Finite Group Databasebeta

← Group #13140104

Character table — Group #13140104

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
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ911-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-11-1i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−i
χ1011-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i-1-111−i−iii1-1-11−iiii−i−i11-1-1-1-111-1-111−i−iii−i−iii
χ1111-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11-11i−i−i−iii-1-11111-1-1-1-111ii−i−i−i−iii
χ1211-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-111ii−i−i-111-1−ii−i−iii-1-111-1-11111-1-1−i−iiiii−i−i
χ1311-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11-11−iiii−i−i-1-11111-1-1-1-111−i−iiiii−i−i
χ1411-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-111−i−iii-111-1i−iii−i−i-1-111-1-11111-1-1ii−i−i−i−iii
χ1511-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-1−i−iii1-11-1−ii−i−iii11-1-111-1-111-1-1−i−iii−i−iii
χ1611-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii-1-111ii−i−i1-1-11i−i−i−iii11-1-1-1-111-1-111ii−i−iii−i−i
χ1722222222222222222222222-122-1-1222-1-1-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000000002222002200000000000000-1-1-1-10000-1-1-1-1
χ1822222222222222222222222-122-1-1222-1-1-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-200-2-200000000000000111100001111
χ192222222222222222222222-12-1-122-1-1-1222-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100002222000000002200000000-1-1-1-10000-1-1-1-10000
χ202222222222222222222222-12-1-122-1-1-1222-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-200000000-2-2000000001111000011110000
χ212222222222222222-2-2-2-2-2-22-122-1-1222-1-1-12-12-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000222200-2-20000000000000011110000-1-1-1-1
χ222222222222222222-2-2-2-2-2-22-122-1-1222-1-1-12-12-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000-2-2-2-2002200000000000000-1-1-1-100001111
χ232222222222222222-2-2-2-2-2-2-12-1-122-1-1-1222-12-12-1-1-1-1-1-1-1-111-2-211-2-2111111110000222200000000-2-200000000-1-1-1-1000011110000
χ242222222222222222-2-2-2-2-2-2-12-1-122-1-1-1222-12-12-1-1-1-1-1-1-1-111-2-211-2-2111111110000-2-2-2-200000000220000000011110000-1-1-1-10000
χ25222-2-22-2-222-22-2-2-22000000222-22-222-222-2-2-2-2-222-2-222-2-200000000000000002-22-2000000000000002-22-200000000000000000000
χ26222-2-22-2-222-22-2-2-22000000222-22-222-222-2-2-2-2-222-2-222-2-20000000000000000-22-2200000000000000-22-2200000000000000000000
χ2722-22-2-2-2222-2-222-2-2000000222-22-2-2-22-2-22-2-22222-2-2-2-22200000000000000002i−2i−2i2i000000000000002i−2i−2i2i00000000000000000000
χ2822-22-2-2-2222-2-222-2-2000000222-22-2-2-22-2-22-2-22222-2-2-2-2220000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i00000000000000000000
χ2922-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-2-21112-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii000000002i2i−2i−2i002-200000000000000-1-1110000−i−iii
χ3022-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-2-21112-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii00000000−2i−2i2i2i00-220000000000000011-1-10000ii−i−i
χ3122-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-122111-2-2-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii000022-2-2000000002i−2i00000000-1-1110000−i−iii0000
χ3222-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-122111-2-2-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii0000-2-22200000000−2i2i0000000011-1-10000ii−i−i0000
χ3322-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-2-21112-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i000000002i2i−2i−2i00-220000000000000011-1-10000−i−iii
χ3422-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-2-21112-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i00000000−2i−2i2i2i002-200000000000000-1-1110000ii−i−i
χ3522-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-122111-2-2-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i000022-2-200000000−2i2i00000000-1-1110000ii−i−i0000
χ3622-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-122111-2-2-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i0000-2-222000000002i−2i0000000011-1-10000−i−iii0000
