Finite Group Databasebeta

← Group #495256

Character table — Group #495256

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222244444444888888884444444488881616161616161616161616161616161644444444444444448888161616161616161622444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111
χ171-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i1-11-1ii−i−iii−i−i1-11-11-11-1
χ181-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii1-11-1ii−i−iii−i−i-11-11-11-11
χ191-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i1-11-1−i−iii−i−iii-11-11-11-11
χ201-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii1-11-1−i−iii−i−iii1-11-11-11-1
χ211-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i−i−iii−i−iii-11-11−i−iii−i−iii1-11-1-11-11
χ221-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iiiii−i−iii−i−i-11-11−i−iii−i−iii-11-111-11-1
χ231-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i−i−iii−i−iii-11-11ii−i−iii−i−i-11-111-11-1
χ241-111-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iiiii−i−iii−i−i-11-11ii−i−iii−i−i1-11-1-11-11
χ251-111-1-1-11-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii1-1-11ii−i−i−i−iii1-1-111-1-11
χ261-111-1-1-11-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i1-1-11ii−i−i−i−iii-111-1-111-1
χ271-111-1-1-11-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii1-1-11−i−iiiii−i−i-111-1-111-1
χ281-111-1-1-11-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11−i−iiiii−i−i1-1-111-1-11
χ291-111-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iiiii−i−i-111-1−i−iiiii−i−i1-1-11-111-1
χ301-111-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i−i−iii-111-1−i−iiiii−i−i-111-11-1-11
χ311-111-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iiiii−i−i-111-1ii−i−i−i−iii-111-11-1-11
χ321-111-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i−i−iii-111-1ii−i−i−i−iii1-1-11-111-1
χ3322222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-2-2-20000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022220000000000000000
χ35222222222222-2-2-2-2-2-2-2-2000000002-22-22-22-2000022−2−222−2−222−2−222−2−2000000000000000000002−22−22−22−200000000
χ36222222222222-2-2-2-2-2-2-2-2000000002-22-22-22-20000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ37222222222222-2-2-2-2-2-2-2-200000000-22-22-22-22000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ38222222222222-2-2-2-2-2-2-2-200000000-22-22-22-220000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
χ3922222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000-2-2220000000000000000
χ4022222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000022-2-20000000000000000
χ4122222222-2-2-2-2-2-22222-2-2000000002-22-2-22-22000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ4222222222-2-2-2-2-2-22222-2-2000000002-22-2-22-220000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ4322222222-2-2-2-2-2-22222-2-200000000-22-222-22-2000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ4422222222-2-2-2-2-2-22222-2-200000000-22-222-22-20000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ4522-2-2-2-2222-22-22-22-22-22-222-2-222-2-2000000002-22-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ4622-2-2-2-2222-22-22-22-22-22-222-2-222-2-2000000002-22-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ4722-2-2-2-2222-22-22-22-22-22-2-2-222-2-22200000000-22-220000000000000000000000002-22-22-22-200000000000000000000
χ4822-2-2-2-2222-22-22-22-22-22-2-2-222-2-22200000000-22-22000000000000000000000000-22-22-22-2200000000000000000000
χ4922-2-2-2-222-22-222-2-22-222-222-2-222-2-200000000-22-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ5022-2-2-2-222-22-222-2-22-222-222-2-222-2-200000000-22-220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ5122-2-2-2-222-22-222-2-22-222-2-2-222-2-222000000002-22-20000000000000000000000002-22-2-22-2200000000000000000000
χ5222-2-2-2-222-22-222-2-22-222-2-2-222-2-222000000002-22-2000000000000000000000000-22-222-22-200000000000000000000
χ532-222-2-2-2222-2-222-2-222-2-2000000002-2-222-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ542-222-2-2-2222-2-222-2-222-2-2000000002-2-222-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ552-222-2-2-2222-2-222-2-222-2-200000000-222-2-222-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ562-222-2-2-2222-2-222-2-222-2-200000000-222-2-222-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ572-222-2-2-2222-2-2-2-222-2-222-2-2-2-2222222-2-222-2-2-2-22200000000000000000000000000000000-22-220000000000000000
χ582-222-2-2-2222-2-2-2-222-2-222-2-2-2-22222-2-222-2-222-2-222000000000000000000000000000000002-22-20000000000000000
χ592-222-2-2-22-2-2222222-2-2-2-2000000002-2-22-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ602-222-2-2-22-2-2222222-2-2-2-2000000002-2-22-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ612-222-2-2-22-2-2222222-2-2-2-200000000-222-22-2-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ622-222-2-2-22-2-2222222-2-2-2-200000000-222-22-2-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ632-222-2-2-22-2-222-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-200000000000000000000000000000000-222-20000000000000000
χ642-222-2-2-22-2-222-2-2-2-22222-2-2-2-22222-2-22222-2-222-2-2000000000000000000000000000000002-2-220000000000000000
χ652-2-2-222-222-2-22-222-2-222-222-2-2-2-222000000002-2-2200000000000000002-2-222-2-220000000000000000000000000000
χ662-2-2-222-222-2-22-222-2-222-222-2-2-2-222000000002-2-220000000000000000-222-2-222-20000000000000000000000000000
χ672-2-2-222-222-2-22-222-2-222-2-2-22222-2-200000000-222-20000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ682-2-2-222-222-2-22-222-2-222-2-2-22222-2-200000000-222-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ692-2-2-222-22-222-2-22-222-22-222-2-2-2-22200000000-222-200000000000000002-2-22-222-20000000000000000000000000000
χ702-2-2-222-22-222-2-22-222-22-222-2-2-2-22200000000-222-20000000000000000-222-22-2-220000000000000000000000000000
χ712-2-2-222-22-222-2-22-222-22-2-2-22222-2-2000000002-2-220000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ722-2-2-222-22-222-2-22-222-22-2-2-22222-2-2000000002-2-22000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ73444-44-4-4-400000000000022−2222−2222−2222−22000000000000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000000
χ74444-44-4-4-400000000000022−2222−2222−2222−2200000000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000000
χ75444-44-4-4-4000000000000−2222−2222−2222−2222000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000000
χ76444-44-4-4-4000000000000−2222−2222−2222−222200000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000000
χ7744-44-44-4-400000000000022−22−222222−22−22220000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000000000000000
χ7844-44-44-4-400000000000022−22−222222−22−2222000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000000000000000
χ7944-44-44-4-4000000000000−222222−22−222222−220000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000000000000000
χ8044-44-44-4-4000000000000−222222−22−222222−22000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000000000000000
χ8144-4-4-4-4444-44-4-44-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-4-444-44-44-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ834-44-4-444-400000000000022−2222−22−2222−2222000000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000000000
χ844-44-4-444-400000000000022−2222−22−2222−222200000000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000000000
χ854-44-4-444-4000000000000−2222−222222−2222−22000000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000000000
χ864-44-4-444-4000000000000−2222−222222−2222−2200000000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000000000
χ874-4-444-44-400000000000022−22−2222−222222−220000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000000000
χ884-4-444-44-400000000000022−22−2222−222222−22000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000000000
χ894-4-444-44-4000000000000−222222−2222−22−22220000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000000000
χ904-4-444-44-4000000000000−222222−2222−22−2222000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000000000
χ914-4-4-444-444-4-444-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44-444-44-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000

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