Finite Group Databasebeta

← Group #156607

Character table — Group #156607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111111111111111111111111111888888888888888888888888888888888888888888888888888888888888
order12222222222222222222222222222222444444444444444444444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ181111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i-1-111-1-111−i−iiiii−i−i−i−iii-1-111-1-111−i−iii−i−iii
χ191111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii11-1-111-1-1ii−i−i−i−iiiii−i−i-1-111-1-111−i−iii−i−iii
χ201111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii-1-111-1-111−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i
χ211111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ221111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii-1-111-1-111ii−i−i−i−iiiii−i−i-1-111-1-111ii−i−iii−i−i
χ231111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−i11-1-111-1-1−i−iiiii−i−i−i−iii-1-111-1-111ii−i−iii−i−i
χ241111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−i-1-111-1-111ii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii
χ251111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i11-1-1-1-111ii−i−i−i−iii−i−iii11-1-1-1-111ii−i−i−i−iii
χ261111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i-1-11111-1-1−i−iii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ271111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iii11-1-1-1-111ii−i−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ281111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iii-1-11111-1-1−i−iiiii−i−iii−i−i11-1-1-1-111ii−i−i−i−iii
χ291111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iii11-1-1-1-111−i−iiiii−i−iii−i−i11-1-1-1-111−i−iiiii−i−i
χ301111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iii-1-11111-1-1ii−i−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ311111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i11-1-1-1-111−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ321111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i-1-11111-1-1ii−i−i−i−iii−i−iii11-1-1-1-111−i−iiiii−i−i
χ332222222-2-2-22222222-2-2-22-2-2-2-2-2-2-2-2-22-200000000000000000000000000002-22-200002-22-20000000000002-22-20000
χ342222222-2-2-22222222-2-2-22-2-2-2-2-2-2-2-2-22-200000000000000000000000000002-22-20000-22-22000000000000-22-220000
χ352222222-2-2-22222222-2-2-22-2-2-2-2-2-2-2-2-22-20000000000000000000000000000-22-2200002-22-2000000000000-22-220000
χ362222222-2-2-22222222-2-2-22-2-2-2-2-2-2-2-2-22-20000000000000000000000000000-22-220000-22-220000000000002-22-20000
χ372222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2200000000000000000000000000002-2-2200002i−2i−2i2i0000000000002i−2i−2i2i0000
χ382222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2200000000000000000000000000002-2-220000−2i2i2i−2i000000000000−2i2i2i−2i0000
χ392222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-220000000000000000000000000000-222-200002i−2i−2i2i000000000000−2i2i2i−2i0000
χ402222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-220000000000000000000000000000-222-20000−2i2i2i−2i0000000000002i−2i−2i2i0000
χ412222-2-2-22222222-2-2-222-2-22-2-2-222-2-2-2-2-22-22-22-22-22-22-2000000000000000000000000000000000000000000000000
χ422222-2-2-22222222-2-2-222-2-22-2-2-222-2-2-2-2-22-22-2-22-22-22-22000000000000000000000000000000000000000000000000
χ432222-2-2-22222222-2-2-222-2-22-2-2-222-2-2-2-2-2-22-222-22-2-22-22000000000000000000000000000000000000000000000000
χ442222-2-2-22222222-2-2-222-2-22-2-2-222-2-2-2-2-2-22-22-22-222-22-2000000000000000000000000000000000000000000000000
χ452222-2-2-2222-2-2-2-2222-2-22-22-2-2-2-2-222-2222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ462222-2-2-2222-2-2-2-2222-2-22-22-2-2-2-2-222-2222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ472222-2-2-2222-2-2-2-2222-2-22-22-2-2-2-2-222-222-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ482222-2-2-2222-2-2-2-2222-2-22-22-2-2-2-2-222-222-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ4922-2-222-222-222-2-222-2-2-22-2-22-2-222-2-22-2200000000000000002i−2i2i−2i0000000000002i−2i2i−2i000000000000000000002-22-2
χ5022-2-222-222-222-2-222-2-2-22-2-22-2-222-2-22-2200000000000000002i−2i2i−2i000000000000−2i2i−2i2i00000000000000000000-22-22
χ5122-2-222-222-222-2-222-2-2-22-2-22-2-222-2-22-220000000000000000−2i2i−2i2i0000000000002i−2i2i−2i00000000000000000000-22-22
χ5222-2-222-222-222-2-222-2-2-22-2-22-2-222-2-22-220000000000000000−2i2i−2i2i000000000000−2i2i−2i2i000000000000000000002-22-2
χ5322-2-222-222-2-2-222-2-2222-2-2-22-2-2-2-22222-200000000000000002i−2i−2i2i0000000000002-2-2200000000000000000000−2i2i2i−2i
