Finite Group Databasebeta

← Group #220950

Character table — Group #220950

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822224444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111
χ171-1-11-11-1111-11-1-1-111111-1-1-1-111-1-1ii−i−i1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−i1-11-11-1ii−i−i11-1-11-1i−ii−i1-1i−ii−i
χ181-1-11-11-1111-11-1-1-111111-1-1-1-111-1-1ii−i−i1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11i−i-11-11-11ii−i−i11-1-1-11−ii−ii-11−ii−ii
χ191-1-11-11-1111-11-1-1-111111-1-1-1-111-1-1−i−iii1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii1-11-11-1−i−iii11-1-11-1−ii−ii1-1−ii−ii
χ201-1-11-11-1111-11-1-1-111111-1-1-1-111-1-1−i−iii1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11−ii-11-11-11−i−iii11-1-1-11i−ii−i-11i−ii−i
χ211-1-11-11-1111-11-1-1-111111-1-1-1-1-1-111ii−i−i1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1i−i1-11-11-1ii−i−i-1-111-11i−ii−i-11−ii−ii
χ221-1-11-11-1111-11-1-1-111111-1-1-1-1-1-111ii−i−i1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−i-11-11-11ii−i−i-1-1111-1−ii−ii1-1i−ii−i
χ231-1-11-11-1111-11-1-1-111111-1-1-1-1-1-111−i−iii1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1−ii1-11-11-1−i−iii-1-111-11−ii−ii-11i−ii−i
χ241-1-11-11-1111-11-1-1-111111-1-1-1-1-1-111−i−iii1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii-11-11-11−i−iii-1-1111-1i−ii−i1-1−ii−ii
χ251-1-11-11-1111-11-1-1-11-1-1-1-1111111-1-1ii−i−i1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-11-1i−i1-1-11-11−i−iii-1-111-11−iii−i1-1i−i−ii
χ261-1-11-11-1111-11-1-1-11-1-1-1-1111111-1-1ii−i−i1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i-111-11-1−i−iii-1-1111-1i−i−ii-11−iii−i
χ271-1-11-11-1111-11-1-1-11-1-1-1-1111111-1-1−i−iii1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11-1−ii1-1-11-11ii−i−i-1-111-11i−i−ii1-1−iii−i
χ281-1-11-11-1111-11-1-1-11-1-1-1-1111111-1-1−i−iii1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−ii-111-11-1ii−i−i-1-1111-1−iii−i-11i−i−ii
χ291-1-11-11-1111-11-1-1-11-1-1-1-11111-1-111ii−i−i1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i1-1-11-11−i−iii11-1-11-1−iii−i-11−iii−i
χ301-1-11-11-1111-11-1-1-11-1-1-1-11111-1-111ii−i−i1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-11i−i-111-11-1−i−iii11-1-1-11i−i−ii1-1i−i−ii
χ311-1-11-11-1111-11-1-1-11-1-1-1-11111-1-111−i−iii1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1−ii1-1-11-11ii−i−i11-1-11-1i−i−ii-11i−i−ii
χ321-1-11-11-1111-11-1-1-11-1-1-1-11111-1-111−i−iii1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11-11−ii-111-11-1ii−i−i11-1-1-11−iii−i1-1−iii−i
χ332222222222-2-2-222-20000000022222222-2-2000022-2-222-2-200000000-2-200-2-200000000000000000000000000
χ342222222222-2-2-222-2000000002222-2-2-2-2-2-20000-2-222-2-22200000000-2-2002200000000000000000000000000
χ352222222222-2-2-222-200000000-2-2-2-22222-2-20000-2-222-2-222000000002200-2-200000000000000000000000000
χ362222222222-2-2-222-200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000022002200000000000000000000000000
χ3722222222-2-2222-2-222222222200000000-2-2-2-2-2-20000000000000000002200-2-2-2-22200000000000000000000
χ3822222222-2-2222-2-222222222200000000-2-2-2-2-2-2000000000000000000-2-2002222-2-200000000000000000000
χ3922222222-2-2222-2-22-2-2-2-2-2-2-2-200000000-2-222220000000000000000002200-2-222-2-200000000000000000000
χ4022222222-2-2222-2-22-2-2-2-2-2-2-2-200000000-2-22222000000000000000000-2-20022-2-22200000000000000000000
χ4122-22-2-22-22-20002-20i2i2−i2−i2i2i2−i2−i22i−2i2i−2i2-22-200i2−i2i2−i22i−2i002i−2i0022−2−222−2−2000000000000i2−i2i2−i22−22−2000000000000
χ4222-22-2-22-22-20002-20i2i2−i2−i2i2i2−i2−i22i−2i2i−2i-22-2200i2−i2i2−i2−2i2i00−2i2i00−2−222−2−222000000000000−i2i2−i2i22−22−2000000000000
χ4322-22-2-22-22-20002-20i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i2-22-200i2−i2i2−i2−2i2i00−2i2i00−2−222−2−222000000000000i2−i2i2−i2−22−22000000000000
χ4422-22-2-22-22-20002-20i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i-22-2200i2−i2i2−i22i−2i002i−2i0022−2−222−2−2000000000000−i2i2−i2i2−22−22000000000000
χ4522-22-2-22-22-20002-20−i2−i2i2i2−i2−i2i2i22i−2i2i−2i2-22-200−i2i2−i2i22i−2i002i−2i00−2−222−2−222000000000000−i2i2−i2i2−22−22000000000000
χ4622-22-2-22-22-20002-20−i2−i2i2i2−i2−i2i2i22i−2i2i−2i-22-2200−i2i2−i2i2−2i2i00−2i2i0022−2−222−2−2000000000000i2−i2i2−i2−22−22000000000000
χ4722-22-2-22-22-20002-20−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i2-22-200−i2i2−i2i2−2i2i00−2i2i0022−2−222−2−2000000000000−i2i2−i2i22−22−2000000000000
