Finite Group Databasebeta

← Group #13140135

Character table — Group #13140135

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444444444121212121212121212121212121212121212121212121212
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
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ911-11-1-1-11111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1i−i1-1ii−i−i11-1-111-1-111-1-1ii−i−iii−i−i
χ1011-11-1-1-11111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i−i−iii-1-1111-1−ii-11ii−i−i11-1-1-1-111-1-111−i−iii−i−iii
χ1111-11-1-1-11111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iiiii−i−i-1-111-11−ii1-1−i−iii-1-11111-1-1-1-111−i−iiiii−i−i
χ1211-11-1-1-11111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11i−i-11−i−iii-1-111-1-11111-1-1ii−i−i−i−iii
χ1311-11-1-1-11111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11−ii-11ii−i−i-1-111-1-11111-1-1−i−iiiii−i−i
χ1411-11-1-1-11111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i−i−iii-1-111-11i−i1-1ii−i−i-1-11111-1-1-1-111ii−i−i−i−iii
χ1511-11-1-1-11111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iiiii−i−i-1-1111-1i−i-11−i−iii11-1-1-1-111-1-111ii−i−iii−i−i
χ1611-11-1-1-11111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-11-1−ii1-1−i−iii11-1-111-1-111-1-1−i−iii−i−iii
χ1722222222222222222222222-122-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000002222002200000000000000-1-1-1-1-1-1-1-10000
χ1822222222222222222222222-122-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-200-2-200000000000000111111110000
χ192222222222222222222222-12-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002222000000002200000000-1-1-1-100000000-1-1-1-1
χ202222222222222222222222-12-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000-2-2000000001111000000001111
χ212222222222222222-2-2-2-2-2-22-122-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000222200-2-200000000000000-1-1-1-111110000
χ222222222222222222-2-2-2-2-2-22-122-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2-2-20022000000000000001111-1-1-1-10000
χ232222222222222222-2-2-2-2-2-2-12-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000222200000000-2-200000000111100000000-1-1-1-1
χ242222222222222222-2-2-2-2-2-2-12-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-2-2-2000000002200000000-1-1-1-1000000001111
χ25222-22-2-2-222-22-2-2-22000000222-22-222-222-2-2-2-2-222-2-222-2-200000000000000002-22-2000000000000002-22-200000000000000000000
χ26222-22-2-2-222-22-2-2-22000000222-22-222-222-2-2-2-2-222-2-222-2-20000000000000000-22-2200000000000000-22-2200000000000000000000
χ2722-22-2-2-22222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-2-21112-11-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000022-2-2002i−2i00000000000000-1-111−i−iii0000
χ2822-22-2-2-22222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-2-21112-11-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000-2-22200−2i2i0000000000000011-1-1ii−i−i0000
χ2922-22-2-2-22222-2-2-22-22i−2i2i2i−2i−2i-12-1-122111-2-2-2-12-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00002i2i−2i−2i000000002-200000000-1-11100000000−i−iii
χ3022-22-2-2-22222-2-2-22-22i−2i2i2i−2i−2i-12-1-122111-2-2-2-12-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii0000−2i−2i2i2i00000000-220000000011-1-100000000ii−i−i
χ3122-22-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-2-21112-11-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000022-2-200−2i2i00000000000000-1-111ii−i−i0000
χ3222-22-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-2-21112-11-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000-2-222002i−2i0000000000000011-1-1−i−iii0000
χ3322-22-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i-12-1-122111-2-2-2-12-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00002i2i−2i−2i00000000-220000000011-1-100000000−i−iii
χ3422-22-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i-12-1-122111-2-2-2-12-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i0000−2i−2i2i2i000000002-200000000-1-11100000000ii−i−i
χ3522-2-2-222-222-2-222-2-2000000222-22-2-2-22-2-22-2-22222-2-2-2-22200000000000000002i−2i−2i2i000000000000002i−2i−2i2i00000000000000000000
χ3622-2-2-222-222-2-222-2-2000000222-22-2-2-22-2-22-2-22222-2-2-2-2220000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i00000000000000000000
