Finite Group Databasebeta

← Group #375760

Character table — Group #375760

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222222222244444444444444448888888888888888888888888888888888888888161616161616
order12222222224444444444444444444444442222224444444444444488888888888888888888444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1711-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-1ii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1i−ii−i1-1
χ1811-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-1ii−i−i-1-111−i−iiiii−i−i11-1-1−i−iii-1-111-1-111−ii−ii-11
χ1911-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-1111-1−i−iii11-1-1ii−i−i−i−iii-1-111ii−i−i11-1-1-1-111−ii−ii-11
χ2011-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-1111-1−i−iii-1-111−i−iii−i−iii-1-111−i−iii-1-11111-1-1i−ii−i1-1
χ2111-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1111-1-1-11ii−i−i11-1-1−i−iii−i−iii-1-111ii−i−i-1-11111-1-1i−i−ii-11
χ2211-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1111-1-1-11ii−i−i-1-111ii−i−i−i−iii-1-111−i−iii11-1-1-1-111−iii−i1-1
χ2311-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111-11−i−iii11-1-1−i−iiiii−i−i11-1-1ii−i−i-1-111-1-111−iii−i1-1
χ2411-1-1111-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111-11−i−iii-1-111ii−i−iii−i−i11-1-1−i−iii11-1-111-1-1i−i−ii-11
χ2511-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1-11−i−iii11-1-1ii−i−iii−i−i-1-111−i−iii-1-11111-1-1−iii−i-11
χ2611-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1-11−i−iii-1-111−i−iiiii−i−i-1-111ii−i−i11-1-1-1-111i−i−ii1-1
χ2711-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-11ii−i−i11-1-1ii−i−i−i−iii11-1-1−i−iii-1-111-1-111i−i−ii1-1
χ2811-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-11ii−i−i-1-111−i−iii−i−iii11-1-1ii−i−i11-1-111-1-1−iii−i-11
χ2911-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-1−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii11-1-111-1-1−ii−ii1-1
χ3011-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-1−i−iii-1-111ii−i−i−i−iii11-1-1ii−i−i-1-111-1-111i−ii−i-11
χ3111-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-1111-1ii−i−i11-1-1−i−iiiii−i−i-1-111−i−iii11-1-1-1-111i−ii−i-11
χ3211-1-1111-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-1111-1ii−i−i-1-111ii−i−iii−i−i-1-111ii−i−i-1-11111-1-1−ii−ii1-1
χ3322222-2-22-2-2-2-222-2-22222-2-222-2-222-2-222-2-2220000-2-200000000000000000000000000000000000000
χ3422222-2-22-2-2-2-222-2-22222-2-222-2-2-2-222-2-222-2-200002200000000000000000000000000000000000000
χ3522222-2-22-2-2-2-222-2-222-2-222-2-22222-2-222-2-2-2-200002200000000000000000000000000000000000000
χ3622222-2-22-2-2-2-222-2-222-2-222-2-222-2-222-2-222220000-2-200000000000000000000000000000000000000
χ372222-22-2-22-22-22-22-22-2000000002-22-22-22-2000000002-22-20000000000002-22-2000000000000000000
χ382222-22-2-22-22-22-22-22-2000000002-22-22-22-200000000-22-22000000000000-22-22000000000000000000
χ392222-22-2-22-22-22-22-22-200000000-22-22-22-22000000002-22-2000000000000-22-22000000000000000000
χ402222-22-2-22-22-22-22-22-200000000-22-22-22-2200000000-22-220000000000002-22-2000000000000000000
χ412222-22-2-22-2-22-22-22-222-22-22-22-2000000000000000000002-22-20000000000002-22-200000000000000
χ422222-22-2-22-2-22-22-22-222-22-22-22-200000000000000000000-22-22000000000000-22-2200000000000000
χ432222-22-2-22-2-22-22-22-22-22-22-22-22000000000000000000002-22-2000000000000-22-2200000000000000
χ442222-22-2-22-2-22-22-22-22-22-22-22-2200000000000000000000-22-220000000000002-22-200000000000000
χ452222-2-22-2-222-2-222-2-222-2-222-2-220000000000000000000000002-22-20000000000002-22-20000000000
