Finite Group Databasebeta

← Group #13140165

Character table — Group #13140165

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121244444444444422444466661212121212121212121212121212121212121212
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
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ911-111-1-1-1111-1-1-11-1i−iii−i−i1111-1-1-1111-1-1-11-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1i−i1-111-1-111-1-1ii−i−iii−i−i11-1-1ii−i−i
χ1011-111-1-1-1111-1-1-11-1i−iii−i−i1111-1-1-1111-1-1-11-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i-1-111−i−iii1-1−ii-1111-1-1-1-111−i−iiiii−i−i-1-111−i−iii
χ1111-111-1-1-1111-1-1-11-1i−iii−i−i1111-1-1-1111-1-1-11-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11i−i-11-1-11111-1-1ii−i−i−i−iii-1-111−i−iii
χ1211-111-1-1-1111-1-1-11-1i−iii−i−i1111-1-1-1111-1-1-11-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii-1-111ii−i−i-11−ii1-1-1-111-1-111−i−iii−i−iii11-1-1ii−i−i
χ1311-111-1-1-1111-1-1-11-1−ii−i−iii1111-1-1-1111-1-1-11-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11−ii-11-1-11111-1-1−i−iiiii−i−i-1-111ii−i−i
χ1411-111-1-1-1111-1-1-11-1−ii−i−iii1111-1-1-1111-1-1-11-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i-1-111−i−iii-11i−i1-1-1-111-1-111ii−i−iii−i−i11-1-1−i−iii
χ1511-111-1-1-1111-1-1-11-1−ii−i−iii1111-1-1-1111-1-1-11-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1−ii1-111-1-111-1-1−i−iii−i−iii11-1-1−i−iii
χ1611-111-1-1-1111-1-1-11-1−ii−i−iii1111-1-1-1111-1-1-11-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii-1-111ii−i−i1-1i−i-1111-1-1-1-111ii−i−i−i−iii-1-111ii−i−i
χ1722222222222222222222222-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200000000220000-1-1-1-100000000-1-1-1-100000000
χ1822222222222222222222222-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000111100000000111100000000
χ192222222222222222222222-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-11111-2-2-2-211111111222200000000-2-20000111100000000-1-1-1-100000000
χ222222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-11111-2-2-2-211111111-2-2-2-200000000220000-1-1-1-100000000111100000000
χ232222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000022220000-2-200000000000000001111-1-1-1-1
χ242222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000-2-2-2-20000220000000000000000-1-1-1-11111
χ25222-2-2-2-2222-22-22-2-2000000222-22-2-22-2-22-22-2-2222-2-22-2-22000000000000000000002i−2i2i−2i000000000000002i−2i2i−2i0000000000000000
χ26222-2-2-2-2222-22-22-2-2000000222-22-2-22-2-22-22-2-2222-2-22-2-2200000000000000000000−2i2i−2i2i00000000000000−2i2i−2i2i0000000000000000
χ2722-222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i2-122-2-2-2-1-1-111121-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii2i2i−2i−2i000000002-20000-1-11100000000−i−iii00000000
χ2822-222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i2-122-2-2-2-1-1-111121-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii−2i−2i2i2i00000000-22000011-1-100000000ii−i−i00000000
χ2922-222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-1111222-2-2-2-1-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii000000002i2i−2i−2i00002-20000000000000000-1-111−i−iii
χ3022-222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-1111222-2-2-2-1-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00000000−2i−2i2i2i0000-22000000000000000011-1-1ii−i−i
χ3122-222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-2-2-2-1-1-111121-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i2i2i−2i−2i00000000-22000011-1-100000000−i−iii00000000
χ3222-222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-2-2-2-1-1-111121-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i−2i−2i2i2i000000002-20000-1-11100000000ii−i−i00000000
χ3322-222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-1111222-2-2-2-1-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i000000002i2i−2i−2i0000-22000000000000000011-1-1−i−iii
χ3422-222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-1111222-2-2-2-1-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00000000−2i−2i2i2i00002-20000000000000000-1-111ii−i−i
χ3522-2-2-222-222-2-22-2-22000000222-2-2222-2-2-22-2-22-222-2-2-222-2000000000000000000002i−2i−2i2i000000000000002i−2i−2i2i0000000000000000
χ3622-2-2-222-222-2-22-2-22000000222-2-2222-2-2-22-2-22-222-2-2-222-200000000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i0000000000000000
χ372-222-22-2-22-2222-2-2-200000022-2-222-2-22-22-2-222-22-22-222-2-20000000000000000000000002i−2i2i−2i000000000000000000000000002i−2i2i−2i
χ382-222-22-2-22-2222-2-2-200000022-2-222-2-22-22-2-222-22-22-222-2-2000000000000000000000000−2i2i−2i2i00000000000000000000000000−2i2i−2i2i
