Finite Group Databasebeta

← Group #135367

Character table — Group #135367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444448888888888888888
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
χ51111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
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
χ17222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2220000000000000000000000000000
χ19222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2220000000000000000000000000000
χ20222222222222-2-2-2-2-2-222222222-2-222-2-2-2-20000000000000000000000000000
χ2122-2-222-2-22-22-20000002i2i−2i−2i2i2i−2i−2i002-20000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ2222-2-222-2-22-22-20000002i2i−2i−2i2i2i−2i−2i002-2000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ2322-2-222-2-22-22-20000002i2i−2i−2i−2i−2i2i2i00-220000000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ2422-2-222-2-22-22-20000002i2i−2i−2i−2i−2i2i2i00-22000000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ2522-2-222-2-22-22-2000000−2i−2i2i2i2i2i−2i−2i00-220000000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ2622-2-222-2-22-22-2000000−2i−2i2i2i2i2i−2i−2i00-22000000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ2722-2-222-2-22-22-2000000−2i−2i2i2i−2i−2i2i2i002-20000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ2822-2-222-2-22-22-2000000−2i−2i2i2i−2i−2i2i2i002-2000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ292-22-22-22-2-222-200002-22i−2i2i−2i00002-200002i−2i000000000000i2−i22−2i2−i22−200000000
χ302-22-22-22-2-222-200002-22i−2i2i−2i00002-200002i−2i000000000000−i2i2−22−i2i2−2200000000
χ312-22-22-22-2-222-200002-2−2i2i−2i2i00002-20000−2i2i000000000000i2−i2−22i2−i2−2200000000
χ322-22-22-22-2-222-200002-2−2i2i−2i2i00002-20000−2i2i000000000000−i2i22−2−i2i22−200000000
χ332-22-22-22-2-222-20000-222i−2i2i−2i0000-220000−2i2i0000000000002−2−i2i2−22i2−i200000000
χ342-22-22-22-2-222-20000-222i−2i2i−2i0000-220000−2i2i000000000000−22i2−i22−2−i2i200000000
χ352-22-22-22-2-222-20000-22−2i2i−2i2i0000-2200002i−2i0000000000002−2i2−i2−22−i2i200000000
χ362-22-22-22-2-222-20000-22−2i2i−2i2i0000-2200002i−2i000000000000−22−i2i22−2i2−i200000000
χ372-2-222-2-2222-2-200002-200002-22-2-22002-20000002i2i−2i−2i002i−2i0000000000000000
χ382-2-222-2-2222-2-200002-200002-22-2-22002-2000000−2i−2i2i2i00−2i2i0000000000000000
χ392-2-222-2-2222-2-200002-20000-22-22-2200-22002i2i−2i−2i00002i−2i000000000000000000
χ402-2-222-2-2222-2-200002-20000-22-22-2200-2200−2i−2i2i2i0000−2i2i000000000000000000
χ412-2-222-2-2222-2-20000-2200002-22-22-200-22002i2i−2i−2i0000−2i2i000000000000000000
χ422-2-222-2-2222-2-20000-2200002-22-22-200-2200−2i−2i2i2i00002i−2i000000000000000000
χ432-2-222-2-2222-2-20000-220000-22-222-2002-20000002i2i−2i−2i00−2i2i0000000000000000
χ442-2-222-2-2222-2-20000-220000-22-222-2002-2000000−2i−2i2i2i002i−2i0000000000000000
χ4544444444-4-4-4-444-4-40000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-4-4440000000000000000000000000000000000000000000000
χ474444-4-4-4-40000004-40000000000000000002-22-22-22-200000000000000000000
χ484444-4-4-4-40000004-4000000000000000000-22-22-22-2200000000000000000000
χ494444-4-4-4-4000000-440000000000000000002-22-2-22-2200000000000000000000
χ504444-4-4-4-4000000-44000000000000000000-22-222-22-200000000000000000000
χ5144-4-444-4-4-44-4400004400000000-4-40000000000000000000000000000000000
χ5244-4-444-4-4-44-440000-4-400000000440000000000000000000000000000000000
χ534-44-44-44-44-4-4400000000004i−4i−4i4i000000000000000000000000000000000000
χ544-44-44-44-44-4-440000000000−4i4i4i−4i000000000000000000000000000000000000
χ554-4-444-4-44-4-4440000004-4-440000000000000000000000000000000000000000
χ564-4-444-4-44-4-444000000-444-40000000000000000000000000000000000000000
χ574-4-44-444-400004-4000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ584-4-44-444-400004-400000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ594-4-44-444-40000-44000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ604-4-44-444-40000-4400000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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