Finite Group Databasebeta

← Group #13178757

Character table — Group #13178757

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11222222244444444444444448888888888888888899181818181818183636363636363636363672721122222224444444444444444888888888888888889918181818181818363636363636363636367272
order1233346663333346666612121212121212121212121212121212121212121212442888812122246662424242461222666466666666466666121212121212121212121212121212121212121212124428888121222466624242424612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1111-1-1111-1-1-1-1-1-1111111111111111111111111111111111111111111111-1-1-1-1111-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-111-1-1-1-1-11-1-1-1-111-1-11-1111111111111111111111111111111111111111111-1-1-111-1-1-1-1-11-1-1-1-111-1-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-11-1-1-1-1-111-11111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-11-1-1-1-1-111-11
χ511111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1-11111-1-111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1-11111-1-1
χ611111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1111-1-1-1-1-1-11111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1111-1-1-1-1-1-111
χ711111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-11111-1-1-1111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-11111-1-1-11
χ811111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-1
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χ2422-122222-1-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-12-1-1-12-1-100000-2-20000-200000110122-122222-1-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-12-1-1-12-1-100000-2-20000-2000001101
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χ2622-122222-1-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-1111-2111-21100000-2-20000200000110-122-122222-1-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-1111-2111-21100000-2-20000200000110-1
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χ6811111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-111-1-1-1-111
χ6911111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-11111111111-1-1-11111-1-11-1-1-1111111-1-1
χ7011111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-11111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-11111111111111-1-11111-11-11-1-1-1-1111-1
χ7111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1111111111111111-1-111-1-111-1-111-1-1-11
χ7222222-222222222022222-200-2-200-2-2-2-2-2000000000022-2000022000-200000000-2-2-2-2-22-2-2-2-2-2-2-2-20-2-2-2-2-22002200222220000000000-2-220000-2-2000200000000
χ7322222-222222222022222-200-2-200-2-2-2-2-20000000000-2-220000-2-2000200000000-2-2-2-2-22-2-2-2-2-2-2-2-20-2-2-2-2-2200220022222000000000022-2000022000-200000000
χ742222-122-122-1-1-1-122-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-12220000-1-1200-1-1-1000000-2-2-2-21-2-21-2-21111-2-21111111-2-2-2-2-21111-2-211111111-2-2-2000011-200111000000
χ752222-122-122-1-1-1-122-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2000011-200111000000-2-2-2-21-2-21-2-21111-2-21111111-2-2-2-2-21111-2-2111111112220000-1-1200-1-1-1000000
