Finite Group Databasebeta

← Group #128752

Character table — Group #128752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order122244442244444444448888888888888888888888888888888888888888888888881616161616161616161616161616161644448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ171111-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1i−ii−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ181111-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1i−ii−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ191111-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1i−ii−i11-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ201111-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1i−ii−i11-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ211111-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−ii−ii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ221111-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−ii−ii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ231111-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−ii−ii11-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ241111-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−ii−ii11-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ251111-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-1-1-1-11111−iii−i11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-11-1-11i−i−ii
χ261111-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-1-1-1-11111−iii−i11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111-111-1−iii−i
χ271111-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-1-1-1-11111−iii−i11-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-111-1−iii−i
χ281111-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-1-1-1-11111−iii−i11-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-1111-1-11i−i−ii
χ291111-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-1-1-1-11111i−i−ii11-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii11-1-1-1-1111-1-11−iii−i
χ301111-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-1-1-1-11111i−i−ii11-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-111-1i−i−ii
χ311111-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-1-1-1-11111i−i−ii11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111-111-1i−i−ii
χ321111-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-1-1-1-11111i−i−ii11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-11-1-11−iii−i
χ332222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ36222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2220000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2220000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3922222222-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222222222222200000000-2-2-2-200000000000000000000000000002−22−2−22−222−22−2−22−2200000000
χ4222222222-2-2-2-2-2-2-2-222222222222200000000-2-2-2-20000000000000000000000000000−22−222−22−2−22−222−22−200000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000222200000000000000000000000000002−22−2−22−22−22−222−22−200000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000022220000000000000000000000000000−22−222−22−22−22−2−22−2200000000
χ452222-2-2-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-222222i−2i2i−2i-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ462222-2-2-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-22222−2i2i−2i2i-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i0000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−222−2−222−200000000
χ482222-2-2-2-222-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i0000000000000000000000000000−i2i2i2−i2−i2i2i2−i22−2−222−2−2200000000
χ492222-2-2-2-222-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i0000000000000000000000000000i2−i2−i2i2i2−i2−i2i22−2−222−2−2200000000
χ502222-2-2-2-222-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i0000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−2−222−200000000
χ512222-2-2-2-2-2-22222-2-2-2-2222i2i−2i−2i−2i−2i2i2i2222-2-2-2-2−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ522222-2-2-2-2-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i2222-2-2-2-22i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ532222-2-2-2-2-2-222-2-22222-2-22i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i00000000000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ542222-2-2-2-2-2-222-2-22222-2-22i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i0000000000000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ552222-2-2-2-2-2-222-2-22222-2-2−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i00000000000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ562222-2-2-2-2-2-222-2-22222-2-2−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i0000000000000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ572-22-22i−2i2i−2i2-22i−2i2-22i−2i2-22i−2i0000000022-2-22i2i−2i−2i00002-22i−2i00000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ582-22-22i−2i2i−2i2-22i−2i2-22i−2i2-22i−2i0000000022-2-22i2i−2i−2i00002-22i−2i0000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ592-22-22i−2i2i−2i2-22i−2i2-22i−2i2-22i−2i00000000-2-222−2i−2i2i2i0000-22−2i2i000000002-22i−2i2-22i−2i00000000000000000000000000000000
