Finite Group Databasebeta

← Group #225697

Character table — Group #225697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822444444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-111-1-1-1-111
χ171-1-1111-1-1-1-111-1-1111111-1-1-1-1ii−i−i-1ii−i−i111-1-11111-1-1-1-11111-1-1-1-11-1i−i1-111-1-1i−iii−i−iii−i−ii−ii−ii−ii−i1-11-1
χ181-1-1111-1-1-1-111-1-1111111-1-1-1-1ii−i−i-1ii−i−i111-1-11111-1-1-1-11111-1-1-1-1-11i−i-11-1-111i−iii−i−iii−i−i−ii−ii−ii−ii-11-11
χ191-1-1111-1-1-1-111-1-1111111-1-1-1-1ii−i−i-1−i−iii111-1-1-1-1-1-11111-1-1-1-111111-1i−i1-111-1-1−iiii−i−i−i−iiii−ii−i−ii−ii-11-11
χ201-1-1111-1-1-1-111-1-1111111-1-1-1-1ii−i−i-1−i−iii111-1-1-1-1-1-11111-1-1-1-11111-11i−i-11-1-111−iiii−i−i−i−iii−ii−iii−ii−i1-11-1
χ211-1-1111-1-1-1-111-1-1111111-1-1-1-1−i−iii-1ii−i−i111-1-1-1-1-1-11111-1-1-1-111111-1−ii1-111-1-1i−i−i−iiiii−i−i−ii−iii−ii−i-11-11
χ221-1-1111-1-1-1-111-1-1111111-1-1-1-1−i−iii-1ii−i−i111-1-1-1-1-1-11111-1-1-1-11111-11−ii-11-1-111i−i−i−iiiii−i−ii−ii−i−ii−ii1-11-1
χ231-1-1111-1-1-1-111-1-1111111-1-1-1-1−i−iii-1−i−iii111-1-11111-1-1-1-11111-1-1-1-11-1−ii1-111-1-1−ii−i−iii−i−iii−ii−ii−ii−ii1-11-1
χ241-1-1111-1-1-1-111-1-1111111-1-1-1-1−i−iii-1−i−iii111-1-11111-1-1-1-11111-1-1-1-1-11−ii-11-1-111−ii−i−iii−i−iiii−ii−ii−ii−i-11-11
χ251-1-1111-1-1-1-111-1-111-1-1-1-11111ii−i−i-1ii−i−i1-1-1111111-1-1-1-1-1-1-1-111111-1i−i1-1-1-111i−i−i−iii−i−iiii−i−iii−i−ii1-1-11
χ261-1-1111-1-1-1-111-1-111-1-1-1-11111ii−i−i-1ii−i−i1-1-1111111-1-1-1-1-1-1-1-11111-11i−i-1111-1-1i−i−i−iii−i−iii−iii−i−iii−i-111-1
χ271-1-1111-1-1-1-111-1-111-1-1-1-11111ii−i−i-1−i−iii1-1-111-1-1-1-111111111-1-1-1-11-1i−i1-1-1-111−ii−i−iiiii−i−ii−i−ii−iii−i-111-1
χ281-1-1111-1-1-1-111-1-111-1-1-1-11111ii−i−i-1−i−iii1-1-111-1-1-1-111111111-1-1-1-1-11i−i-1111-1-1−ii−i−iiiii−i−i−iii−ii−i−ii1-1-11
χ291-1-1111-1-1-1-111-1-111-1-1-1-11111−i−iii-1ii−i−i1-1-111-1-1-1-111111111-1-1-1-11-1−ii1-1-1-111i−iii−i−i−i−iii−iii−ii−i−ii-111-1
χ301-1-1111-1-1-1-111-1-111-1-1-1-11111−i−iii-1ii−i−i1-1-111-1-1-1-111111111-1-1-1-1-11−ii-1111-1-1i−iii−i−i−i−iiii−i−ii−iii−i1-1-11
χ311-1-1111-1-1-1-111-1-111-1-1-1-11111−i−iii-1−i−iii1-1-1111111-1-1-1-1-1-1-1-111111-1−ii1-1-1-111−iiii−i−iii−i−i−iii−i−iii−i1-1-11
χ321-1-1111-1-1-1-111-1-111-1-1-1-11111−i−iii-1−i−iii1-1-1111111-1-1-1-1-1-1-1-11111-11−ii-1111-1-1−iiii−i−iii−i−ii−i−iii−i−ii-111-1
χ332222222222-2-2-2-222000000002222-22222-2000022-2-222-2-20000000000-2-2000000-2-200000000000000000000
χ342222222222-2-2-2-222000000002222-2-2-2-2-2-20000-2-222-2-2220000000000-2-20000002200000000000000000000
χ352222222222-2-2-2-22200000000-2-2-2-2-22222-20000-2-222-2-222000000000022000000-2-200000000000000000000
χ362222222222-2-2-2-22200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000000220000002200000000000000000000
χ3722222222-2-22222-2-2222222220000-20000-2-2-2-2-200000000000000002200-2-22-22-20000000000000000000000
χ3822222222-2-22222-2-2222222220000-20000-2-2-2-2-20000000000000000-2-20022-22-220000000000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-20000-20000-2222200000000000000002200-2-2-22-220000000000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-20000-20000-222220000000000000000-2-200222-22-20000000000000000000000
χ4122-22-2-22-22-200002-2i2i2−i2−i2i2i2−i2−i22-22-202-22-20i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4222-22-2-22-22-200002-2i2i2−i2−i2i2i2−i2−i22-22-20-22-220i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4322-22-2-22-22-200002-2i2i2−i2−i2i2i2−i2−i2-22-2202-22-20i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-22-2-22-22-200002-2i2i2−i2−i2i2i2−i2−i2-22-220-22-220i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4522-22-2-22-22-200002-2−i2−i2i2i2−i2−i2i2i22-22-202-22-20−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4622-22-2-22-22-200002-2−i2−i2i2i2−i2−i2i2i22-22-20-22-220−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4722-22-2-22-22-200002-2−i2−i2i2i2−i2−i2i2i2-22-2202-22-20−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4822-22-2-22-22-200002-2−i2−i2i2i2−i2−i2i2i2-22-220-22-220−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ492-222-2-2-22-2200002-2i2i2−i2−i2−i2−i2i2i22i−2i−2i2i02i−2i−2i2i0i2−i2−i2i22-200-2200i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ502-222-2-2-22