χ762222-122-122-1-1-1-1-22-1-1-1-1-11122-2-22-1-1-1-1-2-2111111112220000-1-1-200-111000000-2-2-2-21-2-21-2-211112-211111-1-1-2-222-2111122-1-1-1-1-1-1-1-1-2-2-20000112001-1-1000000
χ772222-122-122-1-1-1-1-22-1-1-1-1-11122-2-22-1-1-1-1-2-211111111-2-2-20000112001-1-1000000-2-2-2-21-2-21-2-211112-211111-1-1-2-222-2111122-1-1-1-1-1-1-1-12220000-1-1-200-111000000
χ782222-1-22-122-1-1-1-102-1-1-1-11−i3i3-2-200-2111100−i3−i3−i3−i3i3i3i3i322-20000-1-10001−i3i3000000-2-2-2-212-21-2-211110-21111-1i3−i322002-1-1-1-100i3i3i3i3−i3−i3−i3−i3-2-22000011000-1i3−i3000000
χ792222-1-22-122-1-1-1-102-1-1-1-11−i3i3-2-200-2111100−i3−i3−i3−i3i3i3i3i3-2-22000011000-1i3−i3000000-2-2-2-212-21-2-211110-21111-1i3−i322002-1-1-1-100i3i3i3i3−i3−i3−i3−i322-20000-1-10001−i3i3000000
χ802222-1-22-122-1-1-1-102-1-1-1-11i3−i3-2-200-2111100i3i3i3i3−i3−i3−i3−i322-20000-1-10001i3−i3000000-2-2-2-212-21-2-211110-21111-1−i3i322002-1-1-1-100−i3−i3−i3−i3i3i3i3i3-2-22000011000-1−i3i3000000
χ812222-1-22-122-1-1-1-102-1-1-1-11i3−i3-2-200-2111100i3i3i3i3−i3−i3−i3−i3-2-22000011000-1−i3i3000000-2-2-2-212-21-2-211110-21111-1−i3i322002-1-1-1-100−i3−i3−i3−i3i3i3i3i322-20000-1-10001i3−i3000000
χ82222-122-122-12-1-1-12-12-1-1-1222-12-12-12-1-1-1-1-12-1-1-12-1-1-1000220000020000-1-100-10-2-2-21-2-21-2-21-2111-21-2111-2-2-21-21-21-211111-2111-2111000-2-200000-20000110010
χ83222-122-122-12-1-1-12-12-1-1-1222-12-12-12-1-1-1-1-12-1-1-12-1-1-1000-2-200000-20000110010-2-2-21-2-21-2-21-2111-21-2111-2-2-21-21-21-211111-2111-2111000220000020000-1-100-10
χ84222-122-122-12-1-1-1-2-12-1-1-12-2-2-121-2-12-1-1-111-2111-21110002200000-20000-1-10010-2-2-21-2-21-2-21-211121-2111-2221-2-121-2111-1-12-1-1-12-1-1-1000-2-200000200001100-10
χ85222-122-122-12-1-1-1-2-12-1-1-12-2-2-121-2-12-1-1-111-2111-2111000-2-200000200001100-10-2-2-21-2-21-2-21-211121-2111-2221-2-121-2111-1-12-1-1-12-1-1-10002200000-20000-1-10010
χ8622-122222-1-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-12-1-1-12-1-100000220000200000-1-10-1-2-21-2-2-2-2-2111-211-211-211-2-2-2-21-2111-211111-2111-21100000-2-20000-2000001101
χ8722-122222-1-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-12-1-1-12-1-100000-2-20000-2000001101-2-21-2-2-2-2-2111-211-211-211-2-2-2-21-2111-211111-2111-21100000220000200000-1-10-1
χ8822-122222-1-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-1111-2111-21100000220000-200000-1-101-2-21-2-2-2-2-2111-211211-211-222-212-111-211-1-1-12-1-1-12-1-100000-2-20000200000110-1
χ8922-122222-1-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-1111-2111-21100000-2-20000200000110-1-2-21-2-2-2-2-2111-211211-211-222-212-111-211-1-1-12-1-1-12-1-100000220000-200000-1-101
χ902-22220-2-2-2222220-2-2-2-2-200000000000000000000002i−2i0−i2i22−22i−2i000000−i2i22−200-22-2-2-20222-2-2-2-2-20222220000000000000000000000−2i2i0i2−i2−22−2i2i000000i2−i2−2200
χ912-22220-2-2-2222220-2-2-2-2-200000000000000000000002i−2i0i2−i2−222i−2i000000i2−i2−2200-22-2-2-20222-2-2-2-2-20222220000000000000000000000−2i2i0−i2i22−2−2i2i000000−i2i22−200
χ922-22220-2-2-2222220-2-2-2-2-20000000000000000000000−2i2i0−i2i2−22−2i2i000000−i2i2−2200-22-2-2-20222-2-2-2-2-202222200000000000000000000002i−2i0i2−i22−22i−2i000000i2−i22−200
χ932-22220-2-2-2222220-2-2-2-2-20000000000000000000000−2i2i0i2−i22−2−2i2i000000i2−i22−200-22-2-2-20222-2-2-2-2-202222200000000000000000000002i−2i0−i2i2−222i−2i000000−i2i2−2200
