Finite Group Databasebeta

← Group #366713

Character table — Group #366713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444222222444444444444442222444444448888888888888888222244444444444444448888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ911111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ1011111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ1111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111
χ1311111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ1511111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1611111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ171111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i111-111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-1i−ii−i1-1
χ181111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1111-1-111-11ii−i−iii−i−i−i−iii−i−iii-11−ii−ii-11
χ191111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-111-1-111-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii111-1-1-111-1-11-1−i−iiiii−i−iii−i−iii−i−i-11−ii−ii-11
χ201111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-111-1-111-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-1-1-11-1-11111-11−i−iiiii−i−i−i−iii−i−iii1-1i−ii−i1-1
χ211111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-1-1-111-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i11-11-1-111-1-1-11−i−iii−i−iiiii−i−i−i−iii1-1−iii−i-11
χ221111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-1-1-111-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-11-1-1-111111-1−i−iii−i−iii−i−iiiii−i−i-11i−i−ii1-1
χ231111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-1-1-111-1-111ii−i−i-1-1-1-11111−i−i−i−iiiii11-1111-1-1-1-1-11ii−i−i−i−iiiii−i−i−i−iii-11i−i−ii1-1
χ241111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i11-1-1-111-1-111ii−i−i-1-1-1-11111−i−i−i−iiiii-1-11-111-1-1111-1ii−i−i−i−iii−i−iiiii−i−i1-1−iii−i-11
χ251111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii111-111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-1−ii−ii1-1
χ261111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1-1111-1-111-11−i−iii−i−iiiii−i−iii−i−i-11i−ii−i-11
χ271111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-111-1-111-1-1−i−iii-1-1-1-11111iiii−i−i−i−i111-1-1-111-1-11-1ii−i−i−i−iii−i−iii−i−iii-11i−ii−i-11
χ281111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-111-1-111-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-1-11-1-11111-11ii−i−i−i−iiiii−i−iii−i−i1-1−ii−ii1-1
χ291111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-1-1-111-1-111−i−iii1111-1-1-1-1−i−i−i−iiiii11-11-1-111-1-1-11ii−i−iii−i−i−i−iiiii−i−i1-1i−i−ii-11
χ301111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-1-1-111-1-111−i−iii1111-1-1-1-1−i−i−i−iiiii-1-11-1-1-111111-1ii−i−iii−i−iii−i−i−i−iii-11−iii−i1-1
χ311111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-1-1-111-1-111−i−iii-1-1-1-11111iiii−i−i−i−i11-1111-1-1-1-1-11−i−iiiii−i−i−i−iiiii−i−i-11−iii−i1-1
χ321111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii11-1-1-111-1-111−i−iii-1-1-1-11111iiii−i−i−i−i-1-11-111-1-1111-1−i−iiiii−i−iii−i−i−i−iii1-1i−i−ii-11
χ3322222222-2-222-2-2-2-2-20000000022-222-2-2-2-222000022-2-222-2-20000000000002-22-20000000000000000000000000000
χ3422222222-2-222-2-2-2-2-20000000022-222-2-2-2-2220000-2-222-2-222000000000000-22-220000000000000000000000000000
χ3522222222-2-222-2-2-2-2-20000000022-2-2-22222-2-2000022-2-222-2-2000000000000-22-220000000000000000000000000000
χ3622222222-2-222-2-2-2-2-20000000022-2-2-22222-2-20000-2-222-2-2220000000000002-22-20000000000000000000000000000
χ3722222222-2-2-2-22222-222222222-2-2-200000000-2-2-2-20000000000000000002-2000000-220000000000002-22-200000000
χ3822222222-2-2-2-22222-222222222-2-2-200000000-2-2-2-2000000000000000000-220000002-2000000000000-22-2200000000
χ3922222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000002-2000000-22000000000000-22-2200000000
χ4022222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000-220000002-20000000000002-22-200000000
χ412222-2-2-2-2-2-222-2-22222i2i2i2i−2i−2i−2i−2i-2-2200000000−2i−2i2i2i00000000000000000022000000-2-20000000000002i−2i−2i2i00000000
χ422222-2-2-2-2-2-222-2-22222i2i2i2i−2i−2i−2i−2i-2-2200000000−2i−2i2i2i000000000000000000-2-200000022000000000000−2i2i2i−2i00000000
χ432222-2-2-2-2-2-222-2-2222−2i−2i−2i−2i2i2i2i2i-2-22000000002i2i−2i−2i00000000000000000022000000-2-2000000000000−2i2i2i−2i00000000
χ442222-2-2-2-2-2-222-2-2222−2i−2i−2i−2i2i2i2i2i-2-22000000002i2i−2i−2i000000000000000000-2-2000000220000000000002i−2i−2i2i00000000
χ452222-2-2-2-2-2-2-2-222-2-22000000002222222-2-2-2-2000022-2-2-2-2220000000000002-2-220000000000000000000000000000
χ462222-2-2-2-2-2-2-2-222-2-22000000002222222-2-2-2-20000-2-22222-2-2000000000000-222-20000000000000000000000000000
χ472222-2-2-2-2-2-2-2-222-2-2200000000222-2-2-2-22222000022-2-2-2-222000000000000-222-20000000000000000000000000000
χ482222-2-2-2-2-2-2-2-222-2-2200000000222-2-2-2-222220000-2-22222-2-20000000000002-2-220000000000000000000000000000
χ492-2-2222-2-22-22-22-22-2-22i2i−2i−2i2i2i−2i−2i2-222-22-22-22-22i−2i2i−2i000000000000000000000000000000002i−2i2i−2i0000000000000000
χ502-2-2222-2-22-22-22-22-2-22i2i−2i−2i2i2i−2i−2i2-22-22-22-22-222i−2i2i−2i00000000000000000000000000000000−2i2i−2i2i0000000000000000