χ602-22-22i−2i2i−2i2-22i−2i2-22i−2i2-22i−2i00000000-2-222−2i−2i2i2i0000-22−2i2i00000000-22−2i2i-22−2i2i00000000000000000000000000000000
χ612-22-22i−2i2i−2i-22−2i2i2-22i−2i-22−2i2i0000000022-2-22i2i−2i−2i0000-22−2i2i000000002i−2i-22−2i2i2-200000000000000000000000000000000
χ622-22-22i−2i2i−2i-22−2i2i2-22i−2i-22−2i2i0000000022-2-22i2i−2i−2i0000-22−2i2i00000000−2i2i2-22i−2i-2200000000000000000000000000000000
χ632-22-22i−2i2i−2i-22−2i2i2-22i−2i-22−2i2i00000000-2-222−2i−2i2i2i00002-22i−2i00000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000000000000000
χ642-22-22i−2i2i−2i-22−2i2i2-22i−2i-22−2i2i00000000-2-222−2i−2i2i2i00002-22i−2i0000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000000000000000
χ652-22-2−2i2i−2i2i2-2−2i2i2-2−2i2i2-2−2i2i0000000022-2-2−2i−2i2i2i00002-2−2i2i00000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ662-22-2−2i2i−2i2i2-2−2i2i2-2−2i2i2-2−2i2i0000000022-2-2−2i−2i2i2i00002-2−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ672-22-2−2i2i−2i2i2-2−2i2i2-2−2i2i2-2−2i2i00000000-2-2222i2i−2i−2i0000-222i−2i000000002-2−2i2i2-2−2i2i00000000000000000000000000000000
χ682-22-2−2i2i−2i2i2-2−2i2i2-2−2i2i2-2−2i2i00000000-2-2222i2i−2i−2i0000-222i−2i00000000-222i−2i-222i−2i00000000000000000000000000000000
χ692-22-2−2i2i−2i2i-222i−2i2-2−2i2i-222i−2i0000000022-2-2−2i−2i2i2i0000-222i−2i000000002i−2i2-2−2i2i-2200000000000000000000000000000000
χ702-22-2−2i2i−2i2i-222i−2i2-2−2i2i-222i−2i0000000022-2-2−2i−2i2i2i0000-222i−2i00000000−2i2i-222i−2i2-200000000000000000000000000000000
χ712-22-2−2i2i−2i2i-222i−2i2-2−2i2i-222i−2i00000000-2-2222i2i−2i−2i00002-2−2i2i00000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000000000000000
χ722-22-2−2i2i−2i2i-222i−2i2-2−2i2i-222i−2i00000000-2-2222i2i−2i−2i00002-2−2i2i0000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000000000000000
χ7344-4-444-4-40000000000004-44-4000022−2222−2222−2222−2200000000000022−2222−220000000000000000000000000000000000000000
χ7444-4-444-4-40000000000004-44-40000−2222−2222−2222−2222000000000000−2222−22220000000000000000000000000000000000000000
χ7544-4-444-4-4000000000000-44-44000022−2222−2222−2222−22000000000000−2222−22220000000000000000000000000000000000000000
χ7644-4-444-4-4000000000000-44-440000−2222−2222−2222−222200000000000022−2222−220000000000000000000000000000000000000000
χ7744-4-4-4-4440000000000004i−4i−4i4i000022−2222−22−2222−22220000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ7844-4-4-4-4440000000000004i−4i−4i4i0000−2222−222222−2222−22000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ7944-4-4-4-444000000000000−4i4i4i−4i000022−2222−22−2222−2222000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ8044-4-4-4-444000000000000−4i4i4i−4i0000−2222−222222−2222−220000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ814-44-44i−4i4i−4i4-44i−4i-44−4i4i-44−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ824-44-44i−4i4i−4i-44−4i4i-44−4i4i4-44i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i4-4−4i4i-444i−4i-444i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i-444i−4i-444i−4i4-4−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ854-4-444i−4i−4i4i00000000000000004ζ3−4ζ34ζ−4ζ22−22−22222i2−2i2−2i22i2000000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i00000000000000004ζ3−4ζ34ζ−4ζ−222222−22−2i22i22i2−2i200000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i0000000000000000−4ζ34ζ3−4ζ4ζ22−22−22222i2−2i2−2i22i200000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000000000000000
χ884-4-444i−4i−4i4i0000000000000000−4ζ34ζ3−4ζ4ζ−222222−22−2i22i22i2−2i2000000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i00000000000000004ζ−4ζ4ζ3−4ζ322−22−2222−2i22i22i2−2i200000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i00000000000000004ζ−4ζ4ζ3−4ζ3−222222−222i2−2i2−2i22i2000000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i0000000000000000−4ζ4ζ−4ζ34ζ322−22−2222−2i22i22i2−2i2000000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i0000000000000000−4ζ4ζ−4ζ34ζ3−222222−222i2−2i2−2i22i200000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000000000000000

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