-2200002-2i2i2−i2−i2−i2−i2i2i22i−2i−2i2i0−2i2i2i−2i0i2−i2−i2i2-22002-200−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ512-222-2-2-22-2200002-2i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i02i−2i−2i2i0i2−i2−i2i2-22002-200−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ522-222-2-2-22-2200002-2i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i0−2i2i2i−2i0i2−i2−i2i22-200-2200i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ532-222-2-2-22-2200002-2−i2−i2i2i2i2i2−i2−i22i−2i−2i2i02i−2i−2i2i0−i2i2i2−i22-200-2200−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ542-222-2-2-22-2200002-2−i2−i2i2i2i2i2−i2−i22i−2i−2i2i0−2i2i2i−2i0−i2i2i2−i2-22002-200i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ552-222-2-2-22-2200002-2−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i02i−2i−2i2i0−i2i2i2−i2-22002-200i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ562-222-2-2-22-2200002-2−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i0−2i2i2i−2i0−i2i2i2−i22-200-2200−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ572-2-2222-2-22222-2-2-2-22222-2-2-2-2000020000-2-2-22200000000000000002-200-222-2-220000000000000000000000
χ582-2-2222-2-22222-2-2-2-22222-2-2-2-2000020000-2-2-2220000000000000000-22002-2-222-20000000000000000000000
χ592-2-2222-2-22222-2-2-2-2-2-2-2-22222000020000-222-2-200000000000000002-200-22-222-20000000000000000000000
χ602-2-2222-2-22222-2-2-2-2-2-2-2-22222000020000-222-2-20000000000000000-22002-22-2-220000000000000000000000
χ612-2-2222-2-2-2-2-2-22222000000002i2i−2i−2i22i2i−2i−2i-2000022-2-2-2-2220000000000−2i2i000000−2i2i00000000000000000000
χ622-2-2222-2-2-2-2-2-22222000000002i2i−2i−2i2−2i−2i2i2i-20000-2-22222-2-20000000000−2i2i0000002i−2i00000000000000000000
χ632-2-2222-2-2-2-2-2-2222200000000−2i−2i2i2i22i2i−2i−2i-20000-2-22222-2-200000000002i−2i000000−2i2i00000000000000000000
χ642-2-2222-2-2-2-2-2-2222200000000−2i−2i2i2i2−2i−2i2i2i-2000022-2-2-2-22200000000002i−2i0000002i−2i00000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004000040000000000000000000000000000000000000000000000000000
χ66444-44-4-4-4004-44-40000000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ67444-44-4-4-4004-44-400000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ68444-44-4-4-400-44-44004-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ69444-44-4-4-400-44-4400-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ7044-44-4-44-4-440000-442i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ7144-44-4-44-4-440000-44−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ7244-4-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000022−220022−222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ7344-4-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000−222200−2222−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7444-4-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000022−220022−22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7544-4-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000−222200−22222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ764-444-4-4-444-40000-442i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ774-444-4-4-444-40000-44−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ784-44-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000022−2200−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ794-44-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000−22220022−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ804-44-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000022−2200−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ814-44-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000−22220022−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ824-4-4444-4-444-4-444-4-4000000000000-4000040000000000000000000000000000000000000000000000000000
χ834-4-4-44-444004-4-440000000000000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ844-4-4-44-444004-4-4400000000000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ854-4-4-44-44400-444-4004-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ864-4-4-44-44400-444-400-44-444-44-400000000000000000000000000000000000000000000000000000000000000

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