χ462222-2-22-2-222-2-222-2-222-2-222-2-22000000000000000000000000-22-22000000000000-22-220000000000
χ472222-2-22-2-222-2-222-2-22-222-2-222-20000000000000000000000002-22-2000000000000-22-220000000000
χ482222-2-22-2-222-2-222-2-22-222-2-222-2000000000000000000000000-22-220000000000002-22-20000000000
χ492222-2-22-2-22-222-2-222-2000000002-2-222-2-22002-22-2000000000000002-22-20000000000000000000000
χ502222-2-22-2-22-222-2-222-2000000002-2-222-2-2200-22-2200000000000000-22-220000000000000000000000
χ512222-2-22-2-22-222-2-222-200000000-222-2-222-2002-22-200000000000000-22-220000000000000000000000
χ522222-2-22-2-22-222-2-222-200000000-222-2-222-200-22-22000000000000002-22-20000000000000000000000
χ5322-2-22-2-2-2222222-2-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-20000-2200000000000000000000000000000000000000
χ5422-2-22-2-2-2222222-2-2-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-2200002-200000000000000000000000000000000000000
χ5522-2-22-2-2-2222222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-2200002-200000000000000000000000000000000000000
χ5622-2-22-2-2-2222222-2-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-20000-2200000000000000000000000000000000000000
χ5722-2-2-22-22-222-2-22-222-22i−2i2i−2i−2i2i−2i2i000000000000000000002-2-220000000000002i−2i−2i2i00000000000000
χ5822-2-2-22-22-222-2-22-222-22i−2i2i−2i−2i2i−2i2i00000000000000000000-222-2000000000000−2i2i2i−2i00000000000000
χ5922-2-2-22-22-222-2-22-222-2−2i2i−2i2i2i−2i2i−2i000000000000000000002-2-22000000000000−2i2i2i−2i00000000000000
χ6022-2-2-22-22-222-2-22-222-2−2i2i−2i2i2i−2i2i−2i00000000000000000000-222-20000000000002i−2i−2i2i00000000000000
χ6122-2-2-22-22-22-222-22-2-22000000002i−2i2i−2i−2i2i−2i2i000000002i−2i−2i2i0000000000002-2-22000000000000000000
χ6222-2-2-22-22-22-222-22-2-22000000002i−2i2i−2i−2i2i−2i2i00000000−2i2i2i−2i000000000000-222-2000000000000000000
χ6322-2-2-22-22-22-222-22-2-2200000000−2i2i−2i2i2i−2i2i−2i000000002i−2i−2i2i000000000000-222-2000000000000000000
χ6422-2-2-22-22-22-222-22-2-2200000000−2i2i−2i2i2i−2i2i−2i00000000−2i2i2i−2i0000000000002-2-22000000000000000000
χ6522-2-2-2-2222-22-22-2-22-22000000002i−2i−2i2i−2i2i2i−2i002-2-22000000000000002i−2i−2i2i0000000000000000000000
χ6622-2-2-2-2222-22-22-2-22-22000000002i−2i−2i2i−2i2i2i−2i00-222-200000000000000−2i2i2i−2i0000000000000000000000
χ6722-2-2-2-2222-22-22-2-22-2200000000−2i2i2i−2i2i−2i−2i2i002-2-2200000000000000−2i2i2i−2i0000000000000000000000
χ6822-2-2-2-2222-22-22-2-22-2200000000−2i2i2i−2i2i−2i−2i2i00-222-2000000000000002i−2i−2i2i0000000000000000000000
χ6922-2-2-2-2222-2-22-222-22-22i−2i−2i2i−2i2i2i−2i0000000000000000000000002i−2i−2i2i0000000000002-2-220000000000
χ7022-2-2-2-2222-2-22-222-22-22i−2i−2i2i−2i2i2i−2i000000000000000000000000−2i2i2i−2i000000000000-222-20000000000
χ7122-2-2-2-2222-2-22-222-22-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000002i−2i−2i2i000000000000-222-20000000000
χ7222-2-2-2-2222-2-22-222-22-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2i2i2i−2i0000000000002-2-220000000000
χ734444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7444444-4-44-4-444-4-444-4-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4444-4-4-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ7644-4-44-4-4-444-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000
χ778-88-80000000000000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000
χ788-88-8000000000000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000
χ798-8-880000000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000
χ808-8-88000000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000

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