χ372-2222-2-2-22-2222-2-2-200000022-2-2-222-222-222-2-2-22-22-22-22-2000000000000000000002-22-20000000000000000002-22-2000000000000
χ382-2222-2-2-22-2222-2-2-200000022-2-2-222-222-222-2-2-22-22-22-22-200000000000000000000-22-22000000000000000000-22-22000000000000
χ392-2222-2-2-22-2222-2-2-2000000-1211-22-11-12-22-1-21-2-11-11-11-113−3003−30033−3−333−3−300002-22-2000000000000000000-11-1100003−33−30000
χ402-2222-2-2-22-2222-2-2-2000000-1211-22-11-12-22-1-21-2-11-11-11-113−3003−30033−3−333−3−30000-22-220000000000000000001-11-10000−33−330000
χ412-2222-2-2-22-2222-2-2-2000000-1211-22-11-12-22-1-21-2-11-11-11-11−3300−3300−3−333−3−33300002-22-2000000000000000000-11-110000−33−330000
χ422-2222-2-2-22-2222-2-2-2000000-1211-22-11-12-22-1-21-2-11-11-11-11−3300−3300−3−333−3−3330000-22-220000000000000000001-11-100003−33−30000
χ432-22-2-2-2222-2-22-222-200000022-22-2-22-2-22-2-2-22222-2-222-2-220000000000000000000000002-22-2000000000000000000000000002-22-2
χ442-22-2-2-2222-2-22-222-200000022-22-2-22-2-22-2-2-22222-2-222-2-22000000000000000000000000-22-2200000000000000000000000000-22-22
χ452-22-2-2-2222-2-22-222-20000002-1-22112-2-2-111-2-12-1-111-1-111-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i3000000002-22-2000000000000000000−i3i3−i3i30000-11-11
χ462-22-2-2-2222-2-22-222-20000002-1-22112-2-2-111-2-12-1-111-1-111-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i300000000-22-22000000000000000000i3−i3i3−i300001-11-1
χ472-22-2-2-2222-2-22-222-20000002-1-22112-2-2-111-2-12-1-111-1-111-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i3000000002-22-2000000000000000000i3−i3i3−i30000-11-11
χ482-22-2-2-2222-2-22-222-20000002-1-22112-2-2-111-2-12-1-111-1-111-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i300000000-22-22000000000000000000−i3i3−i3i300001-11-1
χ492-2-22-222-22-2-2-22-22200000022-22-2-2-222-222-22-2-22-2-22-222-20000000000000000000000002i−2i−2i2i000000000000000000000000002i−2i−2i2i
χ502-2-22-222-22-2-2-22-22200000022-22-2-2-222-222-22-2-22-2-22-222-2000000000000000000000000−2i2i2i−2i00000000000000000000000000−2i2i2i−2i
χ512-2-22-222-22-2-2-22-2220000002-1-2211-2221-1-1-2-1-21-111-11-1-11003−300−333−33−3−33−33000000002i−2i−2i2i000000000000000000−i3i3i3−i30000−iii−i
χ522-2-22-222-22-2-2-22-2220000002-1-2211-2221-1-1-2-1-21-111-11-1-11003−300−333−33−3−33−3300000000−2i2i2i−2i000000000000000000i3−i3−i3i30000i−i−ii
χ532-2-22-222-22-2-2-22-2220000002-1-2211-2221-1-1-2-1-21-111-11-1-1100−33003−3−33−333−33−3000000002i−2i−2i2i000000000000000000i3−i3−i3i30000−iii−i
χ542-2-22-222-22-2-2-22-2220000002-1-2211-2221-1-1-2-1-21-111-11-1-1100−33003−3−33−333−33−300000000−2i2i2i−2i000000000000000000−i3i3i3−i30000i−i−ii
χ552-2-2-222-222-22-2-22-2200000022-2-2-22-22-2-22-22-2222-22-2-22-22000000000000000000002-2-220000000000000000002-2-22000000000000
χ562-2-2-222-222-22-2-22-2200000022-2-2-22-22-2-22-22-2222-22-2-22-2200000000000000000000-222-2000000000000000000-222-2000000000000
χ572-2-2-222-222-22-2-22-22000000-1211-221-11-22-2-1-2-12-11-111-11-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i300002-2-22000000000000000000-111-10000−i3i3i3−i30000
χ582-2-2-222-222-22-2-22-22000000-1211-221-11-22-2-1-2-12-11-111-11-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i30000-222-20000000000000000001-1-110000i3−i3−i3i30000
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χ9866-6-66-66-6-3-3-3333-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000−2i−2i2i2i00000000-220000ii−i−i11-1-10000000000000000
χ9966-6-66-66-6-3-3-3333-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000002i2i−2i−2i00000000-220000−i−iii11-1-10000000000000000
χ10066-6-66-66-6-3-3-3333-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000−2i−2i2i2i000000002-20000ii−i−i-1-1110000000000000000
χ10112-12121212-12-12-12-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-12-121212-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-1212-121212-12-6666-66-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-121212-1212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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