Finite Group Databasebeta

← Group #364607

Character table — Group #364607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1122222222222222244444444444444448888888888888888888888888888888888881616161616161616
order12222222244444444222244448888888822224444444444448888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ911111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1011111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ1111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1211111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1
χ1511111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111
χ171111-1-11-1-111-111-1-1-111-1-111-1-1iiii−i−i−i−i1-1111-111-1-1-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−iii−i−i1-1i−i1-1i−i
χ181111-1-11-1-111-111-1-1-111-1-111-1-1iiii−i−i−i−i1-1-1-11-111-1-111−i−iii-1-111ii−i−iii−i−iii−i−i−i−iii-11−ii-11−ii
χ191111-1-11-1-111-111-1-1-111-1-111-1-1iiii−i−i−i−i-1111-11-1-111-1-1ii−i−i11-1-1−i−iii−i−iiiii−i−iii−i−i-11−ii-11−ii
χ201111-1-11-1-111-111-1-1-111-1-111-1-1iiii−i−i−i−i-11-1-1-11-1-11111−i−iii-1-111−i−iii−i−iiiii−i−i−i−iii1-1i−i1-1i−i
χ211111-1-11-1-111-111-1-1-111-1-111-1-1−i−i−i−iiiii1-1111-111-1-1-1-1−i−iii11-1-1−i−iii−i−iii−i−iii−i−iii1-1−ii1-1−ii
χ221111-1-11-1-111-111-1-1-111-1-111-1-1−i−i−i−iiiii1-1-1-11-111-1-111ii−i−i-1-111−i−iii−i−iii−i−iiiii−i−i-11i−i-11i−i
χ231111-1-11-1-111-111-1-1-111-1-111-1-1−i−i−i−iiiii-1111-11-1-111-1-1−i−iii11-1-1ii−i−iii−i−i−i−iii−i−iii-11i−i-11i−i
χ241111-1-11-1-111-111-1-1-111-1-111-1-1−i−i−i−iiiii-11-1-1-11-1-11111ii−i−i-1-111ii−i−iii−i−i−i−iiiii−i−i1-1−ii1-1−ii
χ251111-1-11-1-111-111-1-1-1-1-111-1-111iiii−i−i−i−i1-1111-1-1-111-1-1−i−iii-1-111ii−i−i−i−iii−i−iiiii−i−i-11i−i1-1−ii
χ261111-1-11-1-111-111-1-1-1-1-111-1-111iiii−i−i−i−i1-1-1-11-1-1-11111ii−i−i11-1-1ii−i−i−i−iii−i−iii−i−iii1-1−ii-11i−i
χ271111-1-11-1-111-111-1-1-1-1-111-1-111iiii−i−i−i−i-1111-1111-1-1-1-1−i−iii-1-111−i−iiiii−i−i−i−iiiii−i−i1-1−ii-11i−i
χ281111-1-11-1-111-111-1-1-1-1-111-1-111iiii−i−i−i−i-11-1-1-1111-1-111ii−i−i11-1-1−i−iiiii−i−i−i−iii−i−iii-11i−i1-1−ii
χ291111-1-11-1-111-111-1-1-1-1-111-1-111−i−i−i−iiiii1-1111-1-1-111-1-1ii−i−i-1-111−i−iiiii−i−iii−i−i−i−iii-11−ii1-1i−i
χ301111-1-11-1-111-111-1-1-1-1-111-1-111−i−i−i−iiiii1-1-1-11-1-1-11111−i−iii11-1-1−i−iiiii−i−iii−i−iii−i−i1-1i−i-11−ii
χ311111-1-11-1-111-111-1-1-1-1-111-1-111−i−i−i−iiiii-1111-1111-1-1-1-1ii−i−i-1-111ii−i−i−i−iiiii−i−i−i−iii1-1i−i-11−ii
χ321111-1-11-1-111-111-1-1-1-1-111-1-111−i−i−i−iiiii-11-1-1-1111-1-111−i−iii11-1-1ii−i−i−i−iiiii−i−iii−i−i-11−ii1-1i−i
χ33222222222-2-2-2-2-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i0000002-22-2000000000000002i−2i2i−2i0000000000000000
χ34222222222-2-2-2-2-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000-22-2200000000000000−2i2i−2i2i0000000000000000
χ35222222222-2-2-2-2-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i0000002-22-200000000000000−2i2i−2i2i0000000000000000
χ36222222222-2-2-2-2-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000-22-22000000000000002i−2i2i−2i0000000000000000
χ372222-2-22-2-2-2-22-2-22220000000022-2-2-2-2220000002-2-22000000000000002-2-220000000000000000
χ382222-2-22-2-2-2-22-2-22220000000022-2-2-2-222000000-222-200000000000000-222-20000000000000000
χ392222-2-22-2-2-2-22-2-222200000000-2-22222-2-20000002-2-2200000000000000-222-20000000000000000
χ402222-2-22-2-2-2-22-2-222200000000-2-22222-2-2000000-222-2000000000000002-2-220000000000000000
χ41222-222-2-2-22-222-2-22-22-22-22-22-2000000000000000000002i−2i2i−2i00000000000000002i−2i2i−2i00000000
