Finite Group Databasebeta

← Group #106918

Character table — Group #106918

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444422222222444444444444444444444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-111iiii−i−i−i−i-111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-111iiii−i−i−i−i-111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-111−i−i−i−iiiii-111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-111−i−i−i−iiiii-111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111111-111iiii−i−i−i−i-1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111111-111iiii−i−i−i−i-1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111111-111−i−i−i−iiiii-1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111111-111−i−i−i−iiiii-1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ171-1-111-1-1111-1-111-111-1-1-1-111-111-1-111-1-11-1-11-1ii−i−iii−i−i11-11-1i−ii−iii−i−iii−i−i11-1-111-1-111-1-111-1-1i−ii−ii−ii−i
χ181-1-111-1-1111-1-111-111-1-1-1-111-111-1-111-1-11-1-11-1ii−i−iii−i−i11-11-1i−ii−iii−i−iii−i−i-1-111-1-111-1-111-1-111−ii−ii−ii−ii
χ191-1-111-1-1111-1-111-111-1-1-1-111-111-1-111-1-11-1-11-1−i−iii−i−iii11-11-1−ii−ii−i−iii−i−iii11-1-111-1-111-1-111-1-1−ii−ii−ii−ii
χ201-1-111-1-1111-1-111-111-1-1-1-111-111-1-111-1-11-1-11-1−i−iii−i−iii11-11-1−ii−ii−i−iii−i−iii-1-111-1-111-1-111-1-111i−ii−ii−ii−i
χ211-1-111-1-1111-1-111-111-1-1-1-111-1-1-111-1-1111-1-11-1ii−i−iii−i−i1-11-11i−ii−i−i−iii−i−iii11-1-111-1-1-1-111-1-111i−ii−i−ii−ii
χ221-1-111-1-1111-1-111-111-1-1-1-111-1-1-111-1-1111-1-11-1ii−i−iii−i−i1-11-11i−ii−i−i−iii−i−iii-1-111-1-11111-1-111-1-1−ii−iii−ii−i
χ231-1-111-1-1111-1-111-111-1-1-1-111-1-1-111-1-1111-1-11-1−i−iii−i−iii1-11-11−ii−iiii−i−iii−i−i11-1-111-1-1-1-111-1-111−ii−iii−ii−i
χ241-1-111-1-1111-1-111-111-1-1-1-111-1-1-111-1-1111-1-11-1−i−iii−i−iii1-11-11−ii−iiii−i−iii−i−i-1-111-1-11111-1-111-1-1i−ii−i−ii−ii
χ251-1-111-1-11-1-11111-1-1-11111-1-1-111-1-1-1-1111-111-111-1-1-1-111-11-1-111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−iii−i−iii−i
χ261-1-111-1-11-1-11111-1-1-11111-1-1-111-1-1-1-1111-111-111-1-1-1-111-11-1-111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−ii−i−iii−i−ii
χ271-1-111-1-11-1-11111-1-1-11111-1-1-111-1-1-1-1111-111-1-1-11111-1-1-11-1-11-111-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiii−i−iii−i−ii
χ281-1-111-1-11-1-11111-1-1-11111-1-1-111-1-1-1-1111-111-1-1-11111-1-1-11-1-11-111-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−iii−i−iii−i
χ291-1-111-1-11-1-11111-1-1-11111-1-1-1-1-11111-1-11-111-111-1-1-1-111-1-111-11-1-11-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i−iii−ii−i−ii
χ301-1-111-1-11-1-11111-1-1-11111-1-1-1-1-11111-1-11-111-111-1-1-1-111-1-111-11-1-11-1-11111-1-1−i−iiiii−i−iii−i−i−i−iiii−i−ii−iii−i
χ311-1-111-1-11-1-11111-1-1-11111-1-1-1-1-11111-1-11-111-1-1-11111-1-1-1-111-1-111-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i
χ321-1-111-1-11-1-11111-1-1-11111-1-1-1-1-11111-1-11-111-1-1-11111-1-1-1-111-1-111-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii
χ332222222222222222222-2-2-2-2222222222-2-2-2-2-200000000-2-2-2-2-2000000000000000000000000000000000000
χ342222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-22222-200000000-2-2-22222222222-20000-2-2-2-200000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-22222-200000000-2-2-222-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222-2-2000000002000000002-22-22-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222-2-200000000200000000-22-22-22-22000000000000000000000000
χ3922222222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-22-2-2000000002-2-222000000000000000000000000000000000000
χ4022222222-2-2-2-2222-2-2-2-222222-2-2-2-22222-2-22-2-200000000222-2-2000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-222222222-20000000022-2-2-200000000-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4222222222-2-2-2-2-2-2-222222222-20000000022-2-2-200000000-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4322222222-2-2-2-2-2-2-22222-2-2-2-2-200000000-2-22222i2i2i2i−2i−2i−2i−2i20000−2i−2i2i2i00000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-22222-2-2-2-2-200000000-2-2222−2i−2i−2i−2i2i2i2i2i200002i2i−2i−2i00000000000000000000000000000000
χ452222-2-2-2-22-22-22-222-22-20000-22-22-22-22-20000000000000000000000000000002−22−22−22−22−22−22−22−200000000