χ392-222-22-2-22-2222-2-2-2000000-1211-1-11-22-22-2-2-121-11-11-1-11100003−33−333−3−333−3−3000000002i−2i2i−2i0000000000000000000000−i3i3−i3i3−ii−ii
χ402-222-22-2-22-2222-2-2-2000000-1211-1-11-22-22-2-2-121-11-11-1-11100003−33−333−3−333−3−300000000−2i2i−2i2i0000000000000000000000i3−i3i3−i3i−ii−i
χ412-222-22-2-22-2222-2-2-2000000-1211-1-11-22-22-2-2-121-11-11-1-1110000−33−33−3−333−3−333000000002i−2i2i−2i0000000000000000000000i3−i3i3−i3−ii−ii
χ422-222-22-2-22-2222-2-2-2000000-1211-1-11-22-22-2-2-121-11-11-1-1110000−33−33−3−333−3−33300000000−2i2i−2i2i0000000000000000000000−i3i3−i3i3i−ii−i
χ432-22-22-22-22-2-22-2-22200000022-222-22-2-2222-2-2-2-22-2-222-22-200000000000000002i−2i2i−2i000000000000000000000000002i−2i2i−2i00000000
χ442-22-22-22-22-2-22-2-22200000022-222-22-2-2222-2-2-2-22-2-222-22-20000000000000000−2i2i−2i2i00000000000000000000000000−2i2i−2i2i00000000
χ452-22-22-22-22-2-22-2-2220000002-1-222-2211-1-1-11-21-2-111-1-11-113−33−300003−33−33−33−32i−2i2i−2i00000000000000−i3i3−i3i300000000−ii−ii00000000
χ462-22-22-22-22-2-22-2-2220000002-1-222-2211-1-1-11-21-2-111-1-11-113−33−300003−33−33−33−3−2i2i−2i2i00000000000000i3−i3i3−i300000000i−ii−i00000000
χ472-22-22-22-22-2-22-2-2220000002-1-222-2211-1-1-11-21-2-111-1-11-11−33−330000−33−33−33−332i−2i2i−2i00000000000000i3−i3i3−i300000000−ii−ii00000000
χ482-22-22-22-22-2-22-2-2220000002-1-222-2211-1-1-11-21-2-111-1-11-11−33−330000−33−33−33−33−2i2i−2i2i00000000000000−i3i3−i3i300000000i−ii−i00000000
χ492-2-22-2-2222-22-2-22-2200000022-2-2-2-22-22-2-2222-222-22-2-2-2220000000000000000000000002-2-22000000000000000000000000002-2-22
χ502-2-22-2-2222-22-2-22-2200000022-2-2-2-22-22-2-2222-222-22-2-2-222000000000000000000000000-222-200000000000000000000000000-222-2
χ512-2-22-2-2222-22-2-22-22000000-121111-1-22-2-222-1-2-1-11-1111-1-10000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3000000002-2-220000000000000000000000−i3i3i3−i3-111-1
χ522-2-22-2-2222-22-2-22-22000000-121111-1-22-2-222-1-2-1-11-1111-1-10000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i300000000-222-20000000000000000000000i3−i3−i3i31-1-11
χ532-2-22-2-2222-22-2-22-22000000-121111-1-22-2-222-1-2-1-11-1111-1-10000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3000000002-2-220000000000000000000000i3−i3−i3i3-111-1
χ542-2-22-2-2222-22-2-22-22000000-121111-1-22-2-222-1-2-1-11-1111-1-10000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i300000000-222-20000000000000000000000−i3i3i3−i31-1-11
χ552-2-2-222-222-2-2-2222-200000022-22-22-2-2-22-2-22-2222-2-22-22-2200000000000000002-2-22000000000000000000000000002-2-2200000000
χ562-2-2-222-222-2-2-2222-200000022-22-22-2-2-22-2-22-2222-2-22-22-220000000000000000-222-200000000000000000000000000-222-200000000
χ572-2-2-222-222-2-2-2222-20000002-1-22-22-211-111-1-2-12-111-11-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i32-2-2200000000000000−i3i3i3−i300000000-111-100000000
χ582-2-2-222-222-2-2-2222-20000002-1-22-22-211-111-1-2-12-111-11-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i3-222-200000000000000i3−i3−i3i3000000001-1-1100000000
χ592-2-2-222-222-2-2-2222-20000002-1-22-22-211-111-1-2-12-111-11-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i32-2-2200000000000000i3−i3−i3i300000000-111-100000000
χ602-2-2-222-222-2-2-2222-20000002-1-22-22-211-111-1-2-12-111-11-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i3-222-200000000000000−i3i3i3−i3000000001-1-1100000000
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χ844-4-4-444-444-4-4-4444-4000000-2-22-22-2222-222-22-2-21-1-11-11-112i3−2i3−2i32i30000−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000000000
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χ9666-666-6-6-6-3-3-3333-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000-2-2220000002i−2i00000011-1-1−i−iii000000000000
χ9766-6-6-666-6-3-333-333-30033−33−3333000000000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−ii3−i3−i3i3000000000000
χ9866-6-6-666-6-3-333-333-30033−33−333300000000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii−i3i3i3−i3000000000000
χ9966-6-6-666-6-3-333-333-300−333333−33000000000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i−i3i3i3−i3000000000000
χ10066-6-6-666-6-3-333-333-300−333333−3300000000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−iii3−i3−i3i3000000000000
χ10112-121212-1212-12-12-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-1212-1212-12-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-1212-12-121212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-121212-1212-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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