χ372-222-2-22-22-2-22-222-200000022-22-222-2-22-22-2-2-222-22-22-2-220000000000000000000000002i−2i2i−2i0000000000000000002i−2i2i−2i00000000
χ382-222-2-22-22-2-22-222-200000022-22-222-2-22-22-2-2-222-22-22-2-22000000000000000000000000−2i2i−2i2i000000000000000000−2i2i−2i2i00000000
χ392-222-2-22-22-2-22-222-20000002-1-221-12-2-2-11-1-2112-11-11-111-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3000000002i−2i2i−2i000000000000000000−ii−ii3−33−30000
χ402-222-2-22-22-2-22-222-20000002-1-221-12-2-2-11-1-2112-11-11-111-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i300000000−2i2i−2i2i000000000000000000i−ii−i−33−330000
χ412-222-2-22-22-2-22-222-20000002-1-221-12-2-2-11-1-2112-11-11-111-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3000000002i−2i2i−2i000000000000000000−ii−ii−33−330000
χ422-222-2-22-22-2-22-222-20000002-1-221-12-2-2-11-1-2112-11-11-111-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i300000000−2i2i−2i2i000000000000000000i−ii−i3−33−30000
χ432-22-2-22-222-2222-2-2-200000022-2-2-2-22-222-2-2222-22-2-222-22-2000000000000000000002i−2i2i−2i0000000000000000000000000000002i−2i2i−2i
χ442-22-2-22-222-2222-2-2-200000022-2-2-2-22-222-2-2222-22-2-222-22-200000000000000000000−2i2i−2i2i000000000000000000000000000000−2i2i−2i2i
χ452-22-2-22-222-2222-2-2-2000000-1211-2-2-11-12-2-2-1221-111-1-11-1100003−33−33−33−33−33−300002i−2i2i−2i000000000000000000−i3i3−i3i300000000−ii−ii
χ462-22-2-22-222-2222-2-2-2000000-1211-2-2-11-12-2-2-1221-111-1-11-1100003−33−33−33−33−33−30000−2i2i−2i2i000000000000000000i3−i3i3−i300000000i−ii−i
χ472-22-2-22-222-2222-2-2-2000000-1211-2-2-11-12-2-2-1221-111-1-11-110000−33−33−33−33−33−3300002i−2i2i−2i000000000000000000i3−i3i3−i300000000−ii−ii
χ482-22-2-22-222-2222-2-2-2000000-1211-2-2-11-12-2-2-1221-111-1-11-110000−33−33−33−33−33−330000−2i2i−2i2i000000000000000000−i3i3−i3i300000000i−ii−i
χ492-2-2222-2-22-2-2-22-22200000022-22-22-222-22-2-2-22-22-22-2-222-20000000000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i00000000
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χ512-2-2222-2-22-2-2-22-2220000002-1-221-1-2221-11-21-1-2-11-111-1-113−3−33000033−3−3−3−333000000002i−2i−2i2i000000000000000000−iii−ii3−i3−i3i30000
χ522-2-2222-2-22-2-2-22-2220000002-1-221-1-2221-11-21-1-2-11-111-1-113−3−33000033−3−3−3−33300000000−2i2i2i−2i000000000000000000i−i−ii−i3i3i3−i30000
χ532-2-2222-2-22-2-2-22-2220000002-1-221-1-2221-11-21-1-2-11-111-1-11−333−30000−3−33333−3−3000000002i−2i−2i2i000000000000000000−iii−i−i3i3i3−i30000
χ542-2-2222-2-22-2-2-22-2220000002-1-221-1-2221-11-21-1-2-11-111-1-11−333−30000−3−33333−3−300000000−2i2i2i−2i000000000000000000i−i−iii3−i3−i3i30000
χ552-2-2-22-2222-22-2-22-2200000022-2-2-2-2-22-2-22222-222-2-22-22-22000000000000000000002-2-220000000000000000000000000000002-2-22
χ562-2-2-22-2222-22-2-22-2200000022-2-2-2-2-22-2-22222-222-2-22-22-2200000000000000000000-222-2000000000000000000000000000000-222-2
χ572-2-2-22-2222-22-2-22-22000000-1211-2-21-11-222-12-2-1-111-11-11-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i300002-2-22000000000000000000−i3i3i3−i300000000-111-1
χ582-2-2-22-2222-22-2-22-22000000-1211-2-21-11-222-12-2-1-111-11-11-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i30000-222-2000000000000000000i3−i3−i3i3000000001-1-11
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χ9666-66-6-6-66-3-3-3333-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000−2i−2i2i2i000000002-20000ii−i−i-1-1110000000000000000
χ9766-6-6-666-6-3-333-3-33300−3i33i33i3−3i300000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i−333−30000000000000000
χ9866-6-6-666-6-3-333-3-33300−3i33i33i3−3i30000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii3−3−330000000000000000
χ9966-6-6-666-6-3-333-3-333003i3−3i3−3i33i300000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i3−3−330000000000000000
χ10066-6-6-666-6-3-333-3-333003i3−3i3−3i33i30000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii−333−30000000000000000
χ10112-121212-12-1212-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-1212-1212-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-12121212-12-12-6666-66-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-1212-121212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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