Finite Group Databasebeta

← Group #97442

Character table — Group #97442

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444422228888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2222222-2-2-2-22200000000-2-222-2-200000000000000000000
χ18222222222222-2-2-2-22222-2-22222-2-200000000-2-2-2-22200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222-2-2-2-2220000000022-2-22200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002222-2-200000000000000000000
χ2122222222-2-2-2-222-2-200002-222-2-22-2000022-2-2000000002-20000000000000000
χ2222222222-2-2-2-222-2-200002-222-2-22-20000-2-22200000000-220000000000000000
χ2322222222-2-2-2-222-2-20000-22-2-222-22000022-2-200000000-220000000000000000
χ2422222222-2-2-2-222-2-20000-22-2-222-220000-2-222000000002-20000000000000000
χ2522222222-2-2-2-2-2-22200002-2-2-2222-222-2-200000000002-2000000000000000000
χ2622222222-2-2-2-2-2-22200002-2-2-2222-2-2-2220000000000-22000000000000000000
χ2722222222-2-2-2-2-2-2220000-2222-2-2-2222-2-20000000000-22000000000000000000
χ2822222222-2-2-2-2-2-2220000-2222-2-2-22-2-22200000000002-2000000000000000000
χ29222-2-2-22-222-2-2000022-2-2002i−2i2i−2i000000000000002i−2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ30222-2-2-22-222-2-2000022-2-2002i−2i2i−2i000000000000002i−2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ31222-2-2-22-222-2-2000022-2-200−2i2i−2i2i00000000000000−2i2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ32222-2-2-22-222-2-2000022-2-200−2i2i−2i2i00000000000000−2i2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ33222-2-2-22-222-2-20000-2-222002i−2i2i−2i00000000000000−2i2i0000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ34222-2-2-22-222-2-20000-2-222002i−2i2i−2i00000000000000−2i2i000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ35222-2-2-22-222-2-20000-2-22200−2i2i−2i2i000000000000002i−2i0000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ36222-2-2-22-222-2-20000-2-22200−2i2i−2i2i000000000000002i−2i000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ372-2-2-2222-22-22-200002-22-2220000-2-200000000002-2000000i2−i2i2−i2i2−i2i2−i200000000
χ382-2-2-2222-22-22-200002-22-2220000-2-200000000002-2000000−i2i2−i2i2−i2i2−i2i200000000
χ392-2-2-2222-22-22-200002-22-2-2-20000220000000000-220000002−22−2−22−2200000000
χ402-2-2-2222-22-22-200002-22-2-2-20000220000000000-22000000−22−222−22−200000000
χ412-2-2-2222-22-22-20000-22-22220000-2-20000000000-22000000i2−i2−i2i2i2−i2−i2i200000000
χ422-2-2-2222-22-22-20000-22-22220000-2-20000000000-22000000−i2i2i2−i2−i2i2i2−i200000000
χ432-2-2-2222-22-22-20000-22-22-2-200002200000000002-20000002−2−22−222−200000000
χ442-2-2-2222-22-22-20000-22-22-2-200002200000000002-2000000−222−22−2−2200000000
χ45444-4-4-44-4-4-44400000000004i−4i−4i4i000000000000000000000000000000000000
χ46444-4-4-44-4-4-4440000000000−4i4i4i−4i000000000000000000000000000000000000
χ4744-444-4-4-40000004-4000000000000004i−4i000000000000000000000000000000
χ4844-444-4-4-40000004-400000000000000−4i4i000000000000000000000000000000
χ4944-444-4-4-4000000-440000000000004i−4i00000000000000000000000000000000
χ5044-444-4-4-4000000-44000000000000−4i4i00000000000000000000000000000000
χ514-444-44-4-400004-4000000000000000000004i−4i00000000000000000000000000
χ524-444-44-4-400004-400000000000000000000−4i4i00000000000000000000000000
χ534-444-44-4-40000-440000000000000000004i−4i0000000000000000000000000000
χ544-444-44-4-40000-44000000000000000000−4i4i0000000000000000000000000000
χ554-4-44-4-4444-4-4400004-4-44000000000000000000000000000000000000000000
χ564-4-44-4-4444-4-440000-444-4000000000000000000000000000000000000000000
χ574-4-44-4-444-444-40000000000000000000000004-4000000000000000000000000
χ584-4-44-4-444-444-4000000000000000000000000-44000000000000000000000000
χ594-4-4-4444-4-44-44000000004-40000-440000000000000000000000000000000000
χ604-4-4-4444-4-44-4400000000-4400004-40000000000000000000000000000000000
χ6188-8-8-88-88000000000000000000000000000000000000000000000000000000
χ628-88-88-8-88000000000000000000000000000000000000000000000000000000

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