χ94444-24-4-244-24-2-2-20-24-2-2-2-4002-4002-42220000000000000000000000000000000-4-4-42-442-4-42-422202-4222400-2400-24-2-2-20000000000000000000000000000000
χ95444-2-24-2-24-2-21114-2-2111-2-2-2-24-24-2-2111-2-2-2111-2111000000000000000000000-4-4-422-422-422-1-1-1-422-1-1-12222-42-422-1-1-1222-1-1-12-1-1-1000000000000000000000
χ96444-2-24-2-24-2-2111-4-2-2111-222-242-4-2-2111222-1-1-12-1-1-1000000000000000000000-4-4-422-422-422-1-1-1422-1-1-12-2-22-4-2422-1-1-1-2-2-2111-2111000000000000000000000
χ97444-2-2-4-2-24-2-21110-2-21112−2i32i32-40022-1-1-100−2i3i3i3i32i3−i3−i3−i3000000000000000000000-4-4-422422-422-1-1-1022-1-1-1-22i3−2i3-2400-2-2111002i3−i3−i3−i3−2i3i3i3i3000000000000000000000
χ98444-2-2-4-2-24-2-21110-2-211122i3−2i32-40022-1-1-1002i3−i3−i3−i3−2i3i3i3i3000000000000000000000-4-4-422422-422-1-1-1022-1-1-1-2−2i32i3-2400-2-211100−2i3i3i3i32i3−i3−i3−i3000000000000000000000
χ9944-244-444-2-2-24-2-20-2-24-2-2-400-420022-4220000000000000000000000000000000-4-42-4-44-4-4222-422022-4224004-200-2-24-2-20000000000000000000000000000000
χ10044-24-244-2-2-21-2114-21-211-2-2-24-24-2-21-211-2-21-2111-211000000000000000000000-4-42-42-4-4222-12-1-1-42-12-1-1222-42-422-12-1-122-12-1-1-12-1-1000000000000000000000
χ10144-24-244-2-2-21-211-4-21-211-2224-2-42-21-21122-12-1-1-12-1-1000000000000000000000-4-42-42-4-4222-12-1-142-12-1-12-2-2-424-22-12-1-1-2-21-2111-211000000000000000000000
χ10244-24-2-44-2-2-21-2110-21-2112−2i32i3-42002-12-1-100i3−2i3i3i3−i32i3−i3−i3000000000000000000000-4-42-424-4222-12-1-102-12-1-1-22i3−2i34-200-21-21100−i32i3−i3−i3i3−2i3i3i3000000000000000000000
χ10344-24-2-44-2-2-21-2110-21-21122i3−2i3-42002-12-1-100−i32i3−i3−i3i3−2i3i3i3000000000000000000000-4-42-424-4222-12-1-102-12-1-1-2−2i32i34-200-21-21100i3−2i3i3i3−i32i3−i3−i3000000000000000000000
χ10444-2-244-24-21-2-21141-2-211444-2-2-2-21-2-21111-2-211-2-211000000000000000000000-4-422-4-42-42-122-1-1-4-122-1-1-4-4-42222-122-1-1-1-122-1-122-1-1000000000000000000000
χ10544-2-244-24-21-2-211-41-2-2114-4-4-2-2221-2-211-1-122-1-122-1-1000000000000000000000-4-422-4-42-42-122-1-14-122-1-1-44422-2-2-122-1-111-2-211-2-211000000000000000000000
χ10644-2-24-4-24-21-2-21101-2-211-4002200-122-1-13-3003-3003-3000000000000000000000-4-422-442-42-122-1-10-122-1-1400-2-2001-2-211-3300-3300-33000000000000000000000
χ10744-2-24-4-24-21-2-21101-2-211-4002200-122-1-1-3300-3300-33000000000000000000000-4-422-442-42-122-1-10-122-1-1400-2-2001-2-2113-3003-3003-3000000000000000000000
χ10844-2-2-24-2-2-2111−1−3i32−1+3i324111−1−3i32−1+3i32-2-2-2-2-2-2-2111−1−3i32−1+3i321111−1−3i32−1+3i3211−1+3i32−1−3i32000000000000000000000-4-4222-4222-1-1-11+3i321−3i32-4-1-1-11+3i321−3i322222222-1-1-11+3i321−3i32-1-1-1-11+3i321−3i32-1-11−3i321+3i32000000000000000000000
χ10944-2-2-24-2-2-2111−1−3i32−1+3i32-4111−1−3i32−1+3i32-222-2-222111−1−3i32−1+3i32-1-1-1-11+3i321−3i32-1-11−3i321+3i32000000000000000000000-4-4222-4222-1-1-11+3i321−3i324-1-1-11+3i321−3i322-2-222-2-2-1-1-11+3i321−3i321111−1−3i32−1+3i3211−1+3i32−1−3i32000000000000000000000
χ11044-2-2-24-2-2-2111−1+3i32−1−3i324111−1+3i32−1−3i32-2-2-2-2-2-2-2111−1+3i32−1−3i321111−1+3i32−1−3i3211−1−3i32−1+3i32000000000000000000000-4-4222-4222-1-1-11−3i321+3i32-4-1-1-11−3i321+3i322222222-1-1-11−3i321+3i32-1-1-1-11−3i321+3i32-1-11+3i321−3i32000000000000000000000
