Finite Group Databasebeta

← Group #220968

Character table — Group #220968

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822224444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-111
χ171-11-1-11-11-1111-1-11-11111-1-1-1-1ii−i−i111-1-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1-11-1i−i1-11-11-1ii−i−i11-1-1i−ii−i1-11-1i−ii−i
χ181-11-1-11-11-1111-1-11-11111-1-1-1-1ii−i−i111-1-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i-11-11i−i1-1-11-11ii−i−i11-1-1−ii−ii-11-11−ii−ii
χ191-11-1-11-11-1111-1-11-11111-1-1-1-1ii−i−i1-1-111-1−i−iii11-1-1−i−iii−i−i−i−iiiii1-11-1i−i-111-11-1ii−i−i-1-111i−ii−i-11-11−ii−ii
χ201-11-1-11-11-1111-1-11-11111-1-1-1-1ii−i−i1-1-111-1−i−iii11-1-1−i−iii−i−i−i−iiiii-11-11i−i-11-11-11ii−i−i-1-111−ii−ii1-11-1i−ii−i
χ211-11-1-11-11-1111-1-11-11111-1-1-1-1−i−iii111-1-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1-11-1−ii1-11-11-1−i−iii11-1-1−ii−ii1-11-1−ii−ii
χ221-11-1-11-11-1111-1-11-11111-1-1-1-1−i−iii111-1-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii-11-11−ii1-1-11-11−i−iii11-1-1i−ii−i-11-11i−ii−i
χ231-11-1-11-11-1111-1-11-11111-1-1-1-1−i−iii1-1-111-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1-11-1−ii-111-11-1−i−iii-1-111−ii−ii-11-11i−ii−i
χ241-11-1-11-11-1111-1-11-11111-1-1-1-1−i−iii1-1-111-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i-11-11−ii-11-11-11−i−iii-1-111i−ii−i1-11-1−ii−ii
χ251-11-1-11-11-1111-1-11-1-1-1-1-11111ii−i−i111-1-1-1ii−i−i-1-111ii−i−i−i−i−i−iiiii1-1-11i−i1-11-1-11−i−iii-1-111i−i−ii1-1-11i−i−ii
χ261-11-1-11-11-1111-1-11-1-1-1-1-11111ii−i−i111-1-1-1ii−i−i-1-111ii−i−i−i−i−i−iiiii-111-1i−i1-1-111-1−i−iii-1-111−iii−i-111-1−iii−i
χ271-11-1-11-11-1111-1-11-1-1-1-1-11111ii−i−i1-1-111-1−i−iii-1-111−i−iiiiiii−i−i−i−i1-1-11i−i-111-1-11−i−iii11-1-1i−i−ii-111-1−iii−i
χ281-11-1-11-11-1111-1-11-1-1-1-1-11111ii−i−i1-1-111-1−i−iii-1-111−i−iiiiiii−i−i−i−i-111-1i−i-11-111-1−i−iii11-1-1−iii−i1-1-11i−i−ii
χ291-11-1-11-11-1111-1-11-1-1-1-1-11111−i−iii111-1-1-1−i−iii-1-111−i−iiiiiii−i−i−i−i1-1-11−ii1-11-1-11ii−i−i-1-111−iii−i1-1-11−iii−i
χ301-11-1-11-11-1111-1-11-1-1-1-1-11111−i−iii111-1-1-1−i−iii-1-111−i−iiiiiii−i−i−i−i-111-1−ii1-1-111-1ii−i−i-1-111i−i−ii-111-1i−i−ii
χ311-11-1-11-11-1111-1-11-1-1-1-1-11111−i−iii1-1-111-1ii−i−i-1-111ii−i−i−i−i−i−iiiii1-1-11−ii-111-1-11ii−i−i11-1-1−iii−i-111-1i−i−ii
χ321-11-1-11-11-1111-1-11-1-1-1-1-11111−i−iii1-1-111-1ii−i−i-1-111ii−i−i−i−i−i−iiiii-111-1−ii-11-111-1ii−i−i11-1-1i−i−ii1-1-11−iii−i
χ33222222222-2-22-222-2222222220000-20000-20000-2-2-2-200000000000022220000-2-2-2-200000000000000000000
χ34222222222-2-22-222-2222222220000-20000-20000-2-2-2-2000000000000-2-2-2-20000222200000000000000000000
χ35222222222-2-22-222-2-2-2-2-2-2-2-2-20000-20000-20000222200000000000022-2-20000-2-22200000000000000000000
χ36222222222-2-22-222-2-2-2-2-2-2-2-2-20000-20000-200002222000000000000-2-222000022-2-200000000000000000000
χ3722222222-222-22-2-22000000002222-22222-2-2-2-2-200002222000000000000-2-2-2-2000000000000000000000000
χ3822222222-222-22-2-22000000002222-2-2-2-2-2-222220000-2-2-2-2000000000000-2-222000000000000000000000000
χ3922222222-222-22-2-2200000000-2-2-2-2-22222-222220000-2-2-2-200000000000022-2-2000000000000000000000000
χ4022222222-222-22-2-2200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022220000000000002222000000000000000000000000
χ4122-22-22-2-202-20-200222−2−222−2−22i−2i2i−2i02i−2i2i−2i000002−22−22-22-222−2−222−2−2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4222-22-22-2-202-20-200222−2−222−2−22i−2i2i−2i0−2i2i−2i2i000002−22−2-22-22−2−222−2−222000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4322-22-22-2-202-20-200222−2−222−2−2−2i2i−2i2i02i−2i2i−2i000002−22−2-22-22−2−222−2−222000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-22-22-2-202-20-200222−2−222−2−2−2i2i−2i2i0−2i2i−2i2i000002−22−22-22-222−2−222−2−2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4522-22-22-2-202-20-2002−2−222−2−2222i−2i2i−2i02i−2i2i−2i00000−22−222-22-2−2−222−2−222000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4622-22-22-2-202-20-2002−2−222−2−2222i−2i2i−2i0−2i2i−2i2i00000−22−22-22-2222−2−222−2−2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4722-22-22-2-202-20-2002−2−222−2−222−2i2i−2i2i02i−2i2i−2i00000−22−22-22-2222−2−222−2−2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4822-22-22-2-202-20-2002−2−222−2−222−2i2i−2i2i0−2i2i−2i2i00000−22−222-22-2−2−222−2−222000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ492-22-2-22-22222-2-22-2-2000000002i2i−2i−2i-222-2-22−2i−2i2i2i00002i2i−2i−2i000000000000−2i2i-22000000000000000000000000
