Finite Group Databasebeta

← Group #483413

Character table — Group #483413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order1244888822244444448888888888161616161616161616161616161616162244444444888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-11-1-111111111111-1-1-1-111111111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11-1-111111111111-1-1-1-111111111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11-1-111111111111-1-1-1-11111111111111111-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-11-1-111111111111-1-1-1-11111111111111111-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i
χ181111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii
χ191111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−ii−ii−i−ii−ii−ii−ii
χ201111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−ii−iii−ii−ii−ii−i
χ211111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii
χ221111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i
χ231111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1i−ii−i−ii−ii−ii−iii−ii−i
χ241111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1−ii−iii−ii−ii−ii−i−ii−ii
χ251111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-11
χ261111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-111-1
χ271111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-111-1-11-111-1-111-1
χ281111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-111-11-1-111-1-11
χ291111-1-1-1-1-1-11-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11-111-11-1-11-111-1
χ301111-1-1-1-1-1-11-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-11-111-11-1-11
χ311111-1-1-1-1-1-11-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-111111111-11-111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-111-1-111-11-1-11
χ321111-1-1-1-1-1-11-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-111111111-11-111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11-1-111-1-11-111-1
χ332222222222222-2-2-2-2222-2-2-2-2222200000000000000002222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000
χ342222222222222-2-2-2-2222-2-2-2-222220000000000000000-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000000000000000
χ35222222222-2-22-20000-2-2-2000022-2-22222−2−2−2−22222−2−2−2−20000002i−2i2i−2i0000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ36222222222-2-22-20000-2-2-2000022-2-22222−2−2−2−22222−2−2−2−2000000−2i2i−2i2i000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ37222222222-2-22-20000-2-2-2000022-2-2−2−2−2−22222−2−2−2−222220000002i−2i2i−2i0000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ38222222222-2-22-20000-2-2-2000022-2-2−2−2−2−22222−2−2−2−22222000000−2i2i−2i2i000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3922222222-22-2-220000-2-2-20000-2-2222222−2−2−2−22222−2−2−2−20000002i−2i−2i2i0000002i−2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4022222222-22-2-220000-2-2-20000-2-2222222−2−2−2−22222−2−2−2−2000000−2i2i2i−2i000000−2i2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4122222222-22-2-220000-2-2-20000-2-222−2−2−2−22222−2−2−2−222220000002i−2i−2i2i0000002i−2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4222222222-22-2-220000-2-2-20000-2-222−2−2−2−22222−2−2−2−22222000000−2i2i2i−2i000000−2i2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4322222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-2-2-200000000000000002-22-222-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ4422222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-2-2-20000000000000000-22-222222-2-2-2-2222222-2-20000000000000000000000000000000000000000
χ452222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-200000000000000002222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ462222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-222-2-2-2-22222-2-222220000000000000000000000000000000000000000
