Finite Group Databasebeta

← Group #13170506

Character table — Group #13170506

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size11112222222222224444444444446666666666666688889999121212121212121212121212121212121212121218181818181818183636363654541111222222222222444444444444666666666666668888999912121212121212121212121212121212121212121818181818181818363636365454
order1244333666121212121212333666121212121212248888242424242424242436121222446666121212122424242424242424242424246688881212242424242422446666661212121212126666661212121212122488882424242424242424661212224466661212121224242424242424242424242466888812122424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111
χ51111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1i−ii−iii−i−iii−i−i11-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i11i−ii−i-1-1i−ii−i1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1i−ii−iii−i−iii−i−i11-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i11i−ii−i-1-1i−ii−i1-1
χ1011-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1i−i−iiii−i−i−i−iii11-1-1-1-1111111-1-1-1-1i−i−iiii−i−i−i−iii-1-1i−i−ii11i−i−ii-1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1i−i−iiii−i−i−i−iii11-1-1-1-1111111-1-1-1-1i−i−iiii−i−i−i−iii-1-1i−i−ii11i−i−ii-11
χ1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1−iii−i−i−iiiii−i−i11-1-1-1-1111111-1-1-1-1−iii−i−i−iiiii−i−i-1-1−iii−i11−iii−i-1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1−iii−i−i−iiiii−i−i11-1-1-1-1111111-1-1-1-1−iii−i−i−iiiii−i−i-1-1−iii−i11−iii−i-11
χ1211-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1−ii−ii−i−iii−i−iii11-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii11−ii−ii-1-1−ii−ii1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1−ii−ii−i−iii−i−iii11-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii11−ii−ii-1-1−ii−ii1-1
χ1311-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11i−ii−iii−i−iii−i−i11-1-111-1-1-1-1-1-11111i−ii−iii−i−iii−i−i11−ii−ii-1-1−ii−ii-1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11i−ii−iii−i−iii−i−i11-1-111-1-1-1-1-1-11111i−ii−iii−i−iii−i−i11−ii−ii-1-1−ii−ii-11
χ1411-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11i−i−iiii−i−i−i−iii11-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii-1-1−iii−i11−iii−i1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11i−i−iiii−i−i−i−iii11-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii-1-1−iii−i11−iii−i1-1
χ1511-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11−iii−i−i−iiiii−i−i11-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i-1-1i−i−ii11i−i−ii1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11−iii−i−i−iiiii−i−i11-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i-1-1i−i−ii11i−i−ii1-1
χ1611-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11−ii−ii−i−iii−i−iii11-1-111-1-1-1-1-1-11111−ii−ii−i−iii−i−iii11i−ii−i-1-1i−ii−i-1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11−ii−ii−i−iii−i−iii11-1-111-1-1-1-1-1-11111−ii−ii−i−iii−i−iii11i−ii−i-1-1i−ii−i-11
χ17222222-122-1-1-12222-1-12-1-1222-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1-1-12222000000002222-1-1-1-1-1-1-1-1-1-10000-1-1000000222222-122-1-1-12222-1-12-1-1222-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1-1-12222000000002222-1-1-1-1-1-1-1-1-1-10000-1-1000000
χ18222222-122-1-1-12222-1-12-1-1222-1-1-1-10022-2-2-1-1-1-11111-1-1-1-1-2-2-2-20000000022-2-2-1-1-1-1111111000011000000222222-122-1-1-12222-1-12-1-1222-1-1-1-10022-2-2-1-1-1-11111-1-1-1-1-2-2-2-20000000022-2-2-1-1-1-1111111000011000000