χ42222-222-2-2-22-222-2-22-22-22-22-22-200000000000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i00000000
χ43222-222-2-2-22-222-2-22-2-22-22-22-22000000000000000000002i−2i2i−2i0000000000000000−2i2i−2i2i00000000
χ44222-222-2-2-22-222-2-22-2-22-22-22-2200000000000000000000−2i2i−2i2i00000000000000002i−2i2i−2i00000000
χ45222-2-2-2-2222-2-22-22-222-2-222-2-22000000000000000000002-2-2200000000000000002-2-2200000000
χ46222-2-2-2-2222-2-22-22-222-2-222-2-2200000000000000000000-222-20000000000000000-222-200000000
χ47222-2-2-2-2222-2-22-22-22-222-2-222-2000000000000000000002-2-220000000000000000-222-200000000
χ48222-2-2-2-2222-2-22-22-22-222-2-222-200000000000000000000-222-200000000000000002-2-2200000000
χ4922-222-2-22-22-22-222-2-2000000002i−2i2i−2i2i−2i2i−2i2-200-22000000000000002i−2i2i−2i00000000000000000000
χ5022-222-2-22-22-22-222-2-2000000002i−2i2i−2i2i−2i2i−2i-22002-200000000000000−2i2i−2i2i00000000000000000000
χ5122-222-2-22-22-22-222-2-200000000−2i2i−2i2i−2i2i−2i2i2-200-2200000000000000−2i2i−2i2i00000000000000000000
χ5222-222-2-22-22-22-222-2-200000000−2i2i−2i2i−2i2i−2i2i-22002-2000000000000002i−2i2i−2i00000000000000000000
χ5322-222-2-22-2-22-22-2-22222-2-2-2-2222-2-222-2-2200000000000000000000000000002-22-2000000000000
χ5422-222-2-22-2-22-22-2-22222-2-2-2-222-222-2-222-20000000000000000000000000000-22-22000000000000
χ5522-222-2-22-2-22-22-2-222-2-22222-2-22-2-222-2-220000000000000000000000000000-22-22000000000000
χ5622-222-2-22-2-22-22-2-222-2-22222-2-2-222-2-222-200000000000000000000000000002-22-2000000000000
χ5722-22-22-2-222-2-2-22-222000000002-22-2-22-222200-2-2000000000000002-2-2200000000000000000000
χ5822-22-22-2-222-2-2-22-222000000002-22-2-22-22-2-2002200000000000000-222-200000000000000000000
χ5922-22-22-2-222-2-2-22-22200000000-22-222-22-22200-2-200000000000000-222-200000000000000000000
χ6022-22-22-2-222-2-2-22-22200000000-22-222-22-2-2-20022000000000000002-2-2200000000000000000000
χ6122-22-22-2-22-2222-22-2-22222-2-2-2-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000002i−2i−2i2i000000000000
χ6222-22-22-2-22-2222-22-2-22222-2-2-2-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000−2i2i2i−2i000000000000
χ6322-22-22-2-22-2222-22-2-2-2-2-2-222222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000−2i2i2i−2i000000000000
χ6422-22-22-2-22-2222-22-2-2-2-2-2-22222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002i−2i−2i2i000000000000
χ6522-2-22-22-22-2-2-22222-22-2-22-222-200000000002-20000002-200002-22-2000000000000000000000000
χ6622-2-22-22-22-2-2-22222-22-2-22-222-20000000000-22000000-220000-22-22000000000000000000000000
χ6722-2-22-22-22-2-2-22222-2-222-22-2-2200000000002-20000002-20000-22-22000000000000000000000000
χ6822-2-22-22-22-2-2-22222-2-222-22-2-220000000000-22000000-2200002-22-2000000000000000000000000
χ6922-2-2-2222-2-2-2222-2-222-22-2-22-2200000000002-2000000-2200002-2-22000000000000000000000000
χ7022-2-2-2222-2-2-2222-2-222-22-2-22-220000000000-220000002-20000-222-2000000000000000000000000
χ7122-2-2-2222-2-2-2222-2-22-22-222-22-200000000002-2000000-220000-222-2000000000000000000000000
χ7222-2-2-2222-2-2-2222-2-22-22-222-22-20000000000-220000002-200002-2-22000000000000000000000000
χ73444-444-4-4-4-44-4-444-44000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-444-444-44-44-4000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-44-44444-4-4-4-44000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4444-444-4-4-444-4000000000000000000000000000000000000000000000000000000000000
χ7716-16000000000000000000000000000000000000000000000000000000000000000000000000000

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