χ5422-2-222-222-2-2-222-2-2222-2-2-22-2-2-2-22222-200000000000000002i−2i−2i2i000000000000-222-2000000000000000000002i−2i−2i2i
χ5522-2-222-222-2-2-222-2-2222-2-2-22-2-2-2-22222-20000000000000000−2i2i2i−2i0000000000002-2-22000000000000000000002i−2i−2i2i
χ5622-2-222-222-2-2-222-2-2222-2-2-22-2-2-2-22222-20000000000000000−2i2i2i−2i000000000000-222-200000000000000000000−2i2i2i−2i
χ572-22-22-222-2-22-22-22-222-2-2-2222-22-22-2-2-220000000000002-22-2000000002i−2i2i−2i00000000000000002i−2i2i−2i000000000000
χ582-22-22-222-2-22-22-22-222-2-2-2222-22-22-2-2-220000000000002-22-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i000000000000
χ592-22-22-222-2-22-22-22-222-2-2-2222-22-22-2-2-22000000000000-22-22000000002i−2i2i−2i0000000000000000−2i2i−2i2i000000000000
χ602-22-22-222-2-22-22-22-222-2-2-2222-22-22-2-2-22000000000000-22-2200000000−2i2i−2i2i00000000000000002i−2i2i−2i000000000000
χ612-22-22-222-2-2-22-22-22-2-222-2222-2-22-22-22-20000000000002-2-22000000002i−2i−2i2i00000000000000002i−2i−2i2i000000000000
χ622-22-22-222-2-2-22-22-22-2-222-2222-2-22-22-22-20000000000002-2-2200000000−2i2i2i−2i0000000000000000−2i2i2i−2i000000000000
χ632-22-22-222-2-2-22-22-22-2-222-2222-2-22-22-22-2000000000000-222-2000000002i−2i−2i2i0000000000000000−2i2i2i−2i000000000000
χ642-22-22-222-2-2-22-22-22-2-222-2222-2-22-22-22-2000000000000-222-200000000−2i2i2i−2i00000000000000002i−2i−2i2i000000000000
χ652-2-22-222-22-22-2-22-2222-2-2-222-22-22-22-2-22000000000000000000002i−2i2i−2i00000000000000002-22-200002i−2i2i−2i00000000
χ662-2-22-222-22-22-2-22-2222-2-2-222-22-22-22-2-22000000000000000000002i−2i2i−2i0000000000000000-22-220000−2i2i−2i2i00000000
χ672-2-22-222-22-22-2-22-2222-2-2-222-22-22-22-2-2200000000000000000000−2i2i−2i2i00000000000000002-22-20000−2i2i−2i2i00000000
χ682-2-22-222-22-22-2-22-2222-2-2-222-22-22-22-2-2200000000000000000000−2i2i−2i2i0000000000000000-22-2200002i−2i2i−2i00000000
χ692-2-22-222-22-2-222-22-2-2-222-222-222-22-2-22-2000000000000000000002-2-2200000000000000002i−2i−2i2i0000−2i2i2i−2i00000000
χ702-2-22-222-22-2-222-22-2-2-222-222-222-22-2-22-2000000000000000000002-2-220000000000000000−2i2i2i−2i00002i−2i−2i2i00000000
χ712-2-22-222-22-2-222-22-2-2-222-222-222-22-2-22-200000000000000000000-222-200000000000000002i−2i−2i2i00002i−2i−2i2i00000000
χ722-2-22-222-22-2-222-22-2-2-222-222-222-22-2-22-200000000000000000000-222-20000000000000000−2i2i2i−2i0000−2i2i2i−2i00000000
χ734444-4-4-4-4-4-44444-4-4-4-4-44-4-4444-4-4444-44000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-4-4-4-4-4-444444-4-4-444444-4-444-4000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-4-4444-4-444-444-4-44-444-4-444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ7644-4-444-4-4-44-4-444-4-44-4-44-44-44444-4-4-444000000000000000000000000000000000000000000000000000000000000
χ7744-4-4-4-4444-444-4-4-4-44-4-4-44-4-4444444-44-4000000000000000000000000000000000000000000000000000000000000
χ7844-4-4-4-4444-4-4-44444-44444-4-444-4-4-4-4-4-44000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-4-44-4-4444-4-4-4-44444444-4-4-4-4-4-4444000000000000000000000000000000000000000000000000000000000000
χ8044-4-4-4-44-4-44-4-44444-4-4-4-4444-4-444444-4-4000000000000000000000000000000000000000000000000000000000000
χ814-44-44-44-4444-44-44-44-444-4-4-4-44-44-444-4-4000000000000000000000000000000000000000000000000000000000000
χ824-44-44-44-444-44-44-44-44-4-4-4-4-4-444-44-4444000000000000000000000000000000000000000000000000000000000000
χ834-44-4-44-44-4-44-44-4-44-44-4444-4-444-4-4444-4000000000000000000000000000000000000000000000000000000000000
χ844-44-4-44-44-4-4-44-444-44-44-444-4-44-444-44-44000000000000000000000000000000000000000000000000000000000000
χ854-44-4-44-4-4444-44-4-44-4-44-44-444-4-444-4-444000000000000000000000000000000000000000000000000000000000000
χ864-44-4-44-4-444-44-444-444-444-444-44-4-44-4-4-4000000000000000000000000000000000000000000000000000000000000
χ874-4-444-4-44-444-4-444-4-4-44-44-44-444-4-44-444000000000000000000000000000000000000000000000000000000000000
χ884-4-444-4-44-44-444-4-4444-444-44-44-444-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ894-4-444-4-4-44-44-4-444-4-44-4444-44-4-444-444-4000000000000000000000000000000000000000000000000000000000000
χ904-4-444-4-4-44-4-444-4-444-44-444-44-44-4-444-44000000000000000000000000000000000000000000000000000000000000
χ914-4-44-4444-444-4-44-444-444-4-4-44-44-44-44-4-4000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4444-44-444-44-4-44-4-4-4-4-44-4-44-44444000000000000000000000000000000000000000000000000000000000000

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