Finite Group Databasebeta

← Group #498498

Character table — Group #498498

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888822444444448888161616161616161616161616161616164444444488881616161616161616222244444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ5111111111111111111111111-1-111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1
χ9111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1
χ10111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-1-1-111
χ11111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ12111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111
χ171-1111-1-1-11ii−i−i-1-1111-1-1-1-1111-1i−i1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−ii−i1-1ii−i−i11-1-11-11-11-11-1i−ii−i
χ181-1111-1-1-11ii−i−i-1-1111-1-1-1-1111-1i−i1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii−i−iiii−i1-1ii−i−i11-1-1-11-11-11-11−ii−ii
χ191-1111-1-1-11ii−i−i-1-1111-1-1-1-1111-1i−i1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iiii−i1-1−i−iii-1-1111-1-111-1-11i−i−ii
χ201-1111-1-1-11ii−i−i-1-1111-1-1-1-1111-1i−i1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−ii−i1-1−i−iii-1-111-111-1-111-1−iii−i
χ211-1111-1-1-11ii−i−i-1-1111-1-1-1-111-11i−i-11−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i−ii-11−i−iii-1-111-111-11-1-11−ii−ii
χ221-1111-1-1-11ii−i−i-1-1111-1-1-1-111-11i−i-11−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii−i−iii−ii-11−i−iii-1-1111-1-11-111-1i−ii−i
χ231-1111-1-1-11ii−i−i-1-1111-1-1-1-111-11i−i-11−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii−ii-11ii−i−i11-1-1-11-111-11-1−iii−i
χ241-1111-1-1-11ii−i−i-1-1111-1-1-1-111-11i−i-11−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−i−ii-11ii−i−i11-1-11-11-1-11-11i−i−ii
χ251-1111-1-1-11−i−iii-1-1111-1-1-1-1111-1−ii1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii−ii1-1ii−i−i-1-111-111-1-111-1i−i−ii
χ261-1111-1-1-11−i−iii-1-1111-1-1-1-1111-1−ii1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i−ii1-1ii−i−i-1-1111-1-111-1-11−iii−i
χ271-1111-1-1-11−i−iii-1-1111-1-1-1-1111-1−ii1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−i−ii1-1−i−iii11-1-1-11-11-11-11i−ii−i
χ281-1111-1-1-11−i−iii-1-1111-1-1-1-1111-1−ii1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii−ii1-1−i−iii11-1-11-11-11-11-1−ii−ii
χ291-1111-1-1-11−i−iii-1-1111-1-1-1-111-11−ii-11ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iiii−i-11−i−iii11-1-11-11-1-11-11−iii−i
χ301-1111-1-1-11−i−iii-1-1111-1-1-1-111-11−ii-11ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−ii−i-11−i−iii11-1-1-11-111-11-1i−i−ii
χ311-1111-1-1-11−i−iii-1-1111-1-1-1-111-11−ii-11ii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−ii−i-11ii−i−i-1-1111-1-11-111-1−ii−ii
χ321-1111-1-1-11−i−iii-1-1111-1-1-1-111-11−ii-11ii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iiii−i-11ii−i−i-1-111-111-11-1-11i−ii−i
χ332222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000-2-2-2-200000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000000000
χ35222222222-2-2-2-2222-2-2-2-2-2-2-2-222-2-222-2-2-2-2222200000000000000000000000022-2-200000000000000000000
χ36222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000-2-22200000000000000000000
χ3722222222-22222-2-2-20000000022-2-2-2-22-22-2000022−2−222−2−222−2−222−2−20000000000002−22−22−22−2000000000000
χ3822222222-22222-2-2-20000000022-2-2-2-22-22-20000−2−222−2−222−2−222−2−222000000000000−22−22−22−22000000000000
χ3922222222-22222-2-2-200000000-2-2-2-222-22-22000022−2−222−2−222−2−222−2−2000000000000−22−22−22−22000000000000
χ4022222222-22222-2-2-200000000-2-2-2-222-22-220000−2−222−2−222−2−222−2−2220000000000002−22−22−22−2000000000000
χ4122222222-2-2-2-2-2-2-2-2000000002222-2-2-22-22000022−2−222−2−2−2−222−2−2220000000000002−22−2−22−22000000000000
χ4222222222-2-2-2-2-2-2-2-2000000002222-2-2-22-220000−2−222−2−22222−2−222−2−2000000000000−22−222−22−2000000000000
χ4322222222-2-2-2-2-2-2-2-200000000-2-222222-22-2000022−2−222−2−2−2−222−2−222000000000000−22−222−22−2000000000000
χ4422222222-2-2-2-2-2-2-2-200000000-2-222222-22-20000−2−222−2−22222−2−222−2−20000000000002−22−2−22−22000000000000
χ45222-2-2-2-22-200002-222222-2-2-2-200000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000
χ46222-2-2-2-22-200002-222222-2-2-2-200000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-22-22000000000000000000000000
χ47222-2-2-2-22-200002-222222-2-2-2-20000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-22000000000000000000000000