χ472222-2-2-2-22-2-22-20000-2220000-2-2222222−2−2−2−2−2−2−2−222220000002i−2i2i−2i000000−2i2i−2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ482222-2-2-2-22-2-22-20000-2220000-2-2222222−2−2−2−2−2−2−2−22222000000−2i2i−2i2i0000002i−2i2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ492222-2-2-2-22-2-22-20000-2220000-2-222−2−2−2−222222222−2−2−2−20000002i−2i2i−2i000000−2i2i−2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ502222-2-2-2-22-2-22-20000-2220000-2-222−2−2−2−222222222−2−2−2−2000000−2i2i−2i2i0000002i−2i2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ512222-2-2-2-2-22-2-220000-222000022-2-22222−2−2−2−2−2−2−2−222220000002i−2i−2i2i000000−2i2i2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ522222-2-2-2-2-22-2-220000-222000022-2-22222−2−2−2−2−2−2−2−22222000000−2i2i2i−2i0000002i−2i−2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ532222-2-2-2-2-22-2-220000-222000022-2-2−2−2−2−222222222−2−2−2−20000002i−2i−2i2i000000−2i2i2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ542222-2-2-2-2-22-2-220000-222000022-2-2−2−2−2−222222222−2−2−2−2000000−2i2i2i−2i0000002i−2i−2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ552222-2-2-2-2-2-22-2-222222-2-2-2-2-2-2222200000000000000002-22-2-2-222-2-2-2-22222-2-2220000000000000000000000000000000000000000
χ562222-2-2-2-2-2-22-2-222222-2-2-2-2-2-222220000000000000000-22-22-2-2-2-22222-2-22222-2-20000000000000000000000000000000000000000
χ5722-2-22i2i−2i−2i222-2-20000-22i−2i00002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−22-2-220000002i−2i2i−2i000000i2−i2i2−i22−22−2i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ5822-2-22i2i−2i−2i222-2-20000-22i−2i00002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2-222-2000000−2i2i−2i2i000000i2−i2i2−i22−22−2−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ5922-2-22i2i−2i−2i222-2-20000-22i−2i00002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2222-2-220000002i−2i2i−2i000000−i2i2−i2i2−22−22−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ6022-2-22i2i−2i−2i222-2-20000-22i−2i00002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222-222-2000000−2i2i−2i2i000000−i2i2−i2i2−22−22i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ6122-2-22i2i−2i−2i2-2-2-222i2i−2i−2i2−2i2i22-2-22i−2i−2i2i000000000000000000002i−2i000000002-20000000000002-2-22−2i2i2i−2i2-2-22−2i2i2i−2i0000000000000000
χ6222-2-22i2i−2i−2i2-2-2-222i2i−2i−2i2−2i2i22-2-22i−2i−2i2i000000000000000000002i−2i000000002-2000000000000-222-22i−2i−2i2i-222-22i−2i−2i2i0000000000000000
χ6322-2-22i2i−2i−2i2-2-2-22−2i−2i2i2i2−2i2i-2-2222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i22-2-2-2-2220000−2i2i00000000-2200002i−2i−2i2i2-2-2200000000000000000000000000000000
χ6422-2-22i2i−2i−2i2-2-2-22−2i−2i2i2i2−2i2i-2-2222i−2i−2i2i−2i−2i2i2i2i2i−2i−2i-2-22222-2-20000−2i2i00000000-220000−2i2i2i−2i-222-200000000000000000000000000000000
χ6522-2-22i2i−2i−2i-22-22-22i2i−2i−2i2−2i2i22-2-2−2i2i2i−2i00000000000000000000−2i2i00000000-220000000000002-2-22−2i2i2i−2i-222-22i−2i−2i2i0000000000000000
χ6622-2-22i2i−2i−2i-22-22-22i2i−2i−2i2−2i2i22-2-2−2i2i2i−2i00000000000000000000−2i2i00000000-22000000000000-222-22i−2i−2i2i2-2-22−2i2i2i−2i0000000000000000
χ6722-2-22i2i−2i−2i-22-22-2−2i−2i2i2i2−2i2i-2-222−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i22-2-2-2-22200002i−2i000000002-20000−2i2i2i−2i-222-200000000000000000000000000000000
χ6822-2-22i2i−2i−2i-22-22-2−2i−2i2i2i2−2i2i-2-222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i-2-22222-2-200002i−2i000000002-200002i−2i−2i2i2-2-2200000000000000000000000000000000
χ6922-2-22i2i−2i−2i-2-22220000-22i−2i0000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−222-2-20000002i−2i−2i2i000000−i2i2−i2i2−22−22i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ7022-2-22i2i−2i−2i-2-22220000-22i−2i0000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2-2-222000000−2i2i2i−2i000000−i2i2−i2i2−22−22−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ7122-2-22i2i−2i−2i-2-22220000-22i−2i0000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22222-2-20000002i−2i−2i2i000000i2−i2i2−i22−22−2−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.