-444444-4-4000000004i−4i000−4i4i00000000000000000000000000000000000
χ604-4-4-4-444444-4-400000000−4i4i0004i−4i00000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-88-88-8-8000000000000000000000000000000000000000000000000000000

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