Finite Group Databasebeta

← Group #72213071

Character table — Group #72213071

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size111111112222222222223333333333333333333333336666666666666666666666666666666666666666666666666666666666666666666632323232323232323232323232323232323232323232323232323232323232324848484848484848484848484848484848484848484848484848484848484848
order12224444224444444444222244444444444444444444224444444444444444444444444444444444444444444444444444444444444444443666666612121212121212121212121212121212121212121212121244444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111
χ51111-1-1-1-1-1-111iiii−i−i−i−i1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i111-1-11-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−i1111-1-1-1-1iiiiii−i−i−i−i−i−i
χ61111-1-1-1-1-1-111iiii−i−i−i−i1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i111-1-11-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii-1-1-1-11111−i−i−i−i−i−iiiiiii
χ71111-1-1-1-1-1-111−i−i−i−iiiii1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii111-1-11-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−i−i−iiiiiii
χ81111-1-1-1-1-1-111−i−i−i−iiiii1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii111-1-11-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−i-1-1-1-11111iiiiii−i−i−i−i−i−i
χ911-1-111-1-1-111-111-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−iii−i−iii−i−iiii−i−i−iiii−i−i−i
χ1011-1-111-1-1-111-111-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−i−iii−i−iii−i−i−iiii−i−i−iiii
χ1111-1-111-1-1-111-1-1-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-111-1-1-1-1-1-11111-1-1-1-11111i−ii−ii−ii−i−ii−iiii−i−iii−i−i−i−i−iiii−i−i−iiii
χ1211-1-111-1-1-111-1-1-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-111-1-1-1-1-1-11111-1-1-1-11111−ii−ii−ii−iii−ii−i−i−iii−i−iiiiii−i−i−iiii−i−i−i
χ1311-1-1-1-1111-11-1ii−i−i−i−iii11-1-1-1-11111-1-1-1-111-1-1-1-111111-11-1ii−i−i−i−iii111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-1-1111-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1ii−i−i−i−iii-1-1-1111111-1-1-1
χ1411-1-1-1-1111-11-1ii−i−i−i−iii11-1-1-1-11111-1-1-1-111-1-1-1-111111-11-1ii−i−i−i−iii111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-1-1111-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i1-1-11−i−iiiii−i−i111-1-1-1-1-1-1111
χ1511-1-1-1-1111-11-1−i−iiiii−i−i11-1-1-1-11111-1-1-1-111-1-1-1-111111-11-1−i−iiiii−i−i111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1-1-1111-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii1-1-11ii−i−i−i−iii111-1-1-1-1-1-1111
χ1611-1-1-1-1111-11-1−i−iiiii−i−i11-1-1-1-11111-1-1-1-111-1-1-1-111111-11-1−i−iiiii−i−i111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1-1-1111-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-111-1−i−iiiii−i−i-1-1-1111111-1-1-1
χ172222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-22222222222222222222222222222-2-2-2-2-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000000000
χ1922222222-2-2-2-200000000222222222222222222222222-2-2-2-20000000022-2-2-2-222-2-2-2-222-2-2-2-222-2-2-2-200000000000000000000000000000000222-2-22-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2022222222-2-2-2-200000000222222222222222222222222-2-2-2-20000000022-2-2-2-222-2-2-2-222-2-2-2-222-2-2-2-200000000000000000000000000000000-1-1-111-1111111-1-1-1-133−3−333−3−333−3−333−3−300000000000000000000000000000000
χ2122222222-2-2-2-200000000222222222222222222222222-2-2-2-20000000022-2-2-2-222-2-2-2-222-2-2-2-222-2-2-2-200000000000000000000000000000000-1-1-111-1111111-1-1-1-1−3−333−3−333−3−333−3−33300000000000000000000000000000000
χ222222-2-2-2-222-2-2000000002222-2-22222-2-2-2-2-2-22222-2-2-2-222-2-20000000022-2-2-2-222-2-2-2-2-2-22222-2-222220000000000000000000000000000000022222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ232222-2-2-2-222-2-2000000002222-2-22222-2-2-2-2-2-22222-2-2-2-222-2-20000000022-2-2-2-222-2-2-2-2-2-22222-2-2222200000000000000000000000000000000-1-1-1-1-1-1-1-111111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000000000000000
χ242222-2-2-2-222-2-2000000002222-2-22222-2-2-2-2-2-22222-2-2-2-222-2-20000000022-2-2-2-222-2-2-2-2-2-22222-2-2222200000000000000000000000000000000-1-1-1-1-1-1-1-111111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000000000000000
χ252222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i2222-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i222222222222-2-2-2-2-2-2-2-2-2-2-2-22i2i2i2i2i2i2i2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i-1-1-111-111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000000000000000
