Finite Group Databasebeta

← Group #13141175

Character table — Group #13141175

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666226666336666666666666636666666666666666666666622224444444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111-11-1-1-11111-1-1-1-11-111-1-111111-1-111-1-1-1-1-1-11111-1-111-1-1111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ10111-11-1-1-11111-1-1-1-11-111-1-111111-1-111-1-1-1-1-1-11111-1-111-1-1111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1−ii−ii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ11111-11-1-1-11111-1-1-1-11-111-1-111111-1-111-1-1-1-1-1-11111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii-1-111ii−i−iii−i−i-1-111−i−iii−i−iii
χ12111-11-1-1-11111-1-1-1-11-111-1-111111-1-111-1-1-1-1-1-11111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i-1-111−i−iii−i−iii-1-111ii−i−iii−i−i
χ13111-11-1-1-11111-1-1-1-1-11-1-11111111-1-111-1-1-1-1-1-111-1-111-1-111111-1-1-1-1-1-1-1-1111111-1-1ii−i−iii−i−i-11−ii−ii11-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ14111-11-1-1-11111-1-1-1-1-11-1-11111111-1-111-1-1-1-1-1-111-1-111-1-111111-1-1-1-1-1-1-1-1111111-1-1−i−iii−i−iii-11i−ii−i11-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ15111-11-1-1-11111-1-1-1-1-11-1-11111111-1-111-1-1-1-1-1-111-1-111-1-111111-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii1-1−iii−i-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ16111-11-1-1-11111-1-1-1-1-11-1-11111111-1-111-1-1-1-1-1-111-1-111-1-111111-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i−ii-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222222222222222-122222-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000220000-1-1-1-100000000-1-1-1-100000000
χ1822222222222222222222222-122222-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000111100000000111100000000
χ192222222222222222222222-12-1-1-1-1-1222222-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1-1-1222222-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-122-1-1-2-2-2-21111-1-1-1-1-1-1-111111111222200000000-2-20000-1-1-1-100000000111100000000
χ222222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-122-1-1-2-2-2-21111-1-1-1-1-1-1-111111111-2-2-2-200000000220000111100000000-1-1-1-100000000
χ232222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-1-12-11111-2-2-2-2-1-1-1-1-1-1-1111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-1-12-11111-2-2-2-2-1-1-1-1-1-1-11111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ25222-22-2-2-22222-2-2-2-22-222-2-22-1222-2-2-1-11111-2-2-1-122-2-2-1-111-1-1-11111-1-1-1-1111122-2-2000000002-20000-1-11100000000-1-11100000000
χ26222-22-2-2-22222-2-2-2-22-222-2-22-1222-2-2-1-11111-2-2-1-122-2-2-1-111-1-1-11111-1-1-1-11111-2-22200000000-22000011-1-10000000011-1-100000000
χ27222-22-2-2-22222-2-2-2-22-222-2-2-12-1-1-11122-2-2-2-2112-1-1-11122-2-2-1-1-11111-1-1-1-11111000000002i2i−2i−2i00002i−2i0000000000000000−i−iii−i−iii
χ28222-22-2-2-22222-2-2-2-22-222-2-2-12-1-1-11122-2-2-2-2112-1-1-11122-2-2-1-1-11111-1-1-1-1111100000000−2i−2i2i2i0000−2i2i0000000000000000ii−i−iii−i−i
χ29222-22-2-2-22222-2-2-2-2-22-2-2222-1222-2-2-1-11111-2-2-1-1-2-22211-1-1-1-1-111111111-1-1-1-122-2-200000000-220000-1-1110000000011-1-100000000
χ30222-22-2-2-22222-2-2-2-2-22-2-2222-1222-2-2-1-11111-2-2-1-1-2-22211-1-1-1-1-111111111-1-1-1-1-2-222000000002-2000011-1-100000000-1-11100000000
χ31222-22-2-2-22222-2-2-2-2-22-2-222-12-1-1-11122-2-2-2-2112-111-1-1-2-222-1-1-111111111-1-1-1-1000000002i2i−2i−2i0000−2i2i0000000000000000−i−iiiii−i−i
χ32222-22-2-2-22222-2-2-2-2-22-2-222-12-1-1-11122-2-2-2-2112-111-1-1-2-222-1-1-111111111-1-1-1-100000000−2i−2i2i2i00002i−2i0000000000000000ii−i−i−i−iii
χ3322-22-22-2-222-2-222-2-2000000222-2-22-22-222-2-22-2-22000000002-2-222-2-20000000000002i−2i2i−2i000000000000002i−2i2i−2i0000000000000000
χ3422-22-22-2-222-2-222-2-2000000222-2-22-22-222-2-22-2-22000000002-2-222-2-2000000000000−2i2i−2i2i00000000000000−2i2i−2i2i0000000000000000
χ3522-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-222-22-22000000002-2-2-2-2220000000000002-2-22000000000000002-2-220000000000000000