χ4822-22-2-22-22-20002-20−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i-22-2200−i2i2−i2i22i−2i002i−2i00−2−222−2−222000000000000i2−i2i2−i22−22−2000000000000
χ492-2222-2-2-22-2000-220i2i2−i2−i2−i2−i2i2i22i−2i−2i2i2i−2i−2i2i00i2−i2−i2i2-22002-200i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ502-2222-2-2-22-2000-220i2i2−i2−i2−i2−i2i2i22i−2i−2i2i−2i2i2i−2i00i2−i2−i2i22-200-2200−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ512-2222-2-2-22-2000-220i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i2i−2i−2i2i00i2−i2−i2i22-200-2200−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ522-2222-2-2-22-2000-220i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i−2i2i2i−2i00i2−i2−i2i2-22002-200i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ532-2222-2-2-22-2000-220−i2−i2i2i2i2i2−i2−i22i−2i−2i2i2i−2i−2i2i00−i2i2i2−i2-22002-200−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ542-2222-2-2-22-2000-220−i2−i2i2i2i2i2−i2−i22i−2i−2i2i−2i2i2i−2i00−i2i2i2−i22-200-2200i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ552-2222-2-2-22-2000-220−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i2i−2i−2i2i00−i2i2i2−i22-200-2200i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ562-2222-2-2-22-2000-220−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i−2i2i2i−2i00−i2i2i2−i2-22002-200−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ572-2-22-22-22222-22-2-2-20000000022-2-22i2i−2i−2i-2200002i2i−2i−2i−2i−2i2i2i00000000-2200−2i2i00000000000000000000000000
χ582-2-22-22-22222-22-2-2-20000000022-2-2−2i−2i2i2i-220000−2i−2i2i2i2i2i−2i−2i00000000-22002i−2i00000000000000000000000000
χ592-2-22-22-22222-22-2-2-200000000-2-2222i2i−2i−2i-220000−2i−2i2i2i2i2i−2i−2i000000002-200−2i2i00000000000000000000000000
χ602-2-22-22-22222-22-2-2-200000000-2-222−2i−2i2i2i-2200002i2i−2i−2i−2i−2i2i2i000000002-2002i−2i00000000000000000000000000
χ612-2-22-22-22-2-2-22-22222222-2-2-2-200000000-22-2-2220000000000000000002-200-22-222-200000000000000000000
χ622-2-22-22-22-2-2-22-22222222-2-2-2-200000000-22-2-222000000000000000000-22002-22-2-2200000000000000000000
χ632-2-22-22-22-2-2-22-2222-2-2-2-2222200000000-2222-2-20000000000000000002-200-222-2-2200000000000000000000
χ642-2-22-22-22-2-2-22-2222-2-2-2-2222200000000-2222-2-2000000000000000000-22002-2-222-200000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ66444-4-4-4-440000000022−2222−2222−2222−2200000000000000002i2−2i2002i2−2i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ67444-4-4-4-440000000022−2222−2222−2222−220000000000000000−2i22i200−2i22i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ68444-4-4-4-4400000000−2222−2222−2222−222200000000000000002i2−2i2002i2−2i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ69444-4-4-4-4400000000−2222−2222−2222−22220000000000000000−2i22i200−2i22i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ7044-44-4-44-4-44000-4402i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ7144-44-4-44-4-44000-440−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ7244-4-444-4-4004-4-40040000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ7344-4-444-4-4004-4-4004000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ7444-4-444-4-400-44400-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-400-44400-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ764-4444-4-4-4-440004-402i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ774-4444-4-4-4-440004-40−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ784-44-4-444-40044-400-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ794-44-4-444-40044-400-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ804-44-4-444-400-4-4400400000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ814-44-4-444-400-4-44004000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000
χ824-4-44-44-44-4-44-4444-400000000000000004-40000000000000000000000000000000000000000000000000000
χ834-4-4-44-4440000000022−2222−22−2222−2222000000000000000022−2200−22222-22-2-22-2200000000000000000000000000000000
χ844-4-4-44-4440000000022−2222−22−2222−22220000000000000000−22220022−22-22-222-22-200000000000000000000000000000000
χ854-4-4-44-44400000000−2222−222222−2222−22000000000000000022−2200−2222-22-222-22-200000000000000000000000000000000
χ864-4-4-44-44400000000−2222−222222−2222−220000000000000000−22220022−222-22-2-22-2200000000000000000000000000000000

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