Finite Group Databasebeta

← Group #106711

Character table — Group #106711

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444422224444444444444444442244444444444444444444444444444488888888
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
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ171-111-1-11-111-1-111-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-111-1-11-11-1ii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1i−ii−ii−ii−i
χ181-111-1-11-111-1-111-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-111-1-11-11-1ii−i−iii−i−iii−i−i-1-111-1-111-1-111-1-111−ii−ii−ii−ii
χ191-111-1-11-111-1-111-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-111-1-11-11-1−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1−ii−ii−ii−ii
χ201-111-1-11-111-1-111-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-111-1-11-11-1−i−iii−i−iii−i−iii-1-111-1-111-1-111-1-111i−ii−ii−ii−i
χ211-111-1-11-111-1-111-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i1-1-1-111-11-11−i−iiiii−i−i−i−iii11-1-111-1-1-1-111-1-111i−ii−i−ii−ii
χ221-111-1-11-111-1-111-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i1-1-1-111-11-11−i−iiiii−i−i−i−iii-1-111-1-11111-1-111-1-1−ii−iii−ii−i
χ231-111-1-11-111-1-111-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii1-1-1-111-11-11ii−i−i−i−iiiii−i−i11-1-111-1-1-1-111-1-111−ii−iii−ii−i
χ241-111-1-11-111-1-111-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii1-1-1-111-11-11ii−i−i−i−iiiii−i−i-1-111-1-11111-1-111-1-1i−ii−i−ii−ii
χ251-111-1-11-111-1-111-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−i1-1-1-111-111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ261-111-1-11-111-1-111-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−i1-1-1-111-111-1ii−i−i−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ271-111-1-11-111-1-111-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii1-1-1-111-111-1−i−iiiii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ281-111-1-11-111-1-111-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii1-1-1-111-111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ291-111-1-11-111-1-111-1-1-1-1-1-1111111-1-1-1-111iiii−i−i−i−i1-111-1-11-1-11−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ301-111-1-11-111-1-111-1-1-1-1-1-1111111-1-1-1-111iiii−i−i−i−i1-111-1-11-1-11−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ311-111-1-11-111-1-111-1-1-1-1-1-1111111-1-1-1-111−i−i−i−iiiii1-111-1-11-1-11ii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ321-111-1-11-111-1-111-1-1-1-1-1-1111111-1-1-1-111−i−i−i−iiiii1-111-1-11-1-11ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ33222222222222-2-2-2-222222222-2-2-2-2222200000000-2-22222-2-2-2-2000000000000000000000000000000000000
χ34222222222222-2-2-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-2-2-22222000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000-2-2-2-2-2-222-2-2000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-22222-2-222000000000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-222-2-22-22-2000022-2-222-2-2-2-20000000000002-22-20000000000000000000000000000
χ3822222222-2-2-2-2222222-2-222-2-22-22-20000-2-222-2-222-2-2000000000000-22-220000000000000000000000000000
χ3922222222-2-2-2-22222-2-222-2-222-22-22000022-2-222-2-2-2-2000000000000-22-220000000000000000000000000000
χ4022222222-2-2-2-22222-2-222-2-222-22-220000-2-222-2-222-2-20000000000002-22-20000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222-2-222-2-2-22-2200000000000022000000002-22-200002-22-2000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-222-2-222-2-2-22-220000000000002200000000-22-220000-22-22000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222-2-2222-22-200000000000022000000002-22-20000-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222-2-2222-22-20000000000002200000000-22-2200002-22-2000000000000000000000000
