Finite Group Databasebeta

← Group #106971

Character table — Group #106971

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444444444444888888884444888888888888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ9111111111111-1-1-1-1-1111-1-11-111-1-1-11111-1-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i
χ10111111111111-1-1-1-1-1111-1-11-111-1-1-11111-1-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii
χ11111111111111-1-1-1-1-1111-1-11-111-1-1-11111-1-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii
χ12111111111111-1-1-1-1-1111-1-11-111-1-1-11111-1-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i
χ13111111111111-1-1-1-1-1111-1-11-111-1-1-1-1-1-1-11111-1iiii−i−i−i−i-1-1111111-1-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii
χ14111111111111-1-1-1-1-1111-1-11-111-1-1-1-1-1-1-11111-1iiii−i−i−i−i-1-111-1-1-1-11111ii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i
χ15111111111111-1-1-1-1-1111-1-11-111-1-1-1-1-1-1-11111-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i
χ16111111111111-1-1-1-1-1111-1-11-111-1-1-1-1-1-1-11111-1−i−i−i−iiiii-1-111-1-1-1-11111−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii
χ171-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-111-1-111-1-11ii−i−iii−i−i1-11-1ii−i−iii−i−ii−ii−iii−i−iii−i−i11-1-111-1-1i−ii−i1-11-1
χ181-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-111-1-111-1-11ii−i−iii−i−i1-11-1−i−iii−i−iiii−ii−iii−i−iii−i−i-1-111-1-111−ii−ii-11-11
χ191-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-111-1-111-1-11−i−iii−i−iii1-11-1ii−i−iii−i−i−ii−ii−i−iii−i−iii-1-111-1-111i−ii−i-11-11
χ201-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-111-1-111-1-11−i−iii−i−iii1-11-1−i−iii−i−iii−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii1-11-1
χ211-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-1-1-111-1-1111ii−i−iii−i−i-11-11ii−i−iii−i−ii−ii−i−i−iii−i−iii11-1-111-1-1−ii−ii-11-11
χ221-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-1-1-111-1-1111ii−i−iii−i−i-11-11−i−iii−i−iiii−ii−i−i−iii−i−iii-1-111-1-111i−ii−i1-11-1
χ231-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-1-1-111-1-1111−i−iii−i−iii-11-11ii−i−iii−i−i−ii−iiii−i−iii−i−i-1-111-1-111−ii−ii1-11-1
χ241-1-1-1111-111-1-1111-1-111-1-11-1-11-11-1-1-1-111-1-1111−i−iii−i−iii-11-11−i−iii−i−iii−ii−iiii−i−iii−i−i11-1-111-1-1i−ii−i-11-11
χ251-1-1-1111-111-1-1-1-1-11111-11-1-111-1-11111-1-1-1-111-111-1-1-1-1111-1-11ii−i−i−i−iii1-1-1111-1-1-1-111−i−iiiii−i−ii−i−ii−iii−i
χ261-1-1-1111-111-1-1-1-1-11111-11-1-111-1-11111-1-1-1-111-111-1-1-1-1111-1-11−i−iiiii−i−i1-1-1111-1-1-1-111ii−i−i−i−iii−iii−ii−i−ii
χ271-1-1-1111-111-1-1-1-1-11111-11-1-111-1-11111-1-1-1-111-1-1-11111-1-11-1-11ii−i−i−i−iii-111-1-1-11111-1-1ii−i−i−i−iiii−i−iii−i−ii
χ281-1-1-1111-111-1-1-1-1-11111-11-1-111-1-11111-1-1-1-111-1-1-11111-1-11-1-11−i−iiiii−i−i-111-1-1-11111-1-1−i−iiiii−i−i−iii−i−iii−i
χ291-1-1-1111-111-1-1-1-1-11111-11-1-111-1-111-1-11111-1-1-111-1-1-1-111-111-1ii−i−i−i−iii1-1-11-1-11111-1-1−i−iiiii−i−i−iii−ii−i−ii
