Finite Group Databasebeta

← Group #129115

Character table — Group #129115

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order1222444422448888888888888888161616161616161616161616161616164444444444448888888816161616161616161616161616161616161616161616161616161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711-1-111-1-11-11-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811-1-111-1-11-11-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ1911-1-111-1-11-11-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ2011-1-111-1-11-11-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ2111-1-111-1-11-11-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i11-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ2211-1-111-1-11-11-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i11-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ2311-1-111-1-11-11-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iii11-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ2411-1-111-1-11-11-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iii11-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ2511-1-111-1-11-11-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-111−i−iii−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1-111-1
χ2611-1-111-1-11-11-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-111−i−iii−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i1-1-111-1-11
χ2711-1-111-1-11-11-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-111ii−i−iii−i−i−i−iii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii1-1-111-1-11
χ2811-1-111-1-11-11-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-111ii−i−iii−i−i−i−iii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-111-1-111-1
χ2911-1-111-1-11-11-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i-1-111−i−iii−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11
χ3011-1-111-1-11-11-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i-1-111−i−iii−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1
χ3111-1-111-1-11-11-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii-1-111ii−i−iii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1
χ3211-1-111-1-11-11-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii-1-111ii−i−iii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11
χ332222222222222222-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222-2-2-2-2222222220000000000000000000000000000000000000000
χ3722222222-2-2-2-222-2-200000000-2-2222222−2−2−2−22222−2−2−2−2000000002i−2i2i−2i00002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3822222222-2-2-2-222-2-200000000-2-2222222−2−2−2−22222−2−2−2−200000000−2i2i−2i2i0000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3922222222-2-2-2-222-2-200000000-2-222−2−2−2−22222−2−2−2−22222000000002i−2i2i−2i00002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4022222222-2-2-2-222-2-200000000-2-222−2−2−2−22222−2−2−2−2222200000000−2i2i−2i2i0000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4122222222-2-2-2-2-2-2220000000022-2-22222−2−2−2−22222−2−2−2−2000000002i−2i2i−2i0000−2i2i−2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4222222222-2-2-2-2-2-2220000000022-2-22222−2−2−2−22222−2−2−2−200000000−2i2i−2i2i00002i−2i2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4322222222-2-2-2-2-2-2220000000022-2-2−2−2−2−22222−2−2−2−22222000000002i−2i2i−2i0000−2i2i−2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4422222222-2-2-2-2-2-2220000000022-2-2−2−2−2−22222−2−2−2−2222200000000−2i2i−2i2i00002i−2i2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ452222-2-2-2-222-2-22i−2i2i−2i000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-2000000002i−2i2i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ462222-2-2-2-222-2-22i−2i2i−2i000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-22-2200000000−2i2i−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ472222-2-2-2-222-2-22i−2i2i−2i000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-2000000002i−2i2i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ482222-2-2-2-222-2-22i−2i2i−2i000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-22-2200000000−2i2i−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ492222-2-2-2-222-2-2−2i2i−2i2i00000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-200000000−2i2i−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ502222-2-2-2-222-2-2−2i2i−2i2i00000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-22-22000000002i−2i2i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ512222-2-2-2-222-2-2−2i2i−2i2i00000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-200000000−2i2i−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ522222-2-2-2-222-2-2−2i2i−2i2i00000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-22-22000000002i−2i2i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ532222-2-2-2-2-2-2222i−2i−2i2i22-2-222-2-2−2i2i2i−2i000000000000000000002i−2i2i−2i000000000000000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000
χ542222-2-2-2-2-2-2222i−2i−2i2i22-2-222-2-2−2i2i2i−2i000000000000000000002i−2i2i−2i00000000000000000000-222-2-222-22i−2i−2i2i2i−2i−2i2i0000000000000000
χ552222-2-2-2-2-2-2222i−2i−2i2i-2-222-2-222−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000−2i2i−2i2i0000000000002-2-222-2-2200000000000000000000000000000000
χ562222-2-2-2-2-2-2222i−2i−2i2i-2-222-2-222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000−2i2i−2i2i000000000000-222-2-222-200000000000000000000000000000000
χ572222-2-2-2-2-2-222−2i2i2i−2i22-2-222-2-22i−2i−2i2i00000000000000000000−2i2i−2i2i000000000000000000002-2-222-2-222i−2i−2i2i2i−2i−2i2i0000000000000000
χ582222-2-2-2-2-2-222−2i2i2i−2i22-2-222-2-22i−2i−2i2i00000000000000000000−2i2i−2i2i00000000000000000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i0000000000000000
χ592222-2-2-2-2-2-222−2i2i2i−2i-2-222-2-2222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00002i−2i2i−2i000000000000-222-2-222-200000000000000000000000000000000
χ602222-2-2-2-2-2-222−2i2i2i−2i-2-222-2-2222i−2i−2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00002i−2i2i−2i0000000000002-2-222-2-2200000000000000000000000000000000
χ6122-2-222-2-22-22-222-2-2-2-2-2-2222222-2-200000000000000002i2i−2i−2i-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ6222-2-222-2-22-22-222-2-2-2-2-2-2222222-2-20000000000000000−2i−2i2i2i-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ6322-2-222-2-22-22-2-2-222-2-2-2-22222-2-22200000000000000002i2i−2i−2i22-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ6422-2-222-2-22-22-2-2-222-2-2-2-22222-2-2220000000000000000−2i−2i2i2i22-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ6522-2-222-2-2-22-22222200000000-2-2-2-22222−2−2−2−2−2−2−2−22222000000002-2-2200002-2-2222−2−2−2−22222−2−2−2−22222−2−2−2−2220000000000000000
χ6622-2-222-2-2-22-22222200000000-2-2-2-22222−2−2−2−2−2−2−2−2222200000000-222-20000-222-222−2−2−2−222−2−22222−2−2−2−22222−2−20000000000000000
χ6722-2-222-2-2-22-22222200000000-2-2-2-2−2−2−2−222222222−2−2−2−2000000002-2-2200002-2-22−2−22222−2−2−2−22222−2−2−2−22222−2−20000000000000000
χ6822-2-222-2-2-22-22222200000000-2-2-2-2−2−2−2−222222222−2−2−2−200000000-222-20000-222-2−2−22222−2−222−2−2−2−22222−2−2−2−2220000000000000000
χ6922-2-222-2-2-22-22-2-2-2-20000000022222222−2−2−2−2−2−2−2−22222000000002-2-220000-222-2−2−22222−2−2−2−22222−2−222−2−2−2−2220000000000000000
χ7022-2-222-2-2-22-22-2-2-2-20000000022222222−2−2−2−2−2−2−2−2222200000000-222-200002-2-22−2−22222−2−222−2−2−2−222−2−22222−2−20000000000000000
χ7122-2-222-2-2-22-22-2-2-2-2000000002222−2−2−2−222222222−2−2−2−2000000002-2-220000-222-222−2−2−2−22222−2−2−2−222−2−22222−2−20000000000000000
χ7222-2-222-2-2-22-22-2-2-2-2000000002222−2−2−2−222222222−2−2−2−200000000-222-200002-2-2222−2−2−2−222−2−22222−2−222−2−2−2−2220000000000000000
χ7322-2-2-2-2222-2-222i−2i−2i2i000000002i−2i−2i2ii2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i−2i2i00000000-222-200002−22−2−22−22−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.