χ502-22-2-22-22222-2-22-2-2000000002i2i−2i−2i-2-2-22222i2i−2i−2i0000−2i−2i2i2i000000000000−2i2i2-2000000000000000000000000
χ512-22-2-22-22222-2-22-2-200000000−2i−2i2i2i-222-2-222i2i−2i−2i0000−2i−2i2i2i0000000000002i−2i-22000000000000000000000000
χ522-22-2-22-22222-2-22-2-200000000−2i−2i2i2i-2-2-2222−2i−2i2i2i00002i2i−2i−2i0000000000002i−2i2-2000000000000000000000000
χ532-22-2-22-22-2-2-222-2222222-2-2-2-20000-2000020000-2-2220000000000002-22-20000-22-2200000000000000000000
χ542-22-2-22-22-2-2-222-2222222-2-2-2-20000-2000020000-2-222000000000000-22-2200002-22-200000000000000000000
χ552-22-2-22-22-2-2-222-222-2-2-2-222220000-200002000022-2-20000000000002-2-220000-222-200000000000000000000
χ562-22-2-22-22-2-2-222-222-2-2-2-222220000-200002000022-2-2000000000000-222-200002-2-2200000000000000000000
χ572-2-2-2222-202-20200-222−2−2−2−2222-2-2202i−2i−2i2i000002−2−22−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000002−2−22i2−i2−i2i2000000000000
χ582-2-2-2222-202-20200-222−2−2−2−2222-2-220−2i2i2i−2i000002−2−222i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000002−2−22−i2i2i2−i2000000000000
χ592-2-2-2222-202-20200-222−2−2−2−222-222-202i−2i−2i2i000002−2−222i−2i−2i2ii2i2−i2−i2−i2−i2i2i2000000000000−222−2i2−i2−i2i2000000000000
χ602-2-2-2222-202-20200-222−2−2−2−222-222-20−2i2i2i−2i000002−2−22−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2000000000000−222−2−i2i2i2−i2000000000000
χ612-2-2-2222-202-20200-2−2−22222−2−22-2-2202i−2i−2i2i00000−222−2−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2000000000000−222−2−i2i2i2−i2000000000000
χ622-2-2-2222-202-20200-2−2−22222−2−22-2-220−2i2i2i−2i00000−222−22i−2i−2i2i−i2−i2i2i2i2i2−i2−i2000000000000−222−2i2−i2−i2i2000000000000
χ632-2-2-2222-202-20200-2−2−22222−2−2-222-202i−2i−2i2i00000−222−22i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000002−2−22−i2i2i2−i2000000000000
χ642-2-2-2222-202-20200-2−2−22222−2−2-222-20−2i2i2i−2i00000−222−2−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000002−2−22i2−i2−i2i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004000040000000000000000000000000000000000000000000000000000
χ66444-4-4-44-440040-4-404-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ67444-4-4-44-440040-4-40-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ68444-4-4-44-4-400-404400000000000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ69444-4-4-44-4-400-40440000000000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ7044-44-44-4-40-440400-42222−22−222222−22−2200000000000000−2222−222200000000000000000000000000000000000000000000
χ7144-44-44-4-40-440400-4−22−222222−22−2222220000000000000022−2222−2200000000000000000000000000000000000000000000
χ7244-4-44-4-440000000022−22−222222−22−222200000000002i2−2i22i2−2i2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ7344-4-44-4-440000000022−22−222222−22−22220000000000−2i22i2−2i22i200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7444-4-44-4-4400000000−222222−22−222222−2200000000002i2−2i22i2−2i200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7544-4-44-4-4400000000−222222−22−222222−220000000000−2i22i2−2i22i2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ764-4444-4-4-4400-40-44000000000000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ774-4444-4-4-4400-40-440000000000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ784-4444-4-4-4-400404-404-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ794-4444-4-4-4-400404-40-44-444-44-400000000000000000000000000000000000000000000000000000000000000
χ804-44-4-44-444-4-4-444-4400000000000040000-40000000000000000000000000000000000000000000000000000
χ814-4-44-4-4440000000022−22−2222−222222−22000000000022−22−2222000000002-2-22-222-200000000000000000000000000000000
χ824-4-44-4-4440000000022−22−2222−222222−220000000000−222222−2200000000-222-22-2-2200000000000000000000000000000000
χ834-4-44-4-44400000000−222222−2222−22−2222000000000022−22−222200000000-222-22-2-2200000000000000000000000000000000
χ844-4-44-4-44400000000−222222−2222−22−22220000000000−222222−22000000002-2-22-222-200000000000000000000000000000000
χ854-4-4-4444-40-440-40042222−22−22−22−22222200000000000000−222222−2200000000000000000000000000000000000000000000
χ864-4-4-4444-40-440-4004−22−2222222222−22−220000000000000022−22−222200000000000000000000000000000000000000000000

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