χ48222-2-2-2-22-200002-222222-2-2-2-20000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2000000000000000000000000
χ492-2222-2-2-222i2i−2i−2i-2-22-2-22222-2-22-22i−2i2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i-2200000000000000000000
χ502-2222-2-2-222i2i−2i−2i-2-22-2-22222-2-2-222i−2i-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000002i−2i2-200000000000000000000
χ512-2222-2-2-22−2i−2i2i2i-2-22-2-22222-2-22-2−2i2i2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i-2200000000000000000000
χ522-2222-2-2-22−2i−2i2i2i-2-22-2-22222-2-2-22−2i2i-222i2i−2i−2i2i2i−2i−2i000000000000000000000000−2i2i2-200000000000000000000
χ532-2222-2-2-2-22i2i−2i−2i22-2000000002-2−2i2i-222i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000i2−i2−i2i22−2−22000000000000
χ542-2222-2-2-2-22i2i−2i−2i22-2000000002-2−2i2i-222i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000−i2i2i2−i2−222−2000000000000
χ552-2222-2-2-2-22i2i−2i−2i22-200000000-22−2i2i2-2−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000−i2i2i2−i2−222−2000000000000
χ562-2222-2-2-2-22i2i−2i−2i22-200000000-22−2i2i2-2−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000i2−i2−i2i22−2−22000000000000
χ572-2222-2-2-2-2−2i−2i2i2i22-2000000002-22i−2i-22−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000i2−i2−i2i2−222−2000000000000
χ582-2222-2-2-2-2−2i−2i2i2i22-2000000002-22i−2i-22−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000−i2i2i2−i22−2−22000000000000
χ592-2222-2-2-2-2−2i−2i2i2i22-200000000-222i−2i2-22i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000−i2i2i2−i22−2−22000000000000
χ602-2222-2-2-2-2−2i−2i2i2i22-200000000-222i−2i2-22i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000i2−i2−i2i2−222−2000000000000
χ612-22-2-222-2-20000-22222-2-222-2-200000000000000000000002i−2i2i−2i−2i2i−2i2i2-2-22−2i2i2i−2i000000000000000000000000
χ622-22-2-222-2-20000-22222-2-222-2-200000000000000000000002i−2i2i−2i−2i2i−2i2i-222-22i−2i−2i2i000000000000000000000000
χ632-22-2-222-2-20000-22222-2-222-2-20000000000000000000000−2i2i−2i2i2i−2i2i−2i2-2-222i−2i−2i2i000000000000000000000000
χ642-22-2-222-2-20000-22222-2-222-2-20000000000000000000000−2i2i−2i2i2i−2i2i−2i-222-2−2i2i2i−2i000000000000000000000000
χ65444-4-4-4-4440000-44-40000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ66444-4-4-4-4440000-44-4000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ67444-4-4-4-44-400004-44-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000
χ6844-44-44-4-40000000022−2222−2222−2222−22000000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000000000000000
χ6944-44-44-4-40000000022−2222−2222−2222−2200000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000000000000000
χ7044-44-44-4-400000000−2222−2222−2222−2222000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000000000000000000000
χ7144-44-44-4-400000000−2222−2222−2222−222200000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000000000000000000000
χ7244-4-44-44-404i−4i4i−4i00022−2222−22−2222−222200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ7344-4-44-44-404i−4i4i−4i000−2222−222222−2222−220000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ7444-4-44-44-40−4i4i−4i4i00022−2222−22−2222−22220000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ7544-4-44-44-40−4i4i−4i4i000−2222−222222−2222−2200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ764-44-4-444-4400004-4-40000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ774-44-4-444-4400004-4-4000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ784-44-4-444-4-40000-444-4-444-4-44400000000000000000000000000000000000000000000000000000000000000
χ794-4-44-4-4440000000022−22−2222−222222−22000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000000000
χ804-4-44-4-4440000000022−22−2222−222222−2200000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000000000
χ814-4-44-4-44400000000−222222−2222−22−2222000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000000000
χ824-4-44-4-44400000000−222222−2222−22−222200000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000000000
χ834-4-4-444-4404-4-4400022−22−222222−22−2222000000000022−22−2222000000000000000000000000000000000000000000000000
χ844-4-4-444-4404-4-44000−222222−22−222222−220000000000−222222−22000000000000000000000000000000000000000000000000
χ854-4-4-444-440-444-400022−22−222222−22−22220000000000−222222−22000000000000000000000000000000000000000000000000
χ864-4-4-444-440-444-4000−222222−22−222222−22000000000022−22−2222000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.