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χ47222-2-2-2-222-22-200002i−2i2i−2i2i−2i2i−2i0000-22-220000000000−2i2i−2i2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ48222-2-2-2-222-22-200002i−2i2i−2i2i−2i2i−2i0000-22-220000000000−2i2i−2i2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ49222-2-2-2-222-22-20000−2i2i−2i2i−2i2i−2i2i00002-22-20000000000−2i2i−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ50222-2-2-2-222-22-20000−2i2i−2i2i−2i2i−2i2i00002-22-20000000000−2i2i−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ51222-2-2-2-222-22-20000−2i2i−2i2i−2i2i−2i2i0000-22-2200000000002i−2i2i−2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ52222-2-2-2-222-22-20000−2i2i−2i2i−2i2i−2i2i0000-22-2200000000002i−2i2i−2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ532-222-2-22-222-2-2-2-2222222-2-2-2-222-2-222-2-200000000-2222-2-2-22-22000000000000000000000000000000000000
χ542-222-2-22-222-2-2-2-2222222-2-2-2-222-2-2-2-22200000000-22-2-2222-22-2000000000000000000000000000000000000
χ552-222-2-22-222-2-2-2-222-2-2-2-22222-2-22222-2-200000000-22-2-2222-2-22000000000000000000000000000000000000
χ562-222-2-22-222-2-2-2-222-2-2-2-22222-2-222-2-22200000000-2222-2-2-222-2000000000000000000000000000000000000
χ572-222-2-22-2-2-22222-2-222-2-2-2-222-222-200002i2i−2i−2i−2i−2i2i2i-220000000000002i−2i−2i2i0000000000000000000000000000
χ582-222-2-22-2-2-22222-2-222-2-2-2-222-222-20000−2i−2i2i2i2i2i−2i−2i-22000000000000−2i2i2i−2i0000000000000000000000000000
χ592-222-2-22-2-2-22222-2-2-2-22222-2-22-2-2200002i2i−2i−2i−2i−2i2i2i-22000000000000−2i2i2i−2i0000000000000000000000000000
χ602-222-2-22-2-2-22222-2-2-2-22222-2-22-2-220000−2i−2i2i2i2i2i−2i−2i-220000000000002i−2i−2i2i0000000000000000000000000000
χ612-222-2-22-2-2-222-2-22222-2-2-2-2222-2-220000000000002-2000000002i−2i−2i2i00002i−2i−2i2i000000000000000000000000
χ622-222-2-22-2-2-222-2-22222-2-2-2-2222-2-220000000000002-200000000−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000
χ632-222-2-22-2-2-222-2-222-2-22222-2-2-222-20000000000002-2000000002i−2i−2i2i0000−2i2i2i−2i000000000000000000000000
χ642-222-2-22-2-2-222-2-222-2-22222-2-2-222-20000000000002-200000000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000
χ652-22-222-2-22-2-2200002i−2i2i−2i−2i2i−2i2i00002-2-2200000000002i−2i−2i2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ662-22-222-2-22-2-2200002i−2i2i−2i−2i2i−2i2i00002-2-2200000000002i−2i−2i2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ672-22-222-2-22-2-2200002i−2i2i−2i−2i2i−2i2i0000-222-20000000000−2i2i2i−2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ682-22-222-2-22-2-2200002i−2i2i−2i−2i2i−2i2i0000-222-20000000000−2i2i2i−2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ692-22-222-2-22-2-220000−2i2i−2i2i2i−2i2i−2i00002-2-220000000000−2i2i2i−2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ702-22-222-2-22-2-220000−2i2i−2i2i2i−2i2i−2i00002-2-220000000000−2i2i2i−2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ712-22-222-2-22-2-220000−2i2i−2i2i2i−2i2i−2i0000-222-200000000002i−2i−2i2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ722-22-222-2-22-2-220000−2i2i−2i2i2i−2i2i−2i0000-222-200000000002i−2i−2i2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ73444-4-4-4-44-44-4400004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-44-440000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-44-400004-44-40000000000000000004i−4i004i−4i0000000000000000000000000000000000000000000000
χ7644-4-44-44-400004-44-4000000000000000000−4i4i00−4i4i0000000000000000000000000000000000000000000000
χ7744-4-44-44-40000-44-4400000000000000004i−4i004i−4i000000000000000000000000000000000000000000000000
χ7844-4-44-44-40000-44-440000000000000000−4i4i00−4i4i000000000000000000000000000000000000000000000000
χ794-44-444-4-4-444-400004i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ804-44-444-4-4-444-40000−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4-444400004-4-440000000000000000004-400-440000000000000000000000000000000000000000000000
χ824-4-4-4-444400004-4-44000000000000000000-44004-40000000000000000000000000000000000000000000000
χ834-4-4-4-44440000-444-400000000000000004-400-44000000000000000000000000000000000000000000000000
χ844-4-4-4-44440000-444-40000000000000000-44004-4000000000000000000000000000000000000000000000000
χ8588-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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