Finite Group Databasebeta

← Group #495992

Character table — Group #495992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444888888884444444488881616161616161616161616161616161644444444444444448888161616161616161644444444
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1
χ911111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ1211111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111
χ1711-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1ii−i−i11-1-11-1i−i11-1-1ii−i−ii−ii−i1-11-1
χ1811-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111−i−iii-1-1111-1i−i11-1-1ii−i−i−ii−ii-11-11
χ1911-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1ii−i−i11-1-11-1i−i-1-111−i−iii−ii−ii-11-11
χ2011-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−i-1-1-1-11111−i−i−i−iiiii−i−iii-1-111−i−iii-1-1111-1i−i-1-111−i−iiii−ii−i1-11-1
χ2111-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1−i−iii-1-111-11−ii-1-111−i−iiii−i−ii1-1-11
χ2211-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111ii−i−i11-1-1-11−ii-1-111−i−iii−iii−i-111-1
χ2311-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1−i−iii-1-111-11−ii11-1-1ii−i−i−iii−i-111-1
χ2411-11-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−i-1-1-1-11111−i−i−i−iiiii−i−iii-1-111ii−i−i11-1-1-11−ii11-1-1ii−i−ii−i−ii1-1-11
χ2511-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111ii−i−i-1-1111-1−ii11-1-1−i−iiii−ii−i-11-11
χ2611-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1−i−iii11-1-11-1−ii11-1-1−i−iii−ii−ii1-11-1
χ2711-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iii-1-1-1-11111iiii−i−i−i−iii−i−i-1-111ii−i−i-1-1111-1−ii-1-111ii−i−i−ii−ii1-11-1
χ2811-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iii-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1−i−iii11-1-11-1−ii-1-111ii−i−ii−ii−i-11-11
χ2911-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111−i−iii11-1-1-11i−i-1-111ii−i−ii−i−ii-111-1
χ3011-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1ii−i−i-1-111-11i−i-1-111ii−i−i−iii−i1-1-11
χ3111-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iii-1-1-1-11111iiii−i−i−i−iii−i−i-1-111−i−iii11-1-1-11i−i11-1-1−i−iii−iii−i1-1-11
χ3211-11-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iii-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1ii−i−i-1-111-11i−i11-1-1−i−iiii−i−ii-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
χ35222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000022−2−222−2−222−2−222−2−2000000000000000000002−22−22−22−200000000
χ36222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ37222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ38222222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
χ3922222222-2-2-2-22222-2-2-2-20000000022-2-222-2-2000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ4022222222-2-2-2-22222-2-2-2-20000000022-2-222-2-20000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ4122222222-2-2-2-22222-2-2-2-200000000-2-222-2-222000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ4222222222-2-2-2-22222-2-2-2-200000000-2-222-2-2220000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-222222200000000000000000000000000000000-2-2220000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222220000000000000000000000000000000022-2-20000000000000000
χ4522-22-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2-2-222-2-2222-22i−2i2i−2i2-2−2i−2i2i2i00000000000000000000000000000000-22−2i2i0000000000000000
χ4622-22-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2-2-222-2-222-22−2i2i−2i2i-22−2i−2i2i2i000000000000000000000000000000002-22i−2i0000000000000000
χ4722-22-2-2-222i2i−2i−2i−2i−2i2i2i-2-222000000002-22i−2i−2i2i-22000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22i2−i2−i2i200000000
χ4822-22-2-2-222i2i−2i−2i−2i−2i2i2i-2-222000000002-22i−2i−2i2i-220000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−i2i2i2−i200000000
χ4922-22-2-2-222i2i−2i−2i−2i−2i2i2i-2-22200000000-22−2i2i2i−2i2-2000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−i2i2i2−i200000000
χ5022-22-2-2-222i2i−2i−2i−2i−2i2i2i-2-22200000000-22−2i2i2i−2i2-20000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22i2−i2−i2i200000000
χ5122-22-2-2-22−2i−2i2i2i2i2i−2i−2i-2-222000000002-2−2i2i2i−2i-22000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−i2i2i2−i200000000
χ5222-22-2-2-22−2i−2i2i2i2i2i−2i−2i-2-222000000002-2−2i2i2i−2i-220000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2i2−i2−i2i200000000
χ5322-22-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22200000000-222i−2i−2i2i2-2000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2i2−i2−i2i200000000
