Finite Group Databasebeta

← Group #110382

Character table — Group #110382

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444444444444444444448888888888888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ1711111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−i1-11-1
χ1811111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111−ii−ii-11-11
χ1911111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1−ii−ii-11-11
χ2011111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-111i−ii−i1-11-1
χ2111111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111i−ii−i-11-11
χ2211111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii1-11-1
χ2311111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-111−ii−ii1-11-1
χ2411111-1-1-111-1-1-1-1-11111-1-1-1111-1-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1i−ii−i-11-11
χ2511111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-111-1-1-1-111−i−iiiii−i−i−iii−i-111-1
χ2611111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1-1-11111-1-1ii−i−i−i−iiii−i−ii1-1-11
χ2711111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-11111-1-1-1-111−i−iiiii−i−ii−i−ii1-1-11
χ2811111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1ii−i−i−i−iii−iii−i-111-1
χ2911111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-11111-1-1-1-111ii−i−i−i−iii−iii−i1-1-11
χ3011111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1−i−iiiii−i−ii−i−ii-111-1
χ3111111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-111-1-1-1-111ii−i−i−i−iiii−i−ii-111-1
χ3211111-1-1-111-1-1-1-1-11-1-1-1111-1-1-1111-11-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−iii−i1-1-11
χ332222222222222222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ342222222222222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2222222-2-222-2-2-2-222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2222222-2-222-2-2-2-2-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
χ3722222-2-2-222-2-2-2-2-22222-2-2-2-2-2-22222-2-22-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ3822222-2-2-222-2-2-2-2-22222-2-2-2-2-2-22222-2-22-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ3922222-2-2-222-2-2-2-2-22-2-2-2222222-2-2-2-222-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ4022222-2-2-222-2-2-2-2-22-2-2-2222222-2-2-2-222-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ41222-2-222-2-2-222-2-2-2200000022-22-2-200-220000002i−2i002i−2i2i−2i002i−2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000000000000000
χ42222-2-222-2-2-222-2-2-2200000022-22-2-200-220000002i−2i002i−2i2i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000000000000000
χ43222-2-222-2-2-222-2-2-2200000022-22-2-200-22000000−2i2i00−2i2i−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000000000000000
χ44222-2-222-2-2-222-2-2-2200000022-22-2-200-22000000−2i2i00−2i2i−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000000000000000
χ45222-2-222-2-2-222-2-2-22000000-2-22-222002-20000002i−2i002i−2i−2i2i00−2i2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ46222-2-222-2-2-222-2-2-22000000-2-22-222002-20000002i−2i002i−2i−2i2i00−2i2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ47222-2-222-2-2-222-2-2-22000000-2-22-222002-2000000−2i2i00−2i2i2i−2i002i−2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ48222-2-222-2-2-222-2-2-22000000-2-22-222002-2000000−2i2i00−2i2i2i−2i002i−2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ49222-2-2-2-22-2-2-2-2222200000022-2-22200-2-20000002-200-222-200-2200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ50222-2-2-2-22-2-2-2-2222200000022-2-22200-2-20000002-200-222-200-2200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ51222-2-2-2-22-2-2-2-2222200000022-2-22200-2-2000000-22002-2-22002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ52222-2-2-2-22-2-2-2-2222200000022-2-22200-2-2000000-22002-2-22002-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ53222-2-2-2-22-2-2-2-22222000000-2-222-2-200220000002-200-22-22002-2002−2−22−222−2−222−22−2−22000000000000000000000000
χ54222-2-2-2-22-2-2-2-22222000000-2-222-2-200220000002-200-22-22002-200−222−22−2−222−2−22−222−2000000000000000000000000
χ55222-2-2-2-22-2-2-2-22222000000-2-222-2-20022000000-22002-22-200-22002−2−22−222−22−2−22−222−2000000000000000000000000
