Finite Group Databasebeta

← Group #72225533

Character table — Group #72225533

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134
size111122222222222222222222224444444444444444444444444444888888888888888888888888888888888888888888883232323232323232323232323232323232323232323232323232323232323232128128128128
order122222444444448888888888884488888888888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616444488881616161616161616323232323232323232323232323232322488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ71111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11-1i−i
χ101111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-11−ii
χ111111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-11−ii
χ121111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii-1-1-1-111111-1i−i
χ131111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-111111-1−ii
χ141111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-11i−i
χ151111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-11i−i
χ161111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii
χ172222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222222222000000000000000000000000000000000000
χ192222222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-20000000000002222222200000000-2-2-2-200000000-2-2-2-200000000000000000000000022−2−222−2−222−2−222−2−20000
χ202222222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-20000000000002222222200000000-2-2-2-200000000-2-2-2-2000000000000000000000000−2−222−2−222−2−222−2−2220000
χ212222222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2000000000000-2-2-2-2-2-2-2-200000000222200000000222200000000000000000000000022−2−222−2−2−2−222−2−2220000
χ222222222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2000000000000-2-2-2-2-2-2-2-2000000002222000000002222000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222222222-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-2-2-222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-20000000000000000000000000000
χ2422222222222222-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-2-2-222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-222220000000000000000000000000000
χ2522222222222222-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222222000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222222222-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222222200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-222000000000022000022−2−222−2−22−22−22i2i−2i−2i2i2i−2i−2i22−2−222−2−20000i2i2i2i2−i2−i2−i2−i20000i2i2i2i2−i2−i2−i2−i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ2822222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-222000000000022000022−2−222−2−22−22−22i2i−2i−2i2i2i−2i−2i22−2−222−2−20000i2i2i2i2−i2−i2−i2−i20000i2i2i2i2−i2−i2−i2−i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ2922222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-222000000000022000022−2−222−2−22−22−2−2i−2i2i2i−2i−2i2i2i22−2−222−2−20000−i2−i2−i2−i2i2i2i2i20000−i2−i2−i2−i2i2i2i2i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ3022222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-222000000000022000022−2−222−2−22−22−2−2i−2i2i2i−2i−2i2i2i22−2−222−2−20000−i2−i2−i2−i2i2i2i2i20000−i2−i2−i2−i2i2i2i2i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ3122222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-2220000000000220000−2−222−2−222−22−222i2i−2i−2i2i2i−2i−2i−2−222−2−2220000−i2−i2−i2−i2i2i2i2i20000−i2−i2−i2−i2i2i2i2i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ3222222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-2220000000000220000−2−222−2−222−22−222i2i−2i−2i2i2i−2i−2i−2−222−2−2220000−i2−i2−i2−i2i2i2i2i20000−i2−i2−i2−i2i2i2i2i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ3322222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-2220000000000220000−2−222−2−222−22−22−2i−2i2i2i−2i−2i2i2i−2−222−2−2220000i2i2i2i2−i2−i2−i2−i20000i2i2i2i2−i2−i2−i2−i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ3422222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-2220000000000220000−2−222−2−222−22−22−2i−2i2i2i−2i−2i2i2i−2−222−2−2220000i2i2i2i2−i2−i2−i2−i20000i2i2i2i2−i2−i2−i2−i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ35222222-2-222-2-2-2-20022220000002-20022-2-20000-2-20000002222-2-2-2-2-2-222i2−i2i2−i2i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i2−22−22−22−200000000000000000000
χ36222222-2-222-2-2-2-20022220000002-20022-2-20000-2-20000002222-2-2-2-2-2-222i2−i2i2−i2i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i−22−22−22−2200000000000000000000
χ37222222-2-222-2-2-2-20022220000002-20022-2-20000-2-20000002222-2-2-2-2-2-222−i2i2−i2i2−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i−22−22−22−2200000000000000000000
χ38222222-2-222-2-2-2-20022220000002-20022-2-20000-2-20000002222-2-2-2-2-2-222−i2i2−i2i2−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i2−22−22−22−200000000000000000000
χ39222222-2-222-2-2-2-20022220000002-20022-2-20000-2-2000000-2-2-2-2222222-2-2i2−i2i2−i2i2−i2i2−i200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-22-20000i2−i2−i2i2i2−i2−i2i200000000000000000000
χ40222222-2-222-2-2-2-20022220000002-20022-2-20000-2-2000000-2-2-2-2222222-2-2i2−i2i2−i2i2−i2i2−i200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22-220000−i2i2i2−i2−i2i2i2−i200000000000000000000
χ41222222-2-222-2-2-2-20022220000002-20022-2-20000-2-2000000-2-2-2-2222222-2-2−i2i2−i2i2−i2i2−i2i200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-22-20000−i2i2i2−i2−i2i2i2−i200000000000000000000
χ42222222-2-222-2-2-2-20022220000002-20022-2-20000-2-2000000-2-2-2-2222222-2-2−i2i2−i2i2−i2i2−i2i200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-22-220000i2−i2−i2i2i2−i2−i2i200000000000000000000
χ432222-2-22222-2-2-2-2222222-2-2-2-222-2222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-2222i2i2i2i−2i−2i−2i−2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i000000000000000000000000000000000000
χ442222-2-22222-2-2-2-2222222-2-2-2-222-2222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-222−2i−2i−2i−2i2i2i2i2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000000000000000
χ452222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222-22222222-2-2-2-2-2-2-2-222220000000000002i2i2i2i−2i−2i−2i−2i00000000−2i−2i−2i−2i000000002i2i2i2i000000000000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000
χ462222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222-22222222-2-2-2-2-2-2-2-222220000000000002i2i2i2i−2i−2i−2i−2i00000000−2i−2i−2i−2i000000002i2i2i2i000000000000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000
χ472222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222-22222222-2-2-2-2-2-2-2-22222000000000000−2i−2i−2i−2i2i2i2i2i000000002i2i2i2i00000000−2i−2i−2i−2i000000000000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000
χ482222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222-22222222-2-2-2-2-2-2-2-22222000000000000−2i−2i−2i−2i2i2i2i2i000000002i2i2i2i00000000−2i−2i−2i−2i000000000000000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000
χ492222-2-22222-2-2-2-2-2-222222222-2-2-22-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-222-2-200000000-2-2-2-222220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ502222-2-22222-2-2-2-2-2-222222222-2-2-22-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-222-2-200000000-2-2-2-22222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ512222-2-22222-2-2-2-2-2-222222222-2-2-22-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-222000000002222-2-2-2-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ522222-2-22222-2-2-2-2-2-222222222-2-2-22-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-222000000002222-2-2-2-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ532222-2-222-2-2-2-222-2-200002222-2-22-2220000000000-2-2000022−2−2−2−2222−2−2222-2-2-2-22222−2−2−2−22200002222−2−2−2−20000−2−2−2−222220000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ542222-2-222-2-2-2-222-2-200002222-2-22-2220000000000-2-2000022−2−2−2−2222−2−2222-2-2-2-22222−2−2−2−22200002222−2−2−2−20000−2−2−2−222220000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.