Finite Group Databasebeta

← Group #13141170

Character table — Group #13141170

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666226666336666666666666636666666666666666666666644444444444422444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111-11-1-1-1111-1-1-1-111-111-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111-11-1-1-1111-1-1-1-111-111-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111-11-1-1-1111-1-1-1-111-111-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111-11-1-1-1111-1-1-1-111-111-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111-11-1-1-1111-1-1-1-11-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1ii−i−iii−i−i-11−ii−ii-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ14111-11-1-1-1111-1-1-1-11-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1−i−iii−i−iii-11i−ii−i-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ15111-11-1-1-1111-1-1-1-11-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii1-1−iii−i11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ16111-11-1-1-1111-1-1-1-11-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i−ii11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222222-1222-1-1-122-1-122-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-1222-1-1-122-1-122-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ192222222222222222222222-12-1-1-1222-1-122-1-122-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100002222000000220000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-1-1-1222-1-122-1-122-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000001111111100000000
χ212222222222222222-2-2-2-2-2-22-1222-1-1-122-1-122-1-1-1-2-211-2-211-1-1-1-1-1-1-1111111110000000022220000-2-20000000000000000-1-1-1-11111
χ222222222222222222-2-2-2-2-2-22-1222-1-1-122-1-122-1-1-1-2-211-2-211-1-1-1-1-1-1-11111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ232222222222222222-2-2-2-2-2-2-12-1-1-1222-1-122-1-122-111-2-211-2-2-1-1-1-1-1-1-11111111100002222000000-2-20000000000-1-1-1-1111100000000
χ242222222222222222-2-2-2-2-2-2-12-1-1-1222-1-122-1-122-111-2-211-2-2-1-1-1-1-1-1-1111111110000-2-2-2-20000002200000000001111-1-1-1-100000000
χ25222-22-2-2-2222-2-2-2-222-222-2-22-1222-1-1-1-2-211-2-211-122-1-1-2-211-1-1-11111-1-1-1-11111000000002i2i−2i−2i00002i−2i0000000000000000−i−iii−i−iii
χ26222-22-2-2-2222-2-2-2-222-222-2-22-1222-1-1-1-2-211-2-211-122-1-1-2-211-1-1-11111-1-1-1-1111100000000−2i−2i2i2i0000−2i2i0000000000000000ii−i−iii−i−i
χ27222-22-2-2-2222-2-2-2-222-222-2-2-12-1-1-122211-2-211-2-2-1-1-12211-2-2-1-1-11111-1-1-1-1111100002i2i−2i−2i0000002i−2i0000000000−i−iii−i−iii00000000
χ28222-22-2-2-2222-2-2-2-222-222-2-2-12-1-1-122211-2-211-2-2-1-1-12211-2-2-1-1-11111-1-1-1-111110000−2i−2i2i2i000000−2i2i0000000000ii−i−iii−i−i00000000
χ29222-22-2-2-2222-2-2-2-22-22-2-2222-1222-1-1-1-2-211-2-211-1-2-21122-1-1-1-1-111111111-1-1-1-1000000002i2i−2i−2i0000−2i2i0000000000000000−i−iiiii−i−i
χ30222-22-2-2-2222-2-2-2-22-22-2-2222-1222-1-1-1-2-211-2-211-1-2-21122-1-1-1-1-111111111-1-1-1-100000000−2i−2i2i2i00002i−2i0000000000000000ii−i−i−i−iii
χ31222-22-2-2-2222-2-2-2-22-22-2-222-12-1-1-122211-2-211-2-2-111-2-2-1-122-1-1-111111111-1-1-1-100002i2i−2i−2i000000−2i2i0000000000−i−iiiii−i−i00000000
χ32222-22-2-2-2222-2-2-2-22-22-2-222-12-1-1-122211-2-211-2-2-111-2-2-1-122-1-1-111111111-1-1-1-10000−2i−2i2i2i0000002i−2i0000000000ii−i−i−i−iii00000000
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χ3522-22-22-2-222-222-2-2-2000000-12-1112-2-2-1-12-2112-2-1−i3i300−i3i300-111-1-111−i3−i3i3i3−i3−i3i3i300002i−2i2i−2i000000000000000000−ii−ii3−33−300000000
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χ3922-2-2-2-22222-2-2-222-2000000222-2-22-2-2-2-2-2222-222000000002-2-2-2-2220000000000002-2-220000000000000000002-2-22000000000000
χ4022-2-2-2-22222-2-2-222-2000000222-2-22-2-2-2-2-2222-222000000002-2-2-2-222000000000000-222-2000000000000000000-222-2000000000000
χ4122-2-2-2-22222-2-2-222-2000000-12-1112-2-211-22-1-1-22-1−i3i300i3−i300-11111-1-1−i3−i3i3i3i3i3−i3−i300002-2-22000000000000000000-111-1−i3i3i3−i300000000
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χ502-222-2-22-22-222-22-2-20000002-1-22-21-112-2-1-12-211-100i3−i300i3−i31-11-11-11i3−i3i3−i3i3−i3i3−i300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−3
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χ986-6-6-6666-6-3333-3-33-300−3i33i33i3−3i30000000000000000000000000000000000000000-222-200000000000000i3−i3−i3i31-1-110000000000000000
χ996-6-6-6666-6-3333-3-33-3003i3−3i3−3i33i300000000000000000000000000000000000000002-2-2200000000000000i3−i3−i3i3-111-10000000000000000
χ1006-6-6-6666-6-3333-3-33-3003i3−3i3−3i33i30000000000000000000000000000000000000000-222-200000000000000−i3i3i3−i31-1-110000000000000000
χ1011212-1212-1212-12-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-12-121212-6-6666-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-121212-12-1212-12-66-6-66-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-1212-12-1212-1212-66-66-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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