Finite Group Databasebeta

← Group #106917

Character table — Group #106917

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444444444444888888884444444444448888888888888888888844448888
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
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
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
χ911111111-1-1-1-1-1-111-1-1-1-111-1-11111-11111-1-1-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-1-1-111-1-1-1-111-1-11111-11111-1-1-1-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-1-1-111-1-1-1-111-1-11111-11111-1-1-1-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-1-1-111-1-1-1-111-1-11111-11111-1-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-11111-1iiii−i−i−i−i-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-11111-1iiii−i−i−i−i-1-111−i−i−i−iiiiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-11111-1−i−i−i−iiiii-1-111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-11111-1−i−i−i−iiiii-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111
χ171-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-1111-1-111-1-1-111-1-111-1-11-11-1ii−i−iii−i−i1-11-111-1-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ181-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-1111-1-111-1-1-111-1-111-1-11-11-1−i−iii−i−iii1-11-111-1-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ191-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-1111-1-111-1-1-1-1-111-1-1111-11-1ii−i−iii−i−i-11-11-1-111-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ201-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-1111-1-111-1-1-1-1-111-1-1111-11-1−i−iii−i−iii-11-11-1-111-1-111−i−iii−i−iiii−ii−ii−ii−i
χ211-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-11-1-111-1-111-111-1-111-1-1-11-11ii−i−iii−i−i1-11-1-1-111-1-111−i−iii−i−iiii−ii−i−ii−ii
χ221-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-11-1-111-1-111-111-1-111-1-1-11-11−i−iii−i−iii1-11-1-1-111-1-111ii−i−iii−i−i−ii−iii−ii−i
χ231-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-11-1-111-1-111-1-1-111-1-111-11-11ii−i−iii−i−i-11-1111-1-111-1-1−i−iii−i−iii−ii−iii−ii−i
χ241-1-11-1-11111-1-1-1-11111-1-1-1-1111-11-11-1-111-1-111-1-1-111-1-111-11-11−i−iii−i−iii-11-1111-1-111-1-1ii−i−iii−i−ii−ii−i−ii−ii
χ251-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-111-1-1-1-1111ii−i−i−i−iii1-1-1111-1-1-1-111i−i−iiii−i−i−i−iii11-1-1-1-111−iii−i−iii−i
χ261-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-111-1-1-1-1111ii−i−i−i−iii1-1-11-1-11111-1-1i−i−iiii−i−i−i−iii-1-11111-1-1i−i−iii−i−ii
χ271-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-111-1-1-1-1111−i−iiiii−i−i1-1-1111-1-1-1-111−iii−i−i−iiiii−i−i11-1-1-1-111i−i−iii−i−ii
χ281-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-111-1-1-1-1111−i−iiiii−i−i1-1-11-1-11111-1-1−iii−i−i−iiiii−i−i-1-11111-1-1−iii−i−iii−i
χ291-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-1-1-11111-1-11ii−i−i−i−iii-111-111-1-1-1-111i−i−ii−i−iiiii−i−i-1-11111-1-1−iii−ii−i−ii
χ301-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-1-1-11111-1-11ii−i−i−i−iii-111-1-1-11111-1-1i−i−ii−i−iiiii−i−i11-1-1-1-111i−i−ii−iii−i
χ311-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-1-1-11111-1-11−i−iiiii−i−i-111-111-1-1-1-111−iii−iii−i−i−i−iii-1-11111-1-1i−i−ii−iii−i
χ321-1-11-1-111-1-1111111-1-111-1-1-1-11-11-1-1-1-11111-1-11−i−iiiii−i−i-111-1-1-11111-1-1−iii−iii−i−i−i−iii11-1-1-1-111−iii−ii−i−ii
χ3322222222222222-2-2-2-2-2-2-2-22222-2-2-200000000-222222222000000000000-2-2-2-2000000000000000000000000
χ3422222222222222-2-2-2-2-2-2-2-22222-2-2-200000000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ35222222222222-2-222-2-2-2-222-2-2-2-2-2-222222-2-2-2-2200000000-2-222000000000000000000000000000000000000
χ36222222222222-2-222-2-2-2-222-2-2-2-2-2-22-2-2-2-2222220000000022-2-2000000000000000000000000000000000000
χ37222222222222-2-2-2-22222-2-2-2-2-2-222-200000000-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ38222222222222-2-2-2-22222-2-2-2-2-2-222-200000000-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ3922222222-2-2-2-2222222222222-2-2-2-2-222222222-200000000-2-2-2-2000000000000000000000000000000000000
χ4022222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ4122222222-2-2-2-222-2-2-2-2-2-2-2-222-2-22220000000020000000000000000000000002-22-2-22-220000000000000000