χ11144-2-2-24-2-2-2111−1+3i32−1−3i32-4111−1+3i32−1−3i32-222-2-222111−1+3i32−1−3i32-1-1-1-11−3i321+3i32-1-11+3i321−3i32000000000000000000000-4-4222-4222-1-1-11−3i321+3i324-1-1-11−3i321+3i322-2-222-2-2-1-1-11−3i321+3i321111−1+3i32−1−3i3211−1−3i32−1+3i32000000000000000000000
χ11244-2-2-2-4-2-2-2111−1−3i32−1+3i320111−1−3i32−1+3i322−2i32i32200-1-1-11+3i321−3i323-3i3i3−3−i323−i32−i3−i3−3+i323+i32000000000000000000000-4-42224222-1-1-11+3i321−3i320-1-1-11+3i321−3i32-22i3−2i3-2-200111−1−3i32−1+3i32-33−i3−i33+i32−3+i32i3i33−i32−3−i32000000000000000000000
χ11344-2-2-2-4-2-2-2111−1−3i32−1+3i320111−1−3i32−1+3i3222i3−2i32200-1-1-11+3i321−3i32-33−i3−i33+i32−3+i32i3i33−i32−3−i32000000000000000000000-4-42224222-1-1-11+3i321−3i320-1-1-11+3i321−3i32-2−2i32i3-2-200111−1−3i32−1+3i323-3i3i3−3−i323−i32−i3−i3−3+i323+i32000000000000000000000
χ11444-2-2-2-4-2-2-2111−1+3i32−1−3i320111−1+3i32−1−3i322−2i32i32200-1-1-11−3i321+3i32-33i3i33−i32−3−i32−i3−i33+i32−3+i32000000000000000000000-4-42224222-1-1-11−3i321+3i320-1-1-11−3i321+3i32-22i3−2i3-2-200111−1+3i32−1−3i323-3−i3−i3−3+i323+i32i3i3−3−i323−i32000000000000000000000
χ11544-2-2-2-4-2-2-2111−1+3i32−1−3i320111−1+3i32−1−3i3222i3−2i32200-1-1-11−3i321+3i323-3−i3−i3−3+i323+i32i3i3−3−i323−i32000000000000000000000-4-42224222-1-1-11−3i321+3i320-1-1-11−3i321+3i32-2−2i32i3-2-200111−1+3i32−1−3i32-33i3i33−i32−3−i32−i3−i33+i32−3+i32000000000000000000000
χ1164-444-20-42-44-2-2-2-20-4222200000000000000000000004i−4i00000−2i2i000000000000-44-4-4204-24-4222204-2-2-2-20000000000000000000000−4i4i000002i−2i000000000000
χ1174-444-20-42-44-2-2-2-20-422220000000000000000000000−4i4i000002i−2i000000000000-44-4-4204-24-4222204-2-2-2-200000000000000000000004i−4i00000−2i2i000000000000
χ1184-44-2402-4-4-24-2-2-202-42220000000000000000000000000−2i22i20000000000i2−i20000-44-42-40-2442-42220-24-2-2-200000000000000000000000002i2−2i20000000000−i2i20000
χ1194-44-2402-4-4-24-2-2-202-422200000000000000000000000002i2−2i20000000000−i2i20000-44-42-40-2442-42220-24-2-2-20000000000000000000000000−2i22i20000000000i2−i20000
χ1204-4-2440-4-42-2-24-2-2022-42200000000000000000000000000022−220000000000−2200-442-4-4044-222-4220-2-24-2-2000000000000000000000000000−222200000000002−200
χ1214-4-2440-4-42-2-24-2-2022-422000000000000000000000000000−222200000000002−200-442-4-4044-222-4220-2-24-2-200000000000000000000000000022−220000000000−2200
χ1228-88-4-4044-8-4-4222044-2-2-20000000000000000000000000000000000000000000-88-8440-4-4844-2-2-20-4-42220000000000000000000000000000000000000000000
χ1238-8-48-40-844-42-42204-24-2-20000000000000000000000000000000000000000000-884-8408-4-44-24-2-20-42-4220000000000000000000000000000000000000000000
χ1248-8-4-4804-842-4-4220-244-2-20000000000000000000000000000000000000000000-8844-80-48-4-244-2-202-4-4220000000000000000000000000000000000000000000
χ1258-8-4-4-40444222−1−3i3−1+3i30-2-2-21+3i31−3i30000000000000000000000000000000000000000000-884440-4-4-4-2-2-21+3i31−3i30222−1−3i3−1+3i30000000000000000000000000000000000000000000
χ1268-8-4-4-40444222−1+3i3−1−3i30-2-2-21−3i31+3i30000000000000000000000000000000000000000000-884440-4-4-4-2-2-21−3i31+3i30222−1+3i3−1−3i30000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).