Finite Group Databasebeta

← Group #13161809

Character table — Group #13161809

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222444422333446666666666666121212121212121212121212121212123333366666666666666666666666666666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212128888888824242424242424242424242424242424224444446666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-1-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111-1-1-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111-1-1-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ81111-1-1-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111
χ91-1-1111-1-11-11111-1-1-111-1-1-1-111-1-11111111-1-1-1-111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1i−ii−i1-111-1-1ii−i−iii−i−i11-1-1
χ101-1-1111-1-11-11111-1-1-111-1-1-1-111-1-11111111-1-1-1-111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11−ii−ii-11-1-111−i−iii−i−iii-1-111
χ111-1-1111-1-11-11111-1-1-111-1-1-1-111-1-11111111-1-1-1-111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1−ii−ii1-111-1-1−i−iii−i−iii11-1-1
χ121-1-1111-1-11-11111-1-1-111-1-1-1-111-1-11111111-1-1-1-111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11i−ii−i-11-1-111ii−i−iii−i−i-1-111
χ131-1-11-1-111-111111-1-1-1-1-111-1-111-1-1111-1-1-1-11111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1i−i−ii-1111-1-1ii−i−i−i−iii-1-111
χ141-1-11-1-111-111111-1-1-1-1-111-1-111-1-1111-1-1-1-11111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11−iii−i1-1-1-111−i−iiiii−i−i11-1-1
χ151-1-11-1-111-111111-1-1-1-1-111-1-111-1-1111-1-1-1-11111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1−iii−i-1111-1-1−i−iiiii−i−i-1-111
χ161-1-11-1-111-111111-1-1-1-1-111-1-111-1-1111-1-1-1-11111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11i−i−ii1-1-1-111ii−i−i−i−iii11-1-1
χ17222222222222-122222222-1-12222-12222222222-1-1-1-1222-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000000000000022000022-1-1-1-100000000-1-1-1-1
χ18222222222222-122222222-1-12222-12222222222-1-1-1-1222-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000000000-2-20000-2-21111000000001111
χ1922222222222-1222222222222-1-1-122222-1-122-1-1222222-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000002222000000-1-1-1-1-1-1-1-10000
χ2022222222222-1222222222222-1-1-122222-1-122-1-1222222-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000000-2-2-2-2000000111111110000
χ212222222222-12222-1-1-1-1-1-122-12222-1-1-1-122-1-1222222-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ222222222222-12222-1-1-1-1-1-122-12222-1-1-1-122-1-1222222-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ2322222222-2-2222-2-222-2-2-2-22222222-2-2222222222222-2-222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222000000000000000000000000000000000000000000000000
χ2422222222-2-222-1-2-222-2-2-2-2-1-12222-1-2-222222222-1-1-1-1-2-22-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-1-2-211-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000000000000000000000−i3i3−i3i300000000−i3i3−i3i3
χ2522222222-2-222-1-2-222-2-2-2-2-1-12222-1-2-222222222-1-1-1-1-2-22-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-1-2-211-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000000000000000000000i3−i3i3−i300000000i3−i3i3−i3
χ2622222222-2-22-12-2-222-2-2-2-2222-1-1-12-2-222-1-122-1-12222-2-2-12-1-1-111-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-111-2-211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2722222222-2-22-12-2-222-2-2-2-2222-1-1-12-2-222-1-122-1-12222-2-2-12-1-1-111-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-111-2-211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2822222222-2-2-122-2-2-1-1111122-1222211-1-122-1-122222211-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-2-2-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000033−3−333−3−333−3−333−3−3000000000000000000000000
χ2922222222-2-2-122-2-2-1-1111122-1222211-1-122-1-122222211-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-2-2-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000−3−333−3−333−3−333−3−333000000000000000000000000
χ302222-2-2-2-222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ312222-2-2-2-22222-1-2-2222222-1-12222-1-2-2-2-2-2-2-2-2-2-21111-2-22-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-211111111-2-211111111-2-211111111-2-21111111100000000000000000000000000000000−i3i3−i3i300000000i3−i3i3−i3
χ322222-2-2-2-22222-1-2-2222222-1-12222-1-2-2-2-2-2-2-2-2-2-21111-2-22-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-211111111-2-211111111-2-211111111-2-21111111100000000000000000000000000000000i3−i3i3−i300000000−i3i3−i3i3
χ332222-2-2-2-2222-12-2-2222222222-1-1-12-2-2-2-211-2-211-2-2-2-2-2-2-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-111-2-211-2-211111111-2-211111111-2-211111111-2-2111111000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ342222-2-2-2-2222-12-2-2222222222-1-1-12-2-2-2-211-2-211-2-2-2-2-2-2-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-111-2-211-2-211111111-2-211111111-2-211111111-2-2111111000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ352222-2-2-2-222-122-2-2-1-1-1-1-1-122-122221111-2-211-2-2-2-2-2-211-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-21111-2-211111111-2-211111111-2-211111111-2-211110000000033−3−333−3−3−3−333−3−333000000000000000000000000
χ362222-2-2-2-222-122-2-2-1-1-1-1-1-122-122221111-2-211-2-2-2-2-2-211-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-21111-2-211111111-2-211111111-2-211111111-2-2111100000000−3−333−3−33333−3−333−3−3000000000000000000000000
χ372222-2-2-2-2-2-222-12222-2-2-2-2-1-12222-122-2-2-2-2-2-2-2-21111222-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-211111111000000000000000000000000220000-2-2-1-1-1-1000000001111
χ382222-2-2-2-2-2-222-12222-2-2-2-2-1-12222-122-2-2-2-2-2-2-2-21111222-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-211111111000000000000000000000000-2-2000022111100000000-1-1-1-1
χ392222-2-2-2-2-2-22-122222-2-2-2-2222-1-1-1222-2-211-2-211-2-2-2-222-12-1-1-111-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-21111110000000000000000000000000022-2-2000000-1-1-1-111110000
χ402222-2-2-2-2-2-22-122222-2-2-2-2222-1-1-1222-2-211-2-211-2-2-2-222-12-1-1-111-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-211111100000000000000000000000000-2-2220000001111-1-1-1-10000
χ412222-2-2-2-2-2-2-12222-1-1111122-12222-1-111-2-211-2-2-2-2-2-2-1-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-211112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ422222-2-2-2-2-2-2-12222-1-1111122-12222-1-111-2-211-2-2-2-2-2-2-1-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-21111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.