Finite Group Databasebeta

← Group #189960

Character table — Group #189960

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
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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
χ412-2222-2-2-222-2-222-2-22-20002-200000002i−2i2i−2i2i−2i2i−2i00000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ422-2222-2-2-222-2-222-2-22-20002-200000002i−2i2i−2i2i−2i2i−2i00000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ432-2222-2-2-222-2-222-2-22-20002-20000000−2i2i−2i2i−2i2i−2i2i00000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ442-2222-2-2-222-2-222-2-22-20002-20000000−2i2i−2i2i−2i2i−2i2i00000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ452-2222-2-2-222-2-2-2-222-22000-2200000002i−2i2i−2i−2i2i−2i2i000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ462-2222-2-2-222-2-2-2-222-22000-2200000002i−2i2i−2i−2i2i−2i2i00000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ472-2222-2-2-222-2-2-2-222-22000-220000000−2i2i−2i2i2i−2i2i−2i000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ482-2222-2-2-222-2-2-2-222-22000-220000000−2i2i−2i2i2i−2i2i−2i00000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ492-2222-2-2-2-2-22222-2-2-22000-2200000002i−2i−2i2i2i−2i−2i2i000000000000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ502-2222-2-2-2-2-22222-2-2-22000-2200000002i−2i−2i2i2i−2i−2i2i00000000000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ512-2222-2-2-2-2-22222-2-2-22000-220000000−2i2i2i−2i−2i2i2i−2i000000000000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ522-2222-2-2-2-2-22222-2-2-22000-220000000−2i2i2i−2i−2i2i2i−2i00000000000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ532-2222-2-2-2-2-222-2-2222-20002-200000002i−2i−2i2i−2i2i2i−2i00000000000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000
χ542-2222-2-2-2-2-222-2-2222-20002-200000002i−2i−2i2i−2i2i2i−2i00000000000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000
χ552-2222-2-2-2-2-222-2-2222-20002-20000000−2i2i2i−2i2i−2i−2i2i00000000000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000
χ562-2222-2-2-2-2-222-2-2222-20002-20000000−2i2i2i−2i2i−2i−2i2i00000000000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000
χ572-22-2-222-22-22-22-22-22-22-2-2-2222-22-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ582-22-2-222-22-22-22-22-22-22-2-2-2222-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ592-22-2-222-22-22-22-22-22-2-222-22-2-22-22-22000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ602-22-2-222-22-22-22-22-22-2-222-22-2-22-22-2200000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ612-22-2-222-22-22-2-22-22-222-2-22-22-22-222-2000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ622-22-2-222-22-22-2-22-22-222-2-22-22-22-222-200000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ632-22-2-222-22-22-2-22-22-22-2222-2-22-22-2-220000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ642-22-2-222-22-22-2-22-22-22-2222-2-22-22-2-22000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ652-22-2-222-2-22-222-22-2-222-2-22-22-222-2-22000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ662-22-2-222-2-22-222-22-2-222-2-22-22-222-2-2200000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ672-22-2-222-2-22-222-22-2-22-2222-2-22-2-222-20000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ682-22-2-222-2-22-222-22-2-22-2222-2-22-2-222-2000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ692-22-2-222-2-22-22-22-222-22-2-2-2222-2-22-220000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ702-22-2-222-2-22-22-22-222-22-2-2-2222-2-22-22000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ712-22-2-222-2-22-22-22-222-2-222-22-2-222-22-2000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ722-22-2-222-2-22-22-22-222-2-222-22-2-222-22-200000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ73444-4-4-4-444-4-444-4-4444000-4-4000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-444-4-44-444-4-4-400044000000000000000000000000000000000000000000000000000000000000000
χ75444-4-4-4-44-444-44-4-44-4-400044000000000000000000000000000000000000000000000000000000000000000
χ76444-4-4-4-44-444-4-444-444000-4-4000000000000000000000000000000000000000000000000000000000000000
χ7744-44-44-4-4000000000044-400-40000000000000000000000000000000000000000000000000022−22000022−220000
χ7844-44-44-4-4000000000044-400-400000000000000000000000000000000000000000000000000−22220000−22220000
χ7944-44-44-4-40000000000-4-44004000000000000000000000000000000000000000000000000002i2−2i20000−2i22i20000
χ8044-44-44-4-40000000000-4-4400400000000000000000000000000000000000000000000000000−2i22i200002i2−2i20000
χ814-4-4-444-4400000000004-4400-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000
χ824-4-4-444-4400000000004-4400-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000
χ834-4-4-444-440000000000-44-4004000000000000000000000000000000000000000000000000000022−22−2222000000
χ844-4-4-444-440000000000-44-40040000000000000000000000000000000000000000000000000000−222222−22000000
χ8588-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000

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