χ462222-2-2-2-22-22-22-222-22-20000-22-22-22-22-2000000000000000000000000000000−22−22−22−22−22−22−22−2200000000
χ472222-2-2-2-22-22-22-222-22-20000-2-22-22-22-220000000000000000000000000000002−22−22−22−2−22−22−22−2200000000
χ482222-2-2-2-22-22-22-222-22-20000-2-22-22-22-22000000000000000000000000000000−22−22−22−222−22−22−22−200000000
χ492222-2-2-2-2-22-222-22-22-220000-22-22-2-22-22000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ502222-2-2-2-2-22-222-22-22-220000-22-22-2-22-22000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ512222-2-2-2-2-22-222-22-22-220000-2-22-222-22-2000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ522222-2-2-2-2-22-222-22-22-220000-2-22-222-22-2000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ532-2-222-2-2222-2-222-222-2-222-2-2-222-2-222-2-2-222-2200000000-2-22-22000000000000000000000000000000000000
χ542-2-222-2-2222-2-222-222-2-222-2-2-2-2-222-2-222-222-2200000000-22-22-2000000000000000000000000000000000000
χ552-2-222-2-2222-2-2-2-22-2-22222-2-22000000002-2-2-22000000002000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ562-2-222-2-2222-2-2-2-22-2-22222-2-22000000002-2-2-2200000000200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ572-2-222-2-2222-2-2-2-22-2-222-2-222200000000-2222-22i2i−2i−2i2i2i−2i−2i-20000−2i2i−2i2i00000000000000000000000000000000
χ582-2-222-2-2222-2-2-2-22-2-222-2-222200000000-2222-2−2i−2i2i2i−2i−2i2i2i-200002i−2i2i−2i00000000000000000000000000000000
χ592-2-222-2-22-2-22222-2-2-222-2-222-222-2-2-2-222-22-2-22000000002-222-2000000000000000000000000000000000000
χ602-2-222-2-22-2-22222-2-2-222-2-222-2-2-22222-2-2-22-2-220000000022-2-22000000000000000000000000000000000000
χ612-2-222-2-22-2-222-2-2222-2-222-2-2200000000-22-22-222-2-2-2-22220000-222-200000000000000000000000000000000
χ622-2-222-2-22-2-222-2-2222-2-222-2-2200000000-22-22-2-2-22222-2-2200002-2-2200000000000000000000000000000000
χ632-2-222-2-22-2-222-2-2222-2-2-2-2222000000002-22-2200000000-2000000002-2-22-222-2000000000000000000000000
χ642-2-222-2-22-2-222-2-2222-2-2-2-2222000000002-22-2200000000-200000000-222-22-2-22000000000000000000000000
χ652-2-22-222-22-2-222-2-22-2-22000022-2-222-2-220000000000000000000000000000002−2−222−2−222−2−222−2−2200000000
χ662-2-22-222-22-2-222-2-22-2-22000022-2-222-2-22000000000000000000000000000000−222−2−222−2−222−2−222−200000000
χ672-2-22-222-22-2-222-2-22-2-2200002-222-2-222-20000000000000000000000000000002−2−222−2−22−222−2−222−200000000
χ682-2-22-222-22-2-222-2-22-2-2200002-222-2-222-2000000000000000000000000000000−222−2−222−22−2−222−2−2200000000
χ692-2-22-222-2-222-22-2-2-222-2000022-2-22-222-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ702-2-22-222-2-222-22-2-2-222-2000022-2-22-222-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ712-2-22-222-2-222-22-2-2-222-200002-222-22-2-22000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ722-2-22-222-2-222-22-2-2-222-200002-222-22-2-22000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ734444-4-4-4-44-44-4-44-4-44-440000400000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-44-44-44-44-44-40000400000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-4000000000004i−4i4i−4i000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000000000000000000000000000000000
χ7644-4-444-4-4000000000004i−4i4i−4i00000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000000000000000000000000000000000
χ7744-4-444-4-400000000000−4i4i−4i4i000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000000000000000000000000000000000
χ7844-4-444-4-400000000000−4i4i−4i4i00000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000000000000000000000000000000000
χ794-44-44-44-4000000000004i−4i−4i4i000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000000
χ804-44-44-44-4000000000004i−4i−4i4i00000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000000
χ814-44-44-44-400000000000−4i4i4i−4i000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000000
χ824-44-44-44-400000000000−4i4i4i−4i00000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000000
χ834-4-44-444-44-4-44-444-444-40000-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-444-4-444-4-4444-4-440000-400000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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