χ512-2-2222-2-22-22-22-22-2-2−2i−2i2i2i−2i−2i2i2i2-222-22-22-22-2−2i2i−2i2i00000000000000000000000000000000−2i2i−2i2i0000000000000000
χ522-2-2222-2-22-22-22-22-2-2−2i−2i2i2i−2i−2i2i2i2-22-22-22-22-22−2i2i−2i2i000000000000000000000000000000002i−2i2i−2i0000000000000000
χ532-2-2222-2-2-222-2-22-222000000002-2-22-2-22-222-20000000000002i2i−2i−2i2i2i−2i−2i0000000000002i−2i2i−2i00000000000000000000
χ542-2-2222-2-2-222-2-22-222000000002-2-22-2-22-222-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000−2i2i−2i2i00000000000000000000
χ552-2-2222-2-2-222-2-22-222000000002-2-2-222-22-2-220000000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i00000000000000000000
χ562-2-2222-2-2-222-2-22-222000000002-2-2-222-22-2-22000000000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i00000000000000000000
χ572-2-2222-2-2-22-222-22-222i2i−2i−2i2i2i−2i−2i-22-200000000−2i2i−2i2i00000000000000002-20000002-200000000002i−2i2i−2i000000000000
χ582-2-2222-2-2-22-222-22-222i2i−2i−2i2i2i−2i−2i-22-200000000−2i2i−2i2i0000000000000000-22000000-220000000000−2i2i−2i2i000000000000
χ592-2-2222-2-2-22-222-22-22−2i−2i2i2i−2i−2i2i2i-22-2000000002i−2i2i−2i00000000000000002-20000002-20000000000−2i2i−2i2i000000000000
χ602-2-2222-2-2-22-222-22-22−2i−2i2i2i−2i−2i2i2i-22-2000000002i−2i2i−2i0000000000000000-22000000-2200000000002i−2i2i−2i000000000000
χ612-2-22-2-2222-2-22-222-2222-2-2-2-2222-2-22-2-222-2-222-2-22000000000000000000000000000000002-2-220000000000000000
χ622-2-22-2-2222-2-22-222-2222-2-2-2-2222-2-2-222-2-222-22-2-2200000000000000000000000000000000-222-20000000000000000
χ632-2-22-2-2222-2-22-222-22-2-22222-2-22-2-22-2-222-2-22-222-200000000000000000000000000000000-222-20000000000000000
χ642-2-22-2-2222-2-22-222-22-2-22222-2-22-2-2-222-2-222-2-222-2000000000000000000000000000000002-2-220000000000000000
χ652-2-22-2-222-222-2-222-2-222-2-2-2-222-22200000000-222-200000000000000002-2000000-2200000000002-2-22000000000000
χ662-2-22-2-222-222-2-222-2-222-2-2-2-222-22200000000-222-20000000000000000-220000002-20000000000-222-2000000000000
χ672-2-22-2-222-222-2-222-2-2-2-22222-2-2-222000000002-2-2200000000000000002-2000000-220000000000-222-2000000000000
χ682-2-22-2-222-222-2-222-2-2-2-22222-2-2-222000000002-2-220000000000000000-220000002-200000000002-2-22000000000000
χ692-2-22-2-222-22-222-2-22-2000000002-222-22-2-22-2200000000000022-2-2-2-2220000000000002-2-2200000000000000000000
χ702-2-22-2-222-22-222-2-22-2000000002-222-22-2-22-22000000000000-2-22222-2-2000000000000-222-200000000000000000000
χ712-2-22-2-222-22-222-2-22-2000000002-22-22-222-22-200000000000022-2-2-2-222000000000000-222-200000000000000000000
χ722-2-22-2-222-22-222-2-22-2000000002-22-22-222-22-2000000000000-2-22222-2-20000000000002-2-2200000000000000000000
χ734444444444-4-4-4-4-4-4400000000-4-440000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4444444-4-4-400000000-4-4-40000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000022−22002i2−2i22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000000000
χ7644-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000000000−222200−2i22i2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000000000
χ7744-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000022−22002i2−2i2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000000000
χ7844-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000000000−222200−2i22i22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000022−2200−2i22i2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000000000−2222002i2−2i22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000000000
χ8144-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000022−2200−2i22i22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000000000
χ8244-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000000000−2222002i2−2i2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000000000
χ834-44-44i−4i−4i4i0000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000022−22002i2−2i2002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000000000
χ844-44-44i−4i−4i4i0000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000−222200−2i22i200−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000000000
χ854-44-44i−4i−4i4i000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000022−22002i2−2i200−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000000000
χ864-44-44i−4i−4i4i000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000000000000−222200−2i22i2002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000000000
χ874-44-4−4i4i4i−4i0000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000022−2200−2i22i200−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000000000
χ884-44-4−4i4i4i−4i0000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000000000000000−2222002i2−2i2002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000000000
χ894-44-4−4i4i4i−4i000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000022−2200−2i22i2002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000000000
χ904-44-4−4i4i4i−4i000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000000000−2222002i2−2i200−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000000000
χ914-4-4444-4-44-4-44-44-44-400000000-4440000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4444-44-44-4-44400000000-44-40000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.