Finite Group Databasebeta

← Group #13161830

Character table — Group #13161830

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111122222222222222222244444444444444444444444444444444444444444444181818181818181818181818363636363636363636363636111122222222222222222244444444444444444444444444444444444444444444181818181818181818181818363636363636363636363636
order12442333466666121212121212121233333666666666666666661212121212121212121212121212121212121212121288882424242424242424888824242424242424242244266646666612121212121212126666666666666666666666121212121212121212121212121212121212121212128888242424242424242488882424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i11-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i
χ611-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii11-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ711-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii11-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii
χ811-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i11-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i
χ92222222-122222-1222222-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000220000-1-1-1-12222222-122222-1222222-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1
χ102222222-122222-1222222-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000-2-2000011112222222-122222-1222222-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000-2-200001111
χ11222222-122222-122222-1-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000002200-1-1-1-10000222222-122222-122222-1-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000002200-1-1-1-10000
χ12222222-122222-122222-1-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2-20011110000222222-122222-122222-1-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2-20011110000
χ1322222-1222-1-1-122-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-100000000000022222-1222-1-1-122-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1422222-1222-1-1-122-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-21111111100000000000022222-1222-1-1-122-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111000000000000
χ152222-2222-2-2-222222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-222222222220000000000000000000000002222-2222-2-2-222222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000
χ162222-222-1-2-2-222-122-2-222-1-12-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i32222-222-1-2-2-222-122-2-222-1-12-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3
χ172222-222-1-2-2-222-122-2-222-1-12-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i32222-222-1-2-2-222-122-2-222-1-12-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3
χ182222-22-12-2-2-22-1222-2-2-1-122-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-10000000000000000−i3i3−i3i300002222-22-12-2-2-22-1222-2-2-1-122-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-10000000000000000−i3i3−i3i30000
χ192222-22-12-2-2-22-1222-2-2-1-122-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-10000000000000000i3−i3i3−i300002222-22-12-2-2-22-1222-2-2-1-122-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-10000000000000000i3−i3i3−i30000
χ202222-2-122-211-122-1-1112222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-1000033−3−333−3−30000000000002222-2-122-211-122-1-1112222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-1000033−3−333−3−3000000000000
χ212222-2-122-211-122-1-1112222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-10000−3−333−3−3330000000000002222-2-122-211-122-1-1112222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-10000−3−333−3−333000000000000
χ2222-2-22222-222222-2-2-2-2-2-2-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000022-2-22222-222222-2-2-2-2-2-2-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ2322-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-211111111000000000000000000003−3−3322-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-211111111000000000000000000003−3−33
χ2422-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-21111111100000000000000000000−333−322-2-2222-1-22222-1-2-2-2-2-2-2112-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-21111111100000000000000000000−333−3
χ2522-2-222-12-2222-12-2-2-2-211-2-2-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-211-2-211111111-2-211111100000000000000003−3−33000022-2-222-12-2222-12-2-2-2-211-2-2-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-211-2-211111111-2-211111100000000000000003−3−330000
