Finite Group Databasebeta

← Group #189959

Character table — Group #189959

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444444444444444444224444444444444444448888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii
χ1711111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−ii−ii−i
χ1811111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−ii−ii
χ1911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−ii−ii
χ2011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−ii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−ii−ii
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiii−ii−i
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiii−ii−i
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11
χ2611111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1
χ2711111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-1
χ2811111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111-1-11
χ2911111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-111-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-111-1
χ3011111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-11-1-11
χ3111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-11-1-11
χ3211111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-111-1
χ33222222222222222222-2-2-222-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ34222222222222222222-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2222-2-22-2-2-2-2222222-2-2-2-2-22-2200000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2222-2-22-2-2-2-222-2-2-2-222222-22-200000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2222-2-22-2-222-2-222-2-222-2-2-2-22200000000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2222-2-22-2-222-2-2-2-222-2-22222-2-200000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-222-2-2-2222222-2-2-2-222-222-200000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-222-2-2-22222-2-22222-2-22-2-2200000000000000000000000000000000000000000000
χ41222-2-2-2-2222-2-222-2-22-20002-200000002i−2i2i−2i2i−2i2i−2i00000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ42222-2-2-2-2222-2-222-2-22-20002-200000002i−2i2i−2i2i−2i2i−2i00000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ43222-2-2-2-2222-2-222-2-22-20002-20000000−2i2i−2i2i−2i2i−2i2i00000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ44222-2-2-2-2222-2-222-2-22-20002-20000000−2i2i−2i2i−2i2i−2i2i00000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ45222-2-2-2-2222-2-2-2-222-22000-2200000002i−2i2i−2i−2i2i−2i2i000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ46222-2-2-2-2222-2-2-2-222-22000-2200000002i−2i2i−2i−2i2i−2i2i00000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ47222-2-2-2-2222-2-2-2-222-22000-220000000−2i2i−2i2i2i−2i2i−2i000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ48222-2-2-2-2222-2-2-2-222-22000-220000000−2i2i−2i2i2i−2i2i−2i00000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ49222-2-2-2-22-2-22222-2-2-22000-2200000002i−2i−2i2i2i−2i−2i2i000000000000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ50222-2-2-2-22-2-22222-2-2-22000-2200000002i−2i−2i2i2i−2i−2i2i00000000000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ51222-2-2-2-22-2-22222-2-2-22000-220000000−2i2i2i−2i−2i2i2i−2i000000000000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ52222-2-2-2-22-2-22222-2-2-22000-220000000−2i2i2i−2i−2i2i2i−2i00000000000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ53222-2-2-2-22-2-222-2-2222-20002-200000002i−2i−2i2i−2i2i2i−2i00000000000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000
χ54222-2-2-2-22-2-222-2-2222-20002-200000002i−2i−2i2i−2i2i2i−2i00000000000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000
χ55222-2-2-2-22-2-222-2-2222-20002-20000000−2i2i2i−2i2i−2i−2i2i00000000000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000
χ56222-2-2-2-22-2-222-2-2222-20002-20000000−2i2i2i−2i2i−2i−2i2i00000000000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000
χ572-2222-2-2-22-22-22-22-22-22-2-2-2222-22-22-2000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ582-2222-2-2-22-22-22-22-22-22-2-2-2222-22-22-200000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ592-2222-2-2-22-22-22-22-22-2-222-22-2-22-22-220000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ602-2222-2-2-22-22-22-22-22-2-222-22-2-22-22-22000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ612-2222-2-2-22-22-2-22-22-222-2-22-22-22-222-20000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ622-2222-2-2-22-22-2-22-22-222-2-22-22-22-222-2000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ632-2222-2-2-22-22-2-22-22-22-2222-2-22-22-2-22000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ642-2222-2-2-22-22-2-22-22-22-2222-2-22-22-2-2200000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ652-2222-2-2-2-22-222-22-2-222-2-22-22-222-2-220000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ662-2222-2-2-2-22-222-22-2-222-2-22-22-222-2-22000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ672-2222-2-2-2-22-222-22-2-22-2222-2-22-2-222-2000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ682-2222-2-2-2-22-222-22-2-22-2222-2-22-2-222-200000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ692-2222-2-2-2-22-22-22-222-22-2-2-2222-2-22-22000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ702-2222-2-2-2-22-22-22-222-22-2-2-2222-2-22-2200000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ712-2222-2-2-2-22-22-22-222-2-222-22-2-222-22-20000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ722-2222-2-2-2-22-22-22-222-2-222-22-2-222-22-2000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ7344-44-44-4-4000000000044-400-40000000000000000000000000000000000000000000000000022−22000022−220000
χ7444-44-44-4-4000000000044-400-400000000000000000000000000000000000000000000000000−22220000−22220000
χ7544-44-44-4-40000000000-4-44004000000000000000000000000000000000000000000000000002i2−2i20000−2i22i20000
χ7644-44-44-4-40000000000-4-4400400000000000000000000000000000000000000000000000000−2i22i200002i2−2i20000
χ774-44-4-444-44-4-444-4-4444000-4-4000000000000000000000000000000000000000000000000000000000000000
χ784-44-4-444-44-4-44-444-4-4-400044000000000000000000000000000000000000000000000000000000000000000
χ794-44-4-444-4-444-44-4-44-4-400044000000000000000000000000000000000000000000000000000000000000000
χ804-44-4-444-4-444-4-444-444000-4-4000000000000000000000000000000000000000000000000000000000000000
χ814-4-44-4-44400000000004-4400-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000
χ824-4-44-4-44400000000004-4400-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000
χ834-4-44-4-4440000000000-44-4004000000000000000000000000000000000000000000000000000022−22−2222000000
χ844-4-44-4-4440000000000-44-40040000000000000000000000000000000000000000000000000000−222222−22000000
χ8588-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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