χ301-1-1-1111-111-1-1-1-1-11111-11-1-111-1-111-1-11111-1-1-111-1-1-1-111-111-1−i−iiiii−i−i1-1-11-1-11111-1-1ii−i−i−i−iiii−i−ii−iii−i
χ311-1-1-1111-111-1-1-1-1-11111-11-1-111-1-111-1-11111-1-1-1-1-11111-1-1-111-1ii−i−i−i−iii-111-111-1-1-1-111ii−i−i−i−iii−iii−i−iii−i
χ321-1-1-1111-111-1-1-1-1-11111-11-1-111-1-111-1-11111-1-1-1-1-11111-1-1-111-1−i−iiiii−i−i-111-111-1-1-1-111−i−iiiii−i−ii−i−iii−i−ii
χ3322222222222222222-2-2-222-22-2-2-2-2-200000000-222222222000000000000-2-2-2-2000000000000000000000000
χ3422222222222222222-2-2-222-22-2-2-2-2-200000000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22220000000022i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222000000002−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ3722222222-2-2-2-222-2-2-22222-222-2-222-222222222-200000000-2-2-2-2000000000000000000000000000000000000
χ3822222222-2-2-2-222-2-2-22222-222-2-222-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ3922222222-2-2-2-222-2-2-2-2-2-22-2-2222-2-220000000020000000000000000000000002-22-22-22-20000000000000000
χ4022222222-2-2-2-222-2-2-2-2-2-22-2-2222-2-22000000002000000000000000000000000-22-22-22-220000000000000000
χ4122222222-2-2-2-2-2-2222222-222-2-2-2-2-222222-2-2-2-2200000000-2-222000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2222222-222-2-2-2-2-22-2-2-2-2222220000000022-2-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2222-2-2-2-22-2-22222-200000000-20000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4422222222-2-2-2-2-2-2222-2-2-2-22-2-22222-200000000-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ45222-22-2-2-22-22-22-222-20002-20-2000000000000002-22-22-22-200002−22−22−22−20000000000002−22−22−22−200000000
χ46222-22-2-2-22-22-22-222-20002-20-2000000000000002-22-22-22-20000−22−22−22−22000000000000−22−22−22−2200000000
χ47222-22-2-2-22-22-22-222-20002-20-200000000000000-22-22-22-2200002−22−22−22−2000000000000−22−22−22−2200000000
χ48222-22-2-2-22-22-22-222-20002-20-200000000000000-22-22-22-220000−22−22−22−220000000000002−22−22−22−200000000
χ49222-22-2-2-22-22-2-22-2-22000-2202000000000000002i−2i2i−2i−2i2i−2i2i00002−22−2−22−22000000000000i2−i2i2−i2−i2i2−i2i200000000
χ50222-22-2-2-22-22-2-22-2-22000-2202000000000000002i−2i2i−2i−2i2i−2i2i0000−22−222−22−2000000000000−i2i2−i2i2i2−i2i2−i200000000
χ51222-22-2-2-22-22-2-22-2-22000-220200000000000000−2i2i−2i2i2i−2i2i−2i00002−22−2−22−22000000000000−i2i2−i2i2i2−i2i2−i200000000
χ52222-22-2-2-22-22-2-22-2-22000-220200000000000000−2i2i−2i2i2i−2i2i−2i0000−22−222−22−2000000000000i2−i2i2−i2−i2i2−i2i200000000
χ532-2-222-2-222-2-222-22-22000-2-202000000000000002i−2i−2i2i2i−2i−2i2i0000i2−i2−i2i2i2−i2−i2i20000000000002−2−222−2−2200000000
χ542-2-222-2-222-2-222-22-22000-2-202000000000000002i−2i−2i2i2i−2i−2i2i0000−i2i2i2−i2−i2i2i2−i2000000000000−222−2−222−200000000
χ552-2-222-2-222-2-222-22-22000-2-20200000000000000−2i2i2i−2i−2i2i2i−2i0000i2−i2−i2i2i2−i2−i2i2000000000000−222−2−222−200000000
χ562-2-222-2-222-2-222-22-22000-2-20200000000000000−2i2i2i−2i−2i2i2i−2i0000−i2i2i2−i2−i2i2i2−i20000000000002−2−222−2−2200000000