χ4222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2222000000002000000000000000000000000-22-222-22-20000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-220000000022i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22000000002−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ4522-2-22-22-200002i−2i2-22i−2i2i−2i2-22i−2i000002-22-22i−2i2i−2i00000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4622-2-22-22-200002i−2i2-22i−2i2i−2i2-22i−2i000002-22-22i−2i2i−2i0000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4722-2-22-22-200002i−2i2-22i−2i2i−2i2-22i−2i00000-22-22−2i2i−2i2i00000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4822-2-22-22-200002i−2i2-22i−2i2i−2i2-22i−2i00000-22-22−2i2i−2i2i0000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4922-2-22-22-20000−2i2i2-2−2i2i−2i2i2-2−2i2i000002-22-2−2i2i−2i2i00000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ5022-2-22-22-20000−2i2i2-2−2i2i−2i2i2-2−2i2i000002-22-2−2i2i−2i2i0000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ5122-2-22-22-20000−2i2i2-2−2i2i−2i2i2-2−2i2i00000-22-222i−2i2i−2i00000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ5222-2-22-22-20000−2i2i2-2−2i2i−2i2i2-2−2i2i00000-22-222i−2i2i−2i0000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ532-22-2-222-200002i−2i2-2−2i2i2i−2i-22−2i2i000002-2-22−2i2i2i−2i00000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ542-22-2-222-200002i−2i2-2−2i2i2i−2i-22−2i2i000002-2-22−2i2i2i−2i0000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ552-22-2-222-200002i−2i2-2−2i2i2i−2i-22−2i2i00000-222-22i−2i−2i2i00000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ562-22-2-222-200002i−2i2-2−2i2i2i−2i-22−2i2i00000-222-22i−2i−2i2i0000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ572-22-2-222-20000−2i2i2-22i−2i−2i2i-222i−2i000002-2-222i−2i−2i2i00000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ582-22-2-222-20000−2i2i2-22i−2i−2i2i-222i−2i000002-2-222i−2i−2i2i0000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ592-22-2-222-20000−2i2i2-22i−2i−2i2i-222i−2i00000-222-2−2i2i2i−2i00000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ602-22-2-222-20000−2i2i2-22i−2i−2i2i-222i−2i00000-222-2−2i2i2i−2i0000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ612-2-22-2-22222-2-22222-2-222-2-2-2-2-22-22222-2-2-2-222-200000000-222-2000000000000000000000000000000000000
χ622-2-22-2-22222-2-22222-2-222-2-2-2-2-22-222-2-22222-2-2-2000000002-2-22000000000000000000000000000000000000
χ632-2-22-2-22222-2-222-2-222-2-222-2-2-222-2-20000000020000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ642-2-22-2-22222-2-222-2-222-2-222-2-2-222-2-2000000002000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ652-2-22-2-22222-2-2-2-2-2-2-2-22222222-2-22-200000000222-2-222-2-2000000000000-22-22000000000000000000000000
χ662-2-22-2-22222-2-2-2-2-2-2-2-22222222-2-22-2000000002-2-222-2-2220000000000002-22-2000000000000000000000000
χ672-2-22-2-222-2-22222-2-222-2-222-2-22-2-22200000000-22i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i000000000000000000000000
χ682-2-22-2-222-2-22222-2-222-2-222-2-22-2-22200000000-2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i000000000000000000000000
χ692-2-22-2-222-2-222-2-22222-2-2-2-222-22-22-222-2-222-2-2200000000-22-22000000000000000000000000000000000000
χ702-2-22-2-222-2-222-2-22222-2-2-2-222-22-22-2-2-222-2-2222000000002-22-2000000000000000000000000000000000000
χ712-2-22-2-222-2-222-2-2-2-2-2-2222222-222-2200000000-20000000000000000000000002-2-22-222-20000000000000000
χ722-2-22-2-222-2-222-2-2-2-2-2-2222222-222-2200000000-2000000000000000000000000-222-22-2-220000000000000000
χ73444-4-4-4-444-44-40000000000000000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ74444-4-4-4-444-44-400000000000000000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ75444-4-4-4-44-44-44000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ76444-4-4-4-44-44-4400000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ7744-4-44-44-400004i−4i-44−4i4i−4i4i-444i−4i00000000000000000000000000000000000000000000000000000000000000
χ7844-4-44-44-40000−4i4i-444i−4i4i−4i-44−4i4i00000000000000000000000000000000000000000000000000000000000000
χ794-44-4-444-400004i−4i-444i−4i−4i4i4-4−4i4i00000000000000000000000000000000000000000000000000000000000000
χ804-44-4-444-40000−4i4i-44−4i4i4i−4i4-44i−4i00000000000000000000000000000000000000000000000000000000000000
χ814-4-4-444-444-4-440000000000000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ824-4-4-444-444-4-4400000000000000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ834-4-4-444-44-444-4000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ844-4-4-444-44-444-400000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ8588-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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