χ3622-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-222-22-22000000002-2-2-2-222000000000000-222-200000000000000-222-20000000000000000
χ372-222-2-22-22-22-22-22-200000022-22-222-222-22-2-2-2-2200000000-22-22-22-200000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ382-222-2-22-22-22-22-22-200000022-22-222-222-22-2-2-2-2200000000-22-22-22-20000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
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χ402-222-2-22-22-22-22-22-2000000-121-11-1-1-222-22-211-2-1−i3i3−i3i300001-11-11-11−i3−i3i3i3−i3−i3i3i300000000−2i2i−2i2i0000000000000000000000i−ii−i−33−33
χ412-222-2-22-22-22-22-22-2000000-121-11-1-1-222-22-211-2-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i3000000002i−2i2i−2i0000000000000000000000−ii−ii−33−33
χ422-222-2-22-22-22-22-22-2000000-121-11-1-1-222-22-211-2-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−3
χ432-22-2-22-222-22-2-22-2200000022-22-2-2-2-22-22-2222-2200000000-22-2-22-2200000000000000002-2-2200000000000000000000002-2-220000
χ442-22-2-22-222-22-2-22-2200000022-22-2-2-2-22-22-2222-2200000000-22-2-22-220000000000000000-222-20000000000000000000000-222-20000
χ452-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-1-2-1−i3i3i3−i300001-111-11-1−i3−i3i3i3i3i3−i3−i3000000002-2-220000000000000000000000-111-1−i3i3i3−i3
χ462-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-1-2-1−i3i3i3−i300001-111-11-1−i3−i3i3i3i3i3−i3−i300000000-222-200000000000000000000001-1-11i3−i3−i3i3
χ472-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-1-2-1i3−i3−i3i300001-111-11-1i3i3−i3−i3−i3−i3i3i3000000002-2-220000000000000000000000-111-1i3−i3−i3i3
χ482-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-1-2-1i3−i3−i3i300001-111-11-1i3i3−i3−i3−i3−i3i3i300000000-222-200000000000000000000001-1-11−i3i3i3−i3
χ492-2-222-2-222-2-222-2-2200000022-2-222-2-2-22-2-22-222200000000-2-222-2-22000000002-22-2000000000000002-22-200000000000000000000
χ502-2-222-2-222-2-222-2-2200000022-2-222-2-2-22-2-22-222200000000-2-222-2-2200000000-22-2200000000000000-22-2200000000000000000000
χ512-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-22-1-10000−i3i3−i3i311-1-111-1−i3i3−i3i3−i3i3−i3i32-22-200000000000000-11-1100000000−i3i3−i3i300000000
χ522-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-22-1-10000−i3i3−i3i311-1-111-1−i3i3−i3i3−i3i3−i3i3-22-22000000000000001-11-100000000i3−i3i3−i300000000
χ532-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-22-1-10000i3−i3i3−i311-1-111-1i3−i3i3−i3i3−i3i3−i32-22-200000000000000-11-1100000000i3−i3i3−i300000000
χ542-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-22-1-10000i3−i3i3−i311-1-111-1i3−i3i3−i3i3−i3i3−i3-22-22000000000000001-11-100000000−i3i3−i3i300000000
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χ572-2-2-2222-22-2-22-222-20000002-1-2-22-22111-1-112-2-1-10000−i3i3i3−i311-11-1-11−i3i3−i3i3i3−i3i3−i32-2-2200000000000000-111-100000000−i3i3i3−i300000000
χ582-2-2-2222-22-2-22-222-20000002-1-2-22-22111-1-112-2-1-10000−i3i3i3−i311-11-1-11−i3i3−i3i3i3−i3i3−i3-222-2000000000000001-1-1100000000i3−i3−i3i300000000
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χ9766-6-6-6-666-3-33333-3-300−3i33i33i3−3i3000000000000000000000000000000000000000000002-2-2200000000000000-111-1−i3i3i3−i3000000000000
χ9866-6-6-6-666-3-33333-3-300−3i33i33i3−3i300000000000000000000000000000000000000000000-222-2000000000000001-1-11i3−i3−i3i3000000000000
χ9966-6-6-6-666-3-33333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000000000002-2-2200000000000000-111-1i3−i3−i3i3000000000000
χ10066-6-6-6-666-3-33333-3-3003i3−3i3−3i33i300000000000000000000000000000000000000000000-222-2000000000000001-1-11−i3i3i3−i3000000000000
χ10112-121212-12-1212-12-66-66-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-1212-1212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121212-12-1212-666-6-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-12121212-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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