Finite Group Databasebeta

← Group #13170496

Character table — Group #13170496

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size11112222222244446666666666661818222244444444888812121212121212121212121236363333666666661212121218181818181818181818181854541111222222224444666666666666181822224444444488881212121212121212121212123636333366666666121212121818181818181818181818185454
order12443366121212123612122466881212242424248836121233661212121236121261266242412122424242424242244666612121212661212246688121224242424882244666612121212661212246688121224242424886612126666121212126612126126624241212242424242424224466661212121266121224668812122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1
χ31111111111111111-1-1-1-111-1-11111-1-11111111111111111-1-1-1-111-1-11111-1-11111111111111111-1-1-1-111-1-11111-1-11111111111111111-1-1-1-111-1-11111-1-11111111111111111-1-1-1-111-1-11111-1-11111111111111111-1-1-1-111-1-11111-1-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ511-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i
χ611-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii
χ711-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii
χ811-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i
χ922222-12-1-1-122-1-1-1-122-1-100-1-100000022222-12-1-1-122-1-1-1-122-1-100-1-100000022222-12-1-1-122-1-1-1-122-1-100-1-100000022222-12-1-1-122-1-1-1-122-1-100-1-100000022222-12-1-1-122-1-1-1-122-1-100-1-100000022222-12-1-1-122-1-1-1-122-1-100-1-1000000
χ1022222-12-1-1-122-1-1-1-1-2-211001100000022222-12-1-1-122-1-1-1-1-2-211001100000022222-12-1-1-122-1-1-1-1-2-211001100000022222-12-1-1-122-1-1-1-1-2-211001100000022222-12-1-1-122-1-1-1-1-2-211001100000022222-12-1-1-122-1-1-1-1-2-2110011000000
χ112222-12-1222-1-1-1-1-1-100002200-1-1-1-1002222-12-1222-1-1-1-1-1-100002200-1-1-1-1002222-12-1222-1-1-1-1-1-100002200-1-1-1-1002222-12-1222-1-1-1-1-1-100002200-1-1-1-1002222-12-1222-1-1-1-1-1-100002200-1-1-1-1002222-12-1222-1-1-1-1-1-100002200-1-1-1-100
χ122222-12-1222-1-1-1-1-1-10000-2-2001111002222-12-1222-1-1-1-1-1-10000-2-2001111002222-12-1222-1-1-1-1-1-10000-2-2001111002222-12-1222-1-1-1-1-1-10000-2-2001111002222-12-1222-1-1-1-1-1-10000-2-2001111002222-12-1222-1-1-1-1-1-10000-2-200111100
χ1322-2-22-12-111-2-2-1-1112-2-1-1001100000022-2-22-12-111-2-2-1-1112-2-1-1001100000022-2-22-12-111-2-2-1-1112-2-1-1001100000022-2-22-12-111-2-2-1-1112-2-1-1001100000022-2-22-12-111-2-2-1-1112-2-1-1001100000022-2-22-12-111-2-2-1-1112-2-1-10011000000
χ1422-2-22-12-111-2-2-1-111-221100-1-100000022-2-22-12-111-2-2-1-111-221100-1-100000022-2-22-12-111-2-2-1-111-221100-1-100000022-2-22-12-111-2-2-1-111-221100-1-100000022-2-22-12-111-2-2-1-111-221100-1-100000022-2-22-12-111-2-2-1-111-221100-1-1000000
χ1522-2-2-12-12-2-211-1-11100002i−2i00−i−iii0022-2-2-12-12-2-211-1-11100002i−2i00−i−iii0022-2-2-12-12-2-211-1-11100002i−2i00−i−iii0022-2-2-12-12-2-211-1-11100002i−2i00−i−iii0022-2-2-12-12-2-211-1-11100002i−2i00−i−iii0022-2-2-12-12-2-211-1-11100002i−2i00−i−iii00
χ1622-2-2-12-12-2-211-1-1110000−2i2i00ii−i−i0022-2-2-12-12-2-211-1-1110000−2i2i00ii−i−i0022-2-2-12-12-2-211-1-1110000−2i2i00ii−i−i0022-2-2-12-12-2-211-1-1110000−2i2i00ii−i−i0022-2-2-12-12-2-211-1-1110000−2i2i00ii−i−i0022-2-2-12-12-2-211-1-1110000−2i2i00ii−i−i00
χ172-22i−2i22-2-22i−2i2i−2i2-22i−2i000000000000002-22i−2i22-2-22i−2i2i−2i2-22i−2i000000000000002-22i−2i22-2-22i−2i2i−2i2-22i−2i000000000000002-22i−2i22-2-22i−2i2i−2i2-22i−2i000000000000002-22i−2i22-2-22i−2i2i−2i2-22i−2i000000000000002-22i−2i22-2-22i−2i2i−2i2-22i−2i00000000000000
χ182-22i−2i2-1-21−ii2i−2i-11−ii00−i3i3003−30000002-22i−2i2-1-21−ii2i−2i-11−ii00−i3i3003−30000002-22i−2i2-1-21−ii2i−2i-11−ii00−i3i3003−30000002-22i−2i2-1-21−ii2i−2i-11−ii00−i3i3003−30000002-22i−2i2-1-21−ii2i−2i-11−ii00−i3i3003−30000002-22i−2i2-1-21−ii2i−2i-11−ii00−i3i3003−3000000
χ192-22i−2i2-1-21−ii2i−2i-11−ii00i3−i300−330000002-22i−2i2-1-21−ii2i−2i-11−ii00i3−i300−330000002-22i−2i2-1-21−ii2i−2i-11−ii00i3−i300−330000002-22i−2i2-1-21−ii2i−2i-11−ii00i3−i300−330000002-22i−2i2-1-21−ii2i−2i-11−ii00i3−i300−330000002-22i−2i2-1-21−ii2i−2i-11−ii00i3−i300−33000000
χ202-22i−2i-121-22i−2i−ii-11−ii00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300
χ212-22i−2i-121-22i−2i−ii-11−ii00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13002-22i−2i-121-22i−2i−ii-11−ii00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300
χ222-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i000000000000002-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i000000000000002-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i000000000000002-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i000000000000002-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i000000000000002-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i00000000000000