χ19222222-122-1-1-12222-1-12-1-1222-1-1-1-100-2-2221111-1-1-1-1-1-1-1-1-2-2-2-200000000-2-2221111-1-1-1-111000011000000222222-122-1-1-12222-1-12-1-1222-1-1-1-100-2-2221111-1-1-1-1-1-1-1-1-2-2-2-200000000-2-2221111-1-1-1-111000011000000
χ20222222-122-1-1-12222-1-12-1-1222-1-1-1-100-2-2-2-211111111-1-1-1-1222200000000-2-2-2-211111111-1-10000-1-1000000222222-122-1-1-12222-1-12-1-1222-1-1-1-100-2-2-2-211111111-1-1-1-1222200000000-2-2-2-211111111-1-10000-1-1000000
χ2122222-122-122222-1-12-1-12-1-1-1-122-1-122002200002222-1-1-1-100002-1-1-12-1-1-100-1-10000-1-1-1-10000220000-1-10022222-122-122222-1-12-1-12-1-1-1-122-1-122002200002222-1-1-1-100002-1-1-12-1-1-100-1-10000-1-1-1-10000220000-1-100
χ2222222-122-122222-1-12-1-12-1-1-1-122-1-12200-2-20000-2-2-2-2-1-1-1-100002-1-1-12-1-1-10011000011110000-2-20000110022222-122-122222-1-12-1-12-1-1-1-122-1-12200-2-20000-2-2-2-2-1-1-1-100002-1-1-12-1-1-10011000011110000-2-200001100
χ2322222-122-122222-1-12-1-12-1-1-1-122-1-1-2-2002200002222-1-1-1-10000-2111-211100-1-10000-1-1-1-10000-2-20000110022222-122-122222-1-12-1-12-1-1-1-122-1-1-2-2002200002222-1-1-1-10000-2111-211100-1-10000-1-1-1-10000-2-200001100
χ2422222-122-122222-1-12-1-12-1-1-1-122-1-1-2-200-2-20000-2-2-2-2-1-1-1-10000-2111-21110011000011110000220000-1-10022222-122-122222-1-12-1-12-1-1-1-122-1-1-2-200-2-20000-2-2-2-2-1-1-1-10000-2111-21110011000011110000220000-1-100
χ252222-122-12222-1-122-12-1-12-1-1-1-1-12222220022220000-1-1-1-10000-12-1-1-12-1-1-1-100-1-1-1-1000000220000-1-100002222-122-12222-1-122-12-1-12-1-1-1-1-12222220022220000-1-1-1-10000-12-1-1-12-1-1-1-100-1-1-1-1000000220000-1-10000
χ262222-122-12222-1-122-12-1-12-1-1-1-1-12222-2-200-2-2-2-20000-1-1-1-10000-12-1-1-12-1-111001111000000-2-200001100002222-122-12222-1-122-12-1-12-1-1-1-1-12222-2-200-2-2-2-20000-1-1-1-10000-12-1-1-12-1-111001111000000-2-20000110000
χ272222-122-12222-1-122-12-1-12-1-1-1-1-122-2-2220022220000-1-1-1-100001-2111-211-1-100-1-1-1-1000000-2-200001100002222-122-12222-1-122-12-1-12-1-1-1-1-122-2-2220022220000-1-1-1-100001-2111-211-1-100-1-1-1-1000000-2-20000110000
χ282222-122-12222-1-122-12-1-12-1-1-1-1-122-2-2-2-200-2-2-2-20000-1-1-1-100001-2111-21111001111000000220000-1-100002222-122-12222-1-122-12-1-12-1-1-1-1-122-2-2-2-200-2-2-2-20000-1-1-1-100001-2111-21111001111000000220000-1-10000
χ2922-2-222-122-111-2-2-2-2-1-12-1-12-2-21111002i−2i2i−2i−i−iii−i−iii-1-11122-2-2000000002i−2i2i−2i−i−iii−i−iii-1-100001100000022-2-222-122-111-2-2-2-2-1-12-1-12-2-21111002i−2i2i−2i−i−iii−i−iii-1-11122-2-2000000002i−2i2i−2i−i−iii−i−iii-1-1000011000000
χ3022-2-222-122-111-2-2-2-2-1-12-1-12-2-21111002i−2i−2i2i−i−iiiii−i−i-1-111-2-222000000002i−2i−2i2i−i−iiiii−i−i110000-1-100000022-2-222-122-111-2-2-2-2-1-12-1-12-2-21111002i−2i−2i2i−i−iiiii−i−i-1-111-2-222000000002i−2i−2i2i−i−iiiii−i−i110000-1-1000000
χ3122-2-222-122-111-2-2-2-2-1-12-1-12-2-2111100−2i2i2i−2iii−i−i−i−iii-1-111-2-22200000000−2i2i2i−2iii−i−i−i−iii110000-1-100000022-2-222-122-111-2-2-2-2-1-12-1-12-2-2111100−2i2i2i−2iii−i−i−i−iii-1-111-2-22200000000−2i2i2i−2iii−i−i−i−iii110000-1-1000000
χ3222-2-222-122-111-2-2-2-2-1-12-1-12-2-2111100−2i2i−2i2iii−i−iii−i−i-1-11122-2-200000000−2i2i−2i2iii−i−iii−i−i-1-100001100000022-2-222-122-111-2-2-2-2-1-12-1-12-2-2111100−2i2i−2i2iii−i−iii−i−i-1-11122-2-200000000−2i2i−2i2iii−i−iii−i−i-1-1000011000000
