Finite Group Databasebeta

← Group #72210708

Character table — Group #72210708

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111222222444444444444444488888888888888888888881616161616161616161616161616161632323232323232323232323232323232323232323232323232323232323232326464646464646464
order122222444444444444888888884488888888888816161616161616168888161616161616161616161616161616161616161616161616161616163232323232323232323232323232323222448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ311-1-1ii−i−i
χ101111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-1-111−i−iii
χ111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-1-111−i−iii
χ121111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ311-1-1ii−i−i
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ11-1-1−i−iii
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-1-111ii−i−i
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-1-111ii−i−i
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ11-1-1−i−iii
χ172222222222222222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ1822222222222222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22222222200000000-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−200000000
χ20222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22222222200000000-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−22200000000
χ21222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ22222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ23222222222222-2-2-2-22222222222-2-2-2-2-2-200000000222222220000-2-2-2-20000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ24222222222222-2-2-2-22222222222-2-2-2-2-2-200000000222222220000-2-2-2-200000000−2−222−2−222−2−222−2−222000000000000000000000000
χ25222222222222-2-2-2-22222222222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000222200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ26222222222222-2-2-2-22222222222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000222200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ272222222222-2-22222-2-22222-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i0000−2i−2i2i2i000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000000000
χ282222222222-2-22222-2-22222-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i0000−2i−2i2i2i00000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000000000000000
χ292222222222-2-22222-2-22222-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i00002i2i−2i−2i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000000000
χ302222222222-2-22222-2-22222-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i00002i2i−2i−2i00000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000
χ312222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i2i2i-2-2-2-222220000000000000000000000000000000000000000
χ322222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-2-2-222220000000000000000000000000000000000000000
χ332222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-22i2i2i2i−2i−2i−2i−2i00000000−2i−2i2i2i00000000000000000000000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i00000000
χ342222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-22i2i2i2i−2i−2i−2i−2i00000000−2i−2i2i2i0000000000000000000000000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00000000
χ352222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2−2i−2i−2i−2i2i2i2i2i000000002i2i−2i−2i00000000000000000000000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00000000
χ362222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2−2i−2i−2i−2i2i2i2i2i000000002i2i−2i−2i0000000000000000000000000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00000000
χ372222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ31+i−1−i1−i−1+i000022−2−2i2i2−i2−i21+ζ−1−ζi−ζ3−i+ζ3i+ζ3−i−ζ31−ζ−1+ζζ+i−ζ−i1+ζ3−1−ζ31−ζ3−1+ζ3ζ−i−ζ+i000000000000000000000000