χ232-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i300−330000002-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i300−330000002-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i300−330000002-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i300−330000002-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i300−330000002-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i300−33000000
χ242-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i3003−30000002-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i3003−30000002-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i3003−30000002-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i3003−30000002-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i3003−30000002-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i3003−3000000
χ252-2−2i2i-121-2−2i2ii−i-11i−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300
χ262-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300
χ274444-2-2-2-2-2-2-2-21111000000000000004444-2-2-2-2-2-2-2-21111000000000000004444-2-2-2-2-2-2-2-21111000000000000004444-2-2-2-2-2-2-2-21111000000000000004444-2-2-2-2-2-2-2-21111000000000000004444-2-2-2-2-2-2-2-2111100000000000000
χ2844-4-4-2-2-2-2222211-1-10000000000000044-4-4-2-2-2-2222211-1-10000000000000044-4-4-2-2-2-2222211-1-10000000000000044-4-4-2-2-2-2222211-1-10000000000000044-4-4-2-2-2-2222211-1-10000000000000044-4-4-2-2-2-2222211-1-100000000000000
χ294-44i−4i-2-222−2i2i−2i2i1-1i−i000000000000004-44i−4i-2-222−2i2i−2i2i1-1i−i000000000000004-44i−4i-2-222−2i2i−2i2i1-1i−i000000000000004-44i−4i-2-222−2i2i−2i2i1-1i−i000000000000004-44i−4i-2-222−2i2i−2i2i1-1i−i000000000000004-44i−4i-2-222−2i2i−2i2i1-1i−i00000000000000
χ304-4−4i4i-2-2222i−2i2i−2i1-1−ii000000000000004-4−4i4i-2-2222i−2i2i−2i1-1−ii000000000000004-4−4i4i-2-2222i−2i2i−2i1-1−ii000000000000004-4−4i4i-2-2222i−2i2i−2i1-1−ii000000000000004-4−4i4i-2-2222i−2i2i−2i1-1−ii000000000000004-4−4i4i-2-2222i−2i2i−2i1-1−ii00000000000000
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3211111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ331111111111111111-1-1-1-111-1-11111-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111111111-1-1-1-111-1-11111-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ341111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ3511-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i-1-111-1-1-1-11111-1-111-11-1-1−ii11−i−iii−ii11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i11-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i-1-111-1-1-1-11111-1-111-11-1-1−ii11−i−iii−ii
χ3611-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii-1-111-1-1-1-11111-1-111-11-1-1i−i11ii−i−ii−i11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii11-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii-1-111-1-1-1-11111-1-111-11-1-1i−i11ii−i−ii−i
χ3711-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii-1-111-1-1-1-11111-1-1111-111−ii-1-1−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii-1-111-1-1-1-11111-1-1111-111−ii-1-1−i−iiii−i
χ3811-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i-1-111-1-1-1-11111-1-1111-111i−i-1-1ii−i−i−ii11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i11-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i-1-111-1-1-1-11111-1-1111-111i−i-1-1ii−i−i−ii
χ3922222-12-1-1-122-1-1-1-122-1-100-1-100000022222-12-1-1-122-1-1-1-122-1-100-1-1000000-2-2-2-2-21-2111-2-21111-2-211001100000022222-12-1-1-122-1-1-1-122-1-100-1-100000022222-12-1-1-122-1-1-1-122-1-100-1-1000000-2-2-2-2-21-2111-2-21111-2-2110011000000
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χ1764-4−4i4i-242-4−4i4i2i−2i-222i−2i00000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ2300-222i−2i1-2-122i−2i−ii1-1−ii00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000000000000000-444i−4i2-4-244i−4i−2i2i2-2−2i2i000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23002-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000000000000000
χ1778888-4-4-4-4-4-4-4-4222200000000000000-4-4-4-422222222-1-1-1-100000000000000000000000000000000000000000000-8-8-8-844444444-2-2-2-2000000000000004444-2-2-2-2-2-2-2-2111100000000000000000000000000000000000000000000
χ17888-8-8-4-4-4-4444422-2-200000000000000-4-4442222-2-2-2-2-1-11100000000000000000000000000000000000000000000-8-8884444-4-4-4-4-2-2220000000000000044-4-4-2-2-2-2222211-1-100000000000000000000000000000000000000000000
χ1798-88i−8i-4-444−4i4i−4i4i2-22i−2i00000000000000-44−4i4i22-2-22i−2i2i−2i-11−ii00000000000000000000000000000000000000000000-88−8i8i44-4-44i−4i4i−4i-22−2i2i000000000000004-44i−4i-2-222−2i2i−2i2i1-1i−i00000000000000000000000000000000000000000000
χ1808-8−8i8i-4-4444i−4i4i−4i2-2−2i2i00000000000000-444i−4i22-2-2−2i2i−2i2i-11i−i00000000000000000000000000000000000000000000-888i−8i44-4-4−4i4i−4i4i-222i−2i000000000000004-4−4i4i-2-2222i−2i2i−2i1-1−ii00000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.