Finite Group Databasebeta

← Group #129754

Character table — Group #129754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222224444444444442244444444444422448888888888888888
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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
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
χ172222222222222222-2-2-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-22222-2-2-2-222-2-20000000000000000000000000000
χ19222222222222-2-2-2-2222222-2-2-2-222-2-222-2-20000000000000000000000000000
χ20222222222222-2-2-2-22222-2-22222-2-222-2-2-2-20000000000000000000000000000
χ21222-2-2-22-222-2-222-2-20000002i2i−2i−2i00002i−2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ22222-2-2-22-222-2-222-2-20000002i2i−2i−2i00002i−2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ23222-2-2-22-222-2-222-2-2000000−2i−2i2i2i0000−2i2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ24222-2-2-22-222-2-222-2-2000000−2i−2i2i2i0000−2i2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ25222-2-2-22-222-2-2-2-2220000002i2i−2i−2i0000−2i2i00000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ26222-2-2-22-222-2-2-2-2220000002i2i−2i−2i0000−2i2i0000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ27222-2-2-22-222-2-2-2-222000000−2i−2i2i2i00002i−2i00000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ28222-2-2-22-222-2-2-2-222000000−2i−2i2i2i00002i−2i0000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ292-2-222-22-22-2-222-22-20000220000-2-22-20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ302-2-222-22-22-2-222-22-20000220000-2-22-20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ312-2-222-22-22-2-222-22-20000-2-2000022-2200000000000000002−22−2−22−2200000000
χ322-2-222-22-22-2-222-22-20000-2-2000022-220000000000000000−22−222−22−200000000
χ332-2-222-22-22-2-22-22-220000220000-2-2-220000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ342-2-222-22-22-2-22-22-220000220000-2-2-220000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ352-2-222-22-22-2-22-22-220000-2-20000222-200000000000000002−2−22−222−200000000
χ362-2-222-22-22-2-22-22-220000-2-20000222-20000000000000000−222−22−2−2200000000
χ372-2-2-2-2222-22-22000000002-22-22-22-200002-2000022-2-2002-20000000000000000
χ382-2-2-2-2222-22-22000000002-22-22-22-200002-20000-2-22200-220000000000000000
χ392-2-2-2-2222-22-22000000002-2-22-222-20000-2222-2-200002-2000000000000000000
χ402-2-2-2-2222-22-22000000002-2-22-222-20000-22-2-2220000-22000000000000000000
χ412-2-2-2-2222-22-2200000000-222-22-2-220000-2222-2-20000-22000000000000000000
χ422-2-2-2-2222-22-2200000000-222-22-2-220000-22-2-22200002-2000000000000000000
χ432-2-2-2-2222-22-2200000000-22-22-22-2200002-2000022-2-200-220000000000000000
χ442-2-2-2-2222-22-2200000000-22-22-22-2200002-20000-2-222002-20000000000000000
χ4544444444-4-4-4-4000044-4-4000000000000000000000000000000000000000000
χ4644444444-4-4-4-40000-4-444000000000000000000000000000000000000000000
χ47444-4-4-44-4-4-444000000004-40000-440000000000000000000000000000000000
χ48444-4-4-44-4-4-44400000000-4400004-40000000000000000000000000000000000
χ4944-44-44-4-400000000004i−4i000000000000002i−2i2i−2i2-22-200000000000000000000
χ5044-44-44-4-400000000004i−4i00000000000000−2i2i−2i2i-22-2200000000000000000000
χ5144-44-44-4-40000000000−4i4i000000000000002i−2i2i−2i-22-2200000000000000000000
χ5244-44-44-4-40000000000−4i4i00000000000000−2i2i−2i2i2-22-200000000000000000000
χ534-44-444-4-4000000004i−4i00000000000000002i−2i−2i2i2-2-2200000000000000000000
χ544-44-444-4-4000000004i−4i0000000000000000−2i2i2i−2i-222-200000000000000000000
χ554-44-444-4-400000000−4i4i00000000000000002i−2i−2i2i-222-200000000000000000000
χ564-44-444-4-400000000−4i4i0000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ574-4-444-44-4-444-400000000004i−4i−4i4i000000000000000000000000000000000000
χ584-4-444-44-4-444-40000000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-4-4-44444-44-44-4-440000000000000000000000000000000000000000000000
χ604-4-4-4-44444-44-4-444-40000000000000000000000000000000000000000000000
χ6188-8-88-8-88000000000000000000000000000000000000000000000000000000
χ628-888-8-8-88000000000000000000000000000000000000000000000000000000

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