Finite Group Databasebeta

← Group #150323

Character table — Group #150323

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224444444444444444448888888888888888244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1iiii−i−i−i−i
χ611111111111111-1-1-1-1-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11111−i−i−i−iiiii
χ711111111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1−i−i−i−iiiii
χ811111111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11111iiii−i−i−i−i
χ91111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-11-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-111-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-11-1-111ii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111-11-11-1-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1111-1-1-1-11111-1-1
χ151111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-11-11-11-1-1-111-1-11111-1-1
χ161111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-111-1-1111-1-111-1-1-1-111
χ17222222222222222222222222-2-2-2-2000000000000000000-2-200000000000000
χ1822222222222222-2-2-2-2-2-222-2-22222000000000000000000-2-200000000000000
χ192222-2-2-2-222-2-2-2-22222-2-222-2-2-2-222000000000000000000-2200000000000000
χ202222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2000000000000000000-2200000000000000
χ212-22-22i2i−2i−2i2-22i−2i2i−2i0000002-2002i−2i2-2i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000000000
χ222-22-22i2i−2i−2i2-22i−2i2i−2i0000002-2002i−2i2-2−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000000000
χ232-22-22i2i−2i−2i2-22i−2i2i−2i0000002-200−2i2i-2222−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000000000
χ242-22-22i2i−2i−2i2-22i−2i2i−2i0000002-200−2i2i-22−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000000000
χ252-22-22i2i−2i−2i2-22i−2i−2i2i22-2-22i−2i-222i−2i0000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ262-22-22i2i−2i−2i2-22i−2i−2i2i22-2-22i−2i-222i−2i000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ272-22-22i2i−2i−2i2-22i−2i−2i2i-2-222−2i2i-22−2i2i0000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ282-22-22i2i−2i−2i2-22i−2i−2i2i-2-222−2i2i-22−2i2i000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ292-22-2−2i−2i2i2i2-2−2i2i2i−2i22-2-2−2i2i-22−2i2i0000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ302-22-2−2i−2i2i2i2-2−2i2i2i−2i22-2-2−2i2i-22−2i2i000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ312-22-2−2i−2i2i2i2-2−2i2i2i−2i-2-2222i−2i-222i−2i0000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ322-22-2−2i−2i2i2i2-2−2i2i2i−2i-2-2222i−2i-222i−2i000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ332-22-2−2i−2i2i2i2-2−2i2i−2i2i0000002-2002i−2i-2222−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000000000
χ342-22-2−2i−2i2i2i2-2−2i2i−2i2i0000002-2002i−2i-22−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000000000
χ352-22-2−2i−2i2i2i2-2−2i2i−2i2i0000002-200−2i2i2-2i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000000000
χ362-22-2−2i−2i2i2i2-2−2i2i−2i2i0000002-200−2i2i2-2−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000000000
χ37444444444444-4-4000000-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4000000000000000000000000000000002200-2-2000000000000
χ3944444444-4-4-4-400000000000000000000000000000000-2-20022000000000000
χ404444-4-4-4-444-4-444000000-4-40000000000000000000000000000000000000000
χ414444-4-4-4-4-4-444000000000000000000000000000000002-200-22000000000000
χ424444-4-4-4-4-4-44400000000000000000000000000000000-22002-2000000000000
χ4344-4-44-44-40000002-22-22200-2-200002−22−22−22−22−22−22−22−2000000000000000000
χ4444-4-44-44-40000002-22-22200-2-20000−22−22−22−22−22−22−22−22000000000000000000
χ4544-4-44-44-4000000-22-22-2-200220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ4644-4-44-44-4000000-22-22-2-200220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ4744-4-4-44-440000002-22-2-2-200220000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ4844-4-4-44-440000002-22-2-2-200220000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ4944-4-4-44-44000000-22-222200-2-200002−22−2−22−22−22−222−22−2000000000000000000
χ5044-4-4-44-44000000-22-222200-2-20000−22−222−22−22−22−2−22−22000000000000000000
χ514-44-44i4i−4i−4i-44−4i4i000000000000000000000000000000000000002i−2i2-200000000
χ524-44-44i4i−4i−4i-44−4i4i00000000000000000000000000000000000000−2i2i-2200000000
χ534-44-4−4i−4i4i4i-444i−4i000000000000000000000000000000000000002i−2i-2200000000
χ544-44-4−4i−4i4i4i-444i−4i00000000000000000000000000000000000000−2i2i2-200000000
χ554-4-444i−4i−4i4i0000002-2-222i−2i00−2i2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ564-4-444i−4i−4i4i0000002-2-222i−2i00−2i2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ574-4-444i−4i−4i4i000000-222-2−2i2i002i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ584-4-444i−4i−4i4i000000-222-2−2i2i002i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ594-4-44−4i4i4i−4i0000002-2-22−2i2i002i−2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ604-4-44−4i4i4i−4i0000002-2-22−2i2i002i−2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ614-4-44−4i4i4i−4i000000-222-22i−2i00−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ624-4-44−4i4i4i−4i000000-222-22i−2i00−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000

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