χ262222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2222-2-22222-2-2-2-2-2-22222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i222222222222-2-2-2-2-2-2-2-2-2-2-2-2−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i2i2i2i2i2i2i-1-1-111-111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000000000000000000000
χ2722-2-222-2-22-2-220000000022-2-22222222222-2-2-2-2-2-2-2-2-2-22-2-220000000022-2-2-2-2-2-2222222-2-2-2-2-2-22222000000000000000000000000000000002-2-2222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ2822-2-222-2-22-2-220000000022-2-22222222222-2-2-2-2-2-2-2-2-2-22-2-220000000022-2-2-2-2-2-2222222-2-2-2-2-2-2222200000000000000000000000000000000-111-1-1-11111-1-1-1-11133−3−3−3−33333−3−3−3−33300000000000000000000000000000000
χ2922-2-222-2-22-2-220000000022-2-22222222222-2-2-2-2-2-2-2-2-2-22-2-220000000022-2-2-2-2-2-2222222-2-2-2-2-2-2222200000000000000000000000000000000-111-1-1-11111-1-1-1-111−3−33333−3−3−3−33333−3−300000000000000000000000000000000
χ3022-2-222-2-2-222-222-2-222-2-222-2-22222222222-2-2-2-2-2-2-2-2-2-2-222-222-2-222-2-2222222-2-2-2-2-2-2222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-11111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111100000000000000000000000000000000
χ3122-2-222-2-2-222-2-2-222-2-22222-2-22222222222-2-2-2-2-2-2-2-2-2-2-222-2-2-222-2-222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222-11111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-100000000000000000000000000000000
χ3222-2-2-2-2222-22-22i2i−2i−2i−2i−2i2i2i22-2-2-2-22222-2-2-2-222-2-2-2-222222-22-22i2i−2i−2i−2i−2i2i2i222222-2-2-2-2-2-2-2-2-2-2-2-22222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-111-1-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000000000000000
χ3322-2-2-2-2222-22-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-22222-2-2-2-222-2-2-2-222222-22-2−2i−2i2i2i2i2i−2i−2i222222-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-111-1-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000000000000000
χ3422-2-2-2-222-22-220000000022-2-2-2-22222-2-2-2-222-2-2-2-22222-22-220000000022-2-2-2-2-2-22222-2-2222222-2-2-2-2000000000000000000000000000000002-2-2-2-2222-2-222-2-222000000000000000000000000000000000000000000000000
χ3522-2-2-2-222-22-220000000022-2-2-2-22222-2-2-2-222-2-2-2-22222-22-220000000022-2-2-2-2-2-22222-2-2222222-2-2-2-200000000000000000000000000000000-11111-1-1-111-1-111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000000000000000
χ3622-2-2-2-222-22-220000000022-2-2-2-22222-2-2-2-222-2-2-2-22222-22-220000000022-2-2-2-2-2-22222-2-2222222-2-2-2-200000000000000000000000000000000-11111-1-1-111-1-111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000000000000000
χ372-22-22i−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22-22i−2i22-2-22i2i−2i−2i2i−2i22-2-22i2i−2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002-200002i−2i00002i−2i00001+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i22-200-20000002i−2i2i−2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00000000000000000000000000000000
χ382-22-22i−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22-22i−2i22-2-22i2i−2i−2i2i−2i22-2-22i2i−2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002-200002i−2i00002i−2i00001+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i-1-11−i3i31−i3i33−33−3−ii−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000000000000000000000000000
χ392-22-22i−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22-22i−2i22-2-22i2i−2i−2i2i−2i22-2-22i2i−2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002-200002i−2i00002i−2i00001+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i-1-11i3−i31i3−i3−33−33−ii−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000000000000000000000000000
χ402-22-22i−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22-22i−2i22-2-22i2i−2i−2i2i−2i22-2-22i2i−2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002-200002i−2i00002i−2i0000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i22-200-20000002i−2i2i−2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00000000000000000000000000000000
χ412-22-22i−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22-22i−2i22-2-22i2i−2i−2i2i−2i22-2-22i2i−2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002-200002i−2i00002i−2i0000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i-1-11−i3i31−i3i33−33−3−ii−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000000000000000000000000000
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χ1766-6-66−6i6i6i−6i0000−3+3i3−3i3−3i−3+3i−3−3i3+3i3+3i−3−3i-222-22i−2i−2−4i−2+4i2+4i2−4i−4+2i4+2i4−2i−4−2i−2i2i2+4i2−4i−2−4i−2+4i4−2i−4−2i−4+2i4+2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i2-20000-220000−2i2i00002i−2i0000−1+i−1+i3+i−1−3i1−i1−i−3−i1+3i1−i1−i−3−i1+3i−1+i−1+i3+i−1−3i−1−i−1−i−1+3i3−i1+i1+i1−3i−3+i1+i1+i1−3i−3+i−1−i−1−i−1+3i3−i0000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.