χ2622-2-222-12-2222-12-2-2-2-211-2-2-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-211-2-211111111-2-21111110000000000000000−333−3000022-2-222-12-2222-12-2-2-2-211-2-2-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-211-2-211111111-2-21111110000000000000000−333−30000
χ2722-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-211111111-2-21111000033−3−3−3−33300000000000022-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-211111111-2-21111000033−3−3−3−333000000000000
χ2822-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-211111111-2-211110000−3−33333−3−300000000000022-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-211111111-2-211110000−3−33333−3−3000000000000
χ2922-2-2-222-12-2-222-1-2-222-2-2112-1-1-1-1-21-2-2111111112-1-1-1-12-122-1-1-1-1-1-1-1-1-2-211111111000000000000002i−2i0000−i−iii22-2-2-222-12-2-222-1-2-222-2-2112-1-1-1-1-21-2-2111111112-1-1-1-12-122-1-1-1-1-1-1-1-1-2-211111111000000000000002i−2i0000−i−iii
χ3022-2-2-222-12-2-222-1-2-222-2-2112-1-1-1-1-21-2-2111111112-1-1-1-12-122-1-1-1-1-1-1-1-1-2-21111111100000000000000−2i2i0000ii−i−i22-2-2-222-12-2-222-1-2-222-2-2112-1-1-1-1-21-2-2111111112-1-1-1-12-122-1-1-1-1-1-1-1-1-2-21111111100000000000000−2i2i0000ii−i−i
χ3122-2-2-22-122-2-22-12-2-22211-2-2-12-1-1-11-211-2-2111111-12-1-1-1-12-1-122-1-1-1-1-1-111-2-21111110000000000002i−2i00−i−iii000022-2-2-22-122-2-22-12-2-22211-2-2-12-1-1-11-211-2-2111111-12-1-1-1-12-1-122-1-1-1-1-1-111-2-21111110000000000002i−2i00−i−iii0000
χ3222-2-2-22-122-2-22-12-2-22211-2-2-12-1-1-11-211-2-2111111-12-1-1-1-12-1-122-1-1-1-1-1-111-2-2111111000000000000−2i2i00ii−i−i000022-2-2-22-122-2-22-12-2-22211-2-2-12-1-1-11-211-2-2111111-12-1-1-1-12-1-122-1-1-1-1-1-111-2-2111111000000000000−2i2i00ii−i−i0000
χ3322-2-2-2-122211-12211-1-1-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-122-1-1-1-122-1-1-1-11111-2-2111122-2-2-1-1-1-1111100000000000022-2-2-2-122211-12211-1-1-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-122-1-1-1-122-1-1-1-11111-2-2111122-2-2-1-1-1-11111000000000000
χ3422-2-2-2-122211-12211-1-1-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-122-1-1-1-122-1-1-1-11111-2-21111-2-2221111-1-1-1-100000000000022-2-2-2-122211-12211-1-1-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-122-1-1-1-122-1-1-1-11111-2-21111-2-2221111-1-1-1-1000000000000
χ352-22i−2i0222000-2-2-22i−2i002i−2i2i−2i22222000000000000-2-2-2-2-20000000000002i−2i2i−2i2i−2i2i2i−2i−2i2−2−i2i22−22−2−i2i2−i2i20000000000002-22i−2i0222000-2-2-22i−2i002i−2i2i−2i22222000000000000-2-2-2-2-20000000000002i−2i2i−2i2i−2i2i2i−2i−2i2−2−i2i22−22−2−i2i2−i2i2000000000000
χ362-22i−2i0222000-2-2-22i−2i002i−2i2i−2i22222000000000000-2-2-2-2-20000000000002i−2i2i−2i2i−2i2i2i−2i−2i−22i2−i2−22−22i2−i2i2−i20000000000002-22i−2i0222000-2-2-22i−2i002i−2i2i−2i22222000000000000-2-2-2-2-20000000000002i−2i2i−2i2i−2i2i2i−2i−2i−22i2−i2−22−22i2−i2i2−i2000000000000
χ372-22i−2i0-1220−i3i31-2-2−ii3−32i−2i2i−2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-211003−33−30033−3−3−ii−ii2i−2i−i−iii2−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000002-22i−2i0-1220−i3i31-2-2−ii3−32i−2i2i−2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-211003−33−30033−3−3−ii−ii2i−2i−i−iii2−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ382-22i−2i0-1220−i3i31-2-2−ii3−32i−2i2i−2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-211003−33−30033−3−3−ii−ii2i−2i−i−iii−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000002-22i−2i0-1220−i3i31-2-2−ii3−32i−2i2i−2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-211003−33−30033−3−3−ii−ii2i−2i−i−iii−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ392-22i−2i0-1220i3−i31-2-2−ii−332i−2i2i−2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-21100−33−3300−3−333−ii−ii2i−2i−i−iii2−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000002-22i−2i0-1220i3−i31-2-2−ii−332i−2i2i−2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-21100−33−3300−3−333−ii−ii2i−2i−i−iii2−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ402-22i−2i0-1220i3−i31-2-2−ii−332i−2i2i−2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-21100−33−3300−3−333−ii−ii2i−2i−i−iii−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000002-22i−2i0-1220i3−i31-2-2−ii−332i−2i2i−2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-21100−33−3300−3−333−ii−ii2i−2i−i−iii−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.