χ56222-2-2-2-22-2-2-2-22222000000-2-222-2-20022000000-22002-22-200-2200−222−22−2−22−222−22−2−22000000000000000000000000
χ572-2-2-2-222222-2-2-2-22222-222-22-22-22-2-2-2-222-22-200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ582-2-2-2-222222-2-2-2-22222-222-22-22-22-2-2-2-222-22-20000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ592-2-2-2-222222-2-2-2-22222-222-2-22-22-22-2-22-2-22-22000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ602-2-2-2-222222-2-2-2-22222-222-2-22-22-22-2-22-2-22-2200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ612-2-2-2-222222-2-2-2-222-2-22-2-222-22-22-222-22-22-22000000000000000000000000000000002-22-2-22-220000000000000000
χ622-2-2-2-222222-2-2-2-222-2-22-2-222-22-22-222-22-22-2200000000000000000000000000000000-22-222-22-20000000000000000
χ632-2-2-2-222222-2-2-2-222-2-22-2-22-22-22-22222-22-22-200000000000000000000000000000000000000002-22-2-22-2200000000
χ642-2-2-2-222222-2-2-2-222-2-22-2-22-22-22-22222-22-22-20000000000000000000000000000000000000000-22-222-22-200000000
χ652-2-2-2-2-2-2-2222222-2222-2-2-222-222-22-22-2-22-2-2200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ662-2-2-2-2-2-2-2222222-2222-2-2-222-222-22-22-2-22-2-220000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ672-2-2-2-2-2-2-2222222-2222-2-2-22-22-2-22-2-2222-222-2000000000000000000000000000000002-2-222-2-220000000000000000
χ682-2-2-2-2-2-2-2222222-2222-2-2-22-22-2-22-2-2222-222-200000000000000000000000000000000-222-2-222-20000000000000000
χ692-2-2-2-2-2-2-2222222-22-2-2222-22-222-222-2-2-2-222-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ702-2-2-2-2-2-2-2222222-22-2-2222-22-222-222-2-2-2-222-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ712-2-2-2-2-2-2-2222222-22-2-2222-2-22-2-22-22-2222-2-2200000000000000000000000000000000000000002-2-22-222-200000000
χ722-2-2-2-2-2-2-2222222-22-2-2222-2-22-2-22-22-2222-2-220000000000000000000000000000000000000000-222-22-2-2200000000
χ7344-44-44-444-44-44-4-4-40000000000000000000000000000004-4004-40000000000000000000000000000000000000000
χ7444-44-44-444-44-44-4-4-4000000000000000000000000000000-4400-440000000000000000000000000000000000000000
χ7544-44-4-44-44-4-44-444-40000000000000000000000000000004i−4i00−4i4i0000000000000000000000000000000000000000
χ7644-44-4-44-44-4-44-444-4000000000000000000000000000000−4i4i004i−4i0000000000000000000000000000000000000000
χ7744-4-444-4-4-444-4-444-44-444-44000000-4-400000000000000000000000000000000000000000000000000000000000000
χ7844-4-444-4-4-444-4-444-4-44-4-44-40000004400000000000000000000000000000000000000000000000000000000000000
χ7944-4-44-444-44-444-4-4-44-44-44-4000000-4400000000000000000000000000000000000000000000000000000000000000
χ8044-4-44-444-44-444-4-4-4-44-44-440000004-400000000000000000000000000000000000000000000000000000000000000
χ814-444-44-4-4-44-444-44-44-4-44-4-40000004400000000000000000000000000000000000000000000000000000000000000
χ824-444-44-4-4-44-444-44-4-444-444000000-4-400000000000000000000000000000000000000000000000000000000000000
χ834-444-4-444-444-4-44-4-44-4-4-4440000004-400000000000000000000000000000000000000000000000000000000000000
χ844-444-4-444-444-4-44-4-4-4444-4-4000000-4400000000000000000000000000000000000000000000000000000000000000
χ854-44-444-444-4-44-44-4-4000000000000000000004-4004-400000000000000000000000000000000000000000000000000
χ864-44-444-444-4-44-44-4-400000000000000000000-4400-4400000000000000000000000000000000000000000000000000
χ874-44-44-44-44-44-44-44-4000000000000000000004i−4i00−4i4i00000000000000000000000000000000000000000000000000
χ884-44-44-44-44-44-44-44-400000000000000000000−4i4i004i−4i00000000000000000000000000000000000000000000000000
χ894-4-44444-4-4-4-4-444-440000004-4-4-4-440044000000000000000000000000000000000000000000000000000000000000
χ904-4-44444-4-4-4-4-444-44000000-44444-400-4-4000000000000000000000000000000000000000000000000000000000000
χ914-4-444-4-44-4-444-4-4440000004-4-444-4004-4000000000000000000000000000000000000000000000000000000000000
χ924-4-444-4-44-4-444-4-444000000-444-4-4400-44000000000000000000000000000000000000000000000000000000000000

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