χ572-2-222-2-222-2-22-22-22-2000220-2000000000000002-2-22-222-20000i2−i2−i2i2−i2i2i2−i2000000000000−i2i2i2−i2i2−i2−i2i200000000
χ582-2-222-2-222-2-22-22-22-2000220-2000000000000002-2-22-222-20000−i2i2i2−i2i2−i2−i2i2000000000000i2−i2−i2i2−i2i2i2−i200000000
χ592-2-222-2-222-2-22-22-22-2000220-200000000000000-222-22-2-220000i2−i2−i2i2−i2i2i2−i2000000000000i2−i2−i2i2−i2i2i2−i200000000
χ602-2-222-2-222-2-22-22-22-2000220-200000000000000-222-22-2-220000−i2i2i2−i2i2−i2−i2i2000000000000−i2i2i2−i2i2−i2−i2i200000000
χ612-2-2-2222-222-2-2222-2-2-2-22-222-2-22-22200000000-22i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i000000000000000000000000
χ622-2-2-2222-222-2-2222-2-2-2-22-222-2-22-22200000000-2−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i000000000000000000000000
χ632-2-2-2222-222-2-2-2-2-222-2-222-222-222-2-200000000222-2-2-2-222000000000000-222-2000000000000000000000000
χ642-2-2-2222-222-2-2-2-2-222-2-222-222-222-2-2000000002-2-22222-2-20000000000002-2-22000000000000000000000000
χ652-2-2-2222-2-2-22222-22222-2-2-2-2-2-222-2222-2-222-2-2-200000000-22-22000000000000000000000000000000000000
χ662-2-2-2222-2-2-22222-22222-2-2-2-2-2-222-22-2-222-2-222-2000000002-22-2000000000000000000000000000000000000
χ672-2-2-2222-2-2-22222-222-2-22-2-22-22-2-22-20000000020000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ682-2-2-2222-2-2-22222-222-2-22-2-22-22-2-22-2000000002000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ692-2-2-2222-2-2-222-2-22-2-222-222-22-22-22-222-2-2-2-222200000000-222-2000000000000000000000000000000000000
χ702-2-2-2222-2-2-222-2-22-2-222-222-22-22-22-2-2-22222-2-22000000002-2-22000000000000000000000000000000000000
χ712-2-2-2222-2-2-222-2-22-2-2-2-2222222-22-2200000000-20000000000000000000000002-2-22-222-20000000000000000
χ722-2-2-2222-2-2-222-2-22-2-2-2-2222222-22-2200000000-2000000000000000000000000-222-22-2-220000000000000000
χ73444-44-4-4-4-44-444-4-4-44000440-400000000000000000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-44-44-4444-4000-4-40400000000000000000000000000000000000000000000000000000000000000
χ7544-44-44-4-40000000004-4400-400000000004-44-40000000000000000000000000000000000000000000000000
χ7644-44-44-4-40000000004-4400-40000000000-44-440000000000000000000000000000000000000000000000000
χ7744-44-44-4-4000000000-44-40040000004i−4i4i−4i00000000000000000000000000000000000000000000000000000
χ7844-44-44-4-4000000000-44-4004000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000
χ794-44-4-44-440000000004-4-400400000000004-4-440000000000000000000000000000000000000000000000000
χ804-44-4-44-440000000004-4-40040000000000-444-40000000000000000000000000000000000000000000000000
χ814-44-4-44-44000000000-44400-40000004i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ824-44-4-44-44000000000-44400-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ834-4-444-4-44-444-44-4-44-4000-440400000000000000000000000000000000000000000000000000000000000000
χ844-4-444-4-44-444-4-444-440004-40-400000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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