χ5422-22-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22200000000-222i−2i−2i2i2-20000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−i2i2i2−i200000000
χ5522-22-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2-2-222-2-2222-2−2i2i−2i2i2-22i2i−2i−2i00000000000000000000000000000000-222i−2i0000000000000000
χ5622-22-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2-2-222-2-222-222i−2i2i−2i-222i2i−2i−2i000000000000000000000000000000002-2−2i2i0000000000000000
χ572-2222-2-2-22-22-22-22-22-22-22222-2-2-2-2000000002-22-200000000000000002-22-22-22-20000000000000000000000000000
χ582-2222-2-2-22-22-22-22-22-22-22222-2-2-2-2000000002-22-20000000000000000-22-22-22-220000000000000000000000000000
χ592-2222-2-2-22-22-22-22-22-22-2-2-2-2-2222200000000-22-220000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ602-2222-2-2-22-22-22-22-22-22-2-2-2-2-2222200000000-22-22000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ612-2222-2-2-2-22-22-22-222-22-22222-2-2-2-200000000-22-2200000000000000002-22-2-22-220000000000000000000000000000
χ622-2222-2-2-2-22-22-22-222-22-22222-2-2-2-200000000-22-220000000000000000-22-222-22-20000000000000000000000000000
χ632-2222-2-2-2-22-22-22-222-22-2-2-2-2-22222000000002-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ642-2222-2-2-2-22-22-22-222-22-2-2-2-2-22222000000002-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ652-2-22-222-22i−2i−2i2i2i−2i−2i2i2-2-2222-2-2-2-222000000002i−2i−2i2i00000000000000002i−2i−2i2i2-2-220000000000000000000000000000
χ662-2-22-222-22i−2i−2i2i2i−2i−2i2i2-2-2222-2-2-2-222000000002i−2i−2i2i0000000000000000−2i2i2i−2i-222-20000000000000000000000000000
χ672-2-22-222-22i−2i−2i2i2i−2i−2i2i2-2-22-2-22222-2-200000000−2i2i2i−2i0000000000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ682-2-22-222-22i−2i−2i2i2i−2i−2i2i2-2-22-2-22222-2-200000000−2i2i2i−2i000000000000000000000000-222-22i−2i−2i2i00000000000000000000
χ692-2-22-222-2−2i2i2i−2i−2i2i2i−2i2-2-2222-2-2-2-22200000000−2i2i2i−2i00000000000000002i−2i−2i2i-222-20000000000000000000000000000
χ702-2-22-222-2−2i2i2i−2i−2i2i2i−2i2-2-2222-2-2-2-22200000000−2i2i2i−2i0000000000000000−2i2i2i−2i2-2-220000000000000000000000000000
χ712-2-22-222-2−2i2i2i−2i−2i2i2i−2i2-2-22-2-22222-2-2000000002i−2i−2i2i0000000000000000000000002-2-222i−2i−2i2i00000000000000000000
χ722-2-22-222-2−2i2i2i−2i−2i2i2i−2i2-2-22-2-22222-2-2000000002i−2i−2i2i000000000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ73444-4-4-44-400000000000022−2222−2222−2222−220000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000000000000000
χ74444-4-4-44-400000000000022−2222−2222−2222−22000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000000000000000
χ75444-4-4-44-4000000000000−2222−2222−2222−22220000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000000000000000
χ76444-4-4-44-4000000000000−2222−2222−2222−2222000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000000000000000
χ7744-4-444-4-400000000000022−22−222222−22−22220000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000000000000000
χ7844-4-444-4-400000000000022−22−222222−22−2222000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000000000000000
χ7944-4-444-4-4000000000000−222222−22−222222−220000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000000000000000
χ8044-4-444-4-4000000000000−222222−22−222222−22000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000000000000000
χ814-4444-4-4-44-44-4-44-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ824-4444-4-4-4-44-444-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ834-44-4-44-4400000000000022−2222−22−2222−2222000000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000000000
χ844-44-4-44-4400000000000022−2222−22−2222−222200000000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000000000
χ854-44-4-44-44000000000000−2222−222222−2222−22000000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000000000
χ864-44-4-44-44000000000000−2222−222222−2222−2200000000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000000000
χ874-4-44-444-44i−4i−4i4i−4i4i4i−4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-44-444-4−4i4i4i−4i4i−4i−4i4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4-44-44400000000000022−22−2222−222222−22000000000000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000000
χ904-4-4-44-44400000000000022−22−2222−222222−2200000000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000000
χ914-4-4-44-444000000000000−222222−2222−22−2222000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000000
χ924-4-4-44-444000000000000−222222−2222−22−222200000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000000

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