χ382222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ31+i−1−i1−i−1+i000022−2−2i2i2−i2−i2−1−ζ1+ζ−i+ζ3i−ζ3−i−ζ3i+ζ3−1+ζ1−ζ−ζ−iζ+i−1−ζ31+ζ3−1+ζ31−ζ3−ζ+iζ−i000000000000000000000000
χ392222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ31+i−1−i1−i−1+i0000−2−222−i2−i2i2i21−ζ−1+ζi+ζ3−i−ζ3i−ζ3−i+ζ31+ζ−1−ζ−ζ+iζ−i1−ζ3−1+ζ31+ζ3−1−ζ3−ζ−iζ+i000000000000000000000000
χ402222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ31+i−1−i1−i−1+i0000−2−222−i2−i2i2i2−1+ζ1−ζ−i−ζ3i+ζ3−i+ζ3i−ζ3−1−ζ1+ζζ−i−ζ+i−1+ζ31−ζ3−1−ζ31+ζ3ζ+i−ζ−i000000000000000000000000
χ412222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−1−i1+i−1+i1−i0000−2−222−i2−i2i2i2i−ζ3−i+ζ3−1−ζ1+ζ−1+ζ1−ζi+ζ3−i−ζ31+ζ3−1−ζ3−ζ−iζ+iζ−i−ζ+i−1+ζ31−ζ3000000000000000000000000
χ422222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−1−i1+i−1+i1−i0000−2−222−i2−i2i2i2−i+ζ3i−ζ31+ζ−1−ζ1−ζ−1+ζ−i−ζ3i+ζ3−1−ζ31+ζ3ζ+i−ζ−i−ζ+iζ−i1−ζ3−1+ζ3000000000000000000000000
χ432222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−1−i1+i−1+i1−i000022−2−2i2i2−i2−i2i+ζ3−i−ζ3−1+ζ1−ζ−1−ζ1+ζi−ζ3−i+ζ31−ζ3−1+ζ3ζ−i−ζ+i−ζ−iζ+i−1−ζ31+ζ3000000000000000000000000
χ442222-2-222-2-22i−2i00002i−2i22-2-22i2i−2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−1−i1+i−1+i1−i000022−2−2i2i2−i2−i2−i−ζ3i+ζ31−ζ−1+ζ1+ζ−1−ζ−i+ζ3i−ζ3−1+ζ31−ζ3−ζ+iζ−iζ+i−ζ−i1+ζ3−1−ζ3000000000000000000000000
χ452222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ1−i−1+i1+i−1−i0000−2−222i2i2−i2−i21+ζ3−1−ζ3−ζ−iζ+iζ−i−ζ+i1−ζ3−1+ζ3−i+ζ3i−ζ31+ζ−1−ζ1−ζ−1+ζi+ζ3−i−ζ3000000000000000000000000
χ462222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ1−i−1+i1+i−1−i0000−2−222i2i2−i2−i2−1−ζ31+ζ3ζ+i−ζ−i−ζ+iζ−i−1+ζ31−ζ3i−ζ3−i+ζ3−1−ζ1+ζ−1+ζ1−ζ−i−ζ3i+ζ3000000000000000000000000
χ472222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ1−i−1+i1+i−1−i000022−2−2−i2−i2i2i21−ζ3−1+ζ3ζ−i−ζ+i−ζ−iζ+i1+ζ3−1−ζ3−i−ζ3i+ζ31−ζ−1+ζ1+ζ−1−ζi−ζ3−i+ζ3000000000000000000000000
χ482222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ1−i−1+i1+i−1−i000022−2−2−i2−i2i2i2−1+ζ31−ζ3−ζ+iζ−iζ+i−ζ−i−1−ζ31+ζ3i+ζ3−i−ζ3−1+ζ1−ζ−1−ζ1+ζ−i+ζ3i−ζ3000000000000000000000000
χ492222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−1+i1−i−1−i1+i000022−2−2−i2−i2i2i2ζ+i−ζ−i1+ζ3−1−ζ31−ζ3−1+ζ3−ζ+iζ−i−1−ζ1+ζ−i+ζ3i−ζ3−i−ζ3i+ζ31−ζ−1+ζ000000000000000000000000
χ502222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−1+i1−i−1−i1+i000022−2−2−i2−i2i2i2−ζ−iζ+i−1−ζ31+ζ3−1+ζ31−ζ3ζ−i−ζ+i1+ζ−1−ζi−ζ3−i+ζ3i+ζ3−i−ζ3−1+ζ1−ζ000000000000000000000000
χ512222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−1+i1−i−1−i1+i0000−2−222i2i2−i2−i2ζ−i−ζ+i−1+ζ31−ζ3−1−ζ31+ζ3−ζ−iζ+i1−ζ−1+ζi+ζ3−i−ζ3i−ζ3−i+ζ3−1−ζ1+ζ000000000000000000000000
χ522222-2-222-2-2−2i2i0000−2i2i22-2-2−2i−2i2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−1+i1−i−1−i1+i0000−2−222i2i2−i2−i2−ζ+iζ−i1−ζ3−1+ζ31+ζ3−1−ζ3ζ+i−ζ−i−1+ζ1−ζ−i−ζ3i+ζ3−i+ζ3i−ζ31+ζ−1−ζ000000000000000000000000
χ5322-2-22-22-22-22i−2i2i2i−2i−2i−2i2i000000002-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i00001−i−1+i1+i−1−i2−22−2i2−i2i2−i200000000000000001+ζ3−1−ζ3ζ+i−ζ−iζ−i−ζ+i1−ζ3−1+ζ3i−ζ3−i+ζ31+ζ−1−ζ1−ζ−1+ζi+ζ3−i−ζ300000000
χ5422-2-22-22-22-22i−2i2i2i−2i−2i−2i2i000000002-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i00001−i−1+i1+i−1−i2−22−2i2−i2i2−i20000000000000000−1−ζ31+ζ3−ζ−iζ+i−ζ+iζ−i−1+ζ31−ζ3−i+ζ3i−ζ3−1−ζ1+ζ−1+ζ1−ζ−i−ζ3i+ζ300000000
χ5522-2-22-22-22-22i−2i2i2i−2i−2i−2i2i000000002-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−1+i1−i−1−i1+i−22−22−i2i2−i2i20000000000000000ζ+i−ζ−i−1−ζ31+ζ31−ζ3−1+ζ3−ζ+iζ−i1+ζ−1−ζ−i+ζ3i−ζ3−i−ζ3i+ζ31−ζ−1+ζ00000000
χ5622-2-22-22-22-22i−2i2i2i−2i−2i−2i2i000000002-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−1+i1−i−1−i1+i−22−22−i2i2−i2i20000000000000000−ζ−iζ+i1+ζ3−1−ζ3−1+ζ31−ζ3ζ−i−ζ+i−1−ζ1+ζi−ζ3−i+ζ3i+ζ3−i−ζ3−1+ζ1−ζ00000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.