χ3322-2-22-122-12-2-2-2-2112-1-12-1-111-2-2112-2002i−2i00002i2i−2i−2i-1-11100002-1-1-1-211100−ii0000−i−iii00002i−2i0000−ii0022-2-22-122-12-2-2-2-2112-1-12-1-111-2-2112-2002i−2i00002i2i−2i−2i-1-11100002-1-1-1-211100−ii0000−i−iii00002i−2i0000−ii00
χ3422-2-22-122-12-2-2-2-2112-1-12-1-111-2-2112-200−2i2i0000−2i−2i2i2i-1-11100002-1-1-1-211100i−i0000ii−i−i0000−2i2i0000i−i0022-2-22-122-12-2-2-2-2112-1-12-1-111-2-2112-200−2i2i0000−2i−2i2i2i-1-11100002-1-1-1-211100i−i0000ii−i−i0000−2i2i0000i−i00
χ3522-2-22-122-12-2-2-2-2112-1-12-1-111-2-211-22002i−2i00002i2i−2i−2i-1-1110000-21112-1-1-100−ii0000−i−iii0000−2i2i0000i−i0022-2-22-122-12-2-2-2-2112-1-12-1-111-2-211-22002i−2i00002i2i−2i−2i-1-1110000-21112-1-1-100−ii0000−i−iii0000−2i2i0000i−i00
χ3622-2-22-122-12-2-2-2-2112-1-12-1-111-2-211-2200−2i2i0000−2i−2i2i2i-1-1110000-21112-1-1-100i−i0000ii−i−i00002i−2i0000−ii0022-2-22-122-12-2-2-2-2112-1-12-1-111-2-211-2200−2i2i0000−2i−2i2i2i-1-1110000-21112-1-1-100i−i0000ii−i−i00002i−2i0000−ii00
χ3722-2-2-122-122-2-211-2-2-12-1-12-11111-2-22-22i−2i002i2i−2i−2i0000-1-1110000-12-1-11-211−ii00−i−iii0000002i−2i0000−ii000022-2-2-122-122-2-211-2-2-12-1-12-11111-2-22-22i−2i002i2i−2i−2i0000-1-1110000-12-1-11-211−ii00−i−iii0000002i−2i0000−ii0000
χ3822-2-2-122-122-2-211-2-2-12-1-12-11111-2-22-2−2i2i00−2i−2i2i2i0000-1-1110000-12-1-11-211i−i00ii−i−i000000−2i2i0000i−i000022-2-2-122-122-2-211-2-2-12-1-12-11111-2-22-2−2i2i00−2i−2i2i2i0000-1-1110000-12-1-11-211i−i00ii−i−i000000−2i2i0000i−i0000
χ3922-2-2-122-122-2-211-2-2-12-1-12-11111-2-2-222i−2i002i2i−2i−2i0000-1-11100001-211-12-1-1−ii00−i−iii000000−2i2i0000i−i000022-2-2-122-122-2-211-2-2-12-1-12-11111-2-2-222i−2i002i2i−2i−2i0000-1-11100001-211-12-1-1−ii00−i−iii000000−2i2i0000i−i0000
χ4022-2-2-122-122-2-211-2-2-12-1-12-11111-2-2-22−2i2i00−2i−2i2i2i0000-1-11100001-211-12-1-1i−i00ii−i−i0000002i−2i0000−ii000022-2-2-122-122-2-211-2-2-12-1-12-11111-2-2-22−2i2i00−2i−2i2i2i0000-1-11100001-211-12-1-1i−i00ii−i−i0000002i−2i0000−ii0000
χ412-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i2-22i−2i000000000000000000002-200002i−2i0000002-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i2-22i−2i000000000000000000002-200002i−2i000000
χ422-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i-22−2i2i00000000000000000000-220000−2i2i0000002-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i-22−2i2i00000000000000000000-220000−2i2i000000
χ432-22i−2i22-1-2-21−ii2i−2i2i−2i-1-1211-22i−2i−ii−ii000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13-11−ii2-22i−2i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13-110000−ii0000002-22i−2i22-1-2-21−ii2i−2i2i−2i-1-1211-22i−2i−ii−ii000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13-11−ii2-22i−2i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13-110000−ii000000
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χ901111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-111111111-1-11111-1-1-1-1
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χ10522222-122-122222-1-12-1-12-1-1-1-122-1-122002200002222-1-1-1-100002-1-1-12-1-1-100-1-10000-1-1-1-10000220000-1-100-2-2-2-2-21-2-21-2-2-2-2-211-211-21111-2-211-2-200-2-20000-2-2-2-211110000-2111-21110011000011110000-2-200001100
χ10622222-122-122222-1-12-1-12-1-1-1-122-1-12200-2-20000-2-2-2-2-1-1-1-100002-1-1-12-1-1-10011000011110000-2-200001100-2-2-2-2-21-2-21-2-2-2-2-211-211-21111-2-211-2-200220000222211110000-2111-211100-1-10000-1-1-1-10000220000-1-100
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.