Finite Group Databasebeta

← Group #13162041

Character table — Group #13162041

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222244444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636727272727272727272727272
order1223334466612122333334666666666612121212121212121212121212121212126666666666666666612121212121212121212121212121212128824242424888242424242424246688121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111
χ51111111111111-111111-111-1-111111111-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-11111-1-111-1-1-1-1
χ61111111111111-111111-111-1-111111111-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-111-1-11111
χ71111111111111-111111-111-1-111111111-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-11-1-1-1-111
χ81111111111111-111111-111-1-111111111-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-11-11111-1-1
χ9222222-2-2222-2-202222202200222222-2-200-2-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-2000000000000000002i−2i002i2i−2i−2i000000000000
χ10222222-2-2222-2-202222202200222222-2-200-2-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-200000000000000000−2i2i00−2i−2i2i2i000000000000
χ1122222-1222-122222-1-1-1-122222-12-1-1-1-12-122222-1-1-1-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000000000020-1-12000-1-100
χ1222222-1222-122222-1-1-1-122222-12-1-1-1-12-122222-1-1-1-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000000-2011-20001100
χ1322222-1222-1222-22-1-1-1-1-222-2-2-12-1-1-1-12-1-2-2222-1-1-1-1-1-1-1-1-12-212-1-1-1-1-2-2111111111-22-1-1-1-1-2-21111111100000000000000020-1-1-20001100
χ1422222-1222-1222-22-1-1-1-1-222-2-2-12-1-1-1-12-1-2-2222-1-1-1-1-1-1-1-1-12-212-1-1-1-1-2-2111111111-22-1-1-1-1-2-211111111000000000000000-20112000-1-100
χ152222-122222-1222-12-1-1-122-1222-12-1-1-12222-1-1-122-1-1-1-1-1-12-1-12-12-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-1000000000000000020002-1-100-1-1
χ162222-122222-1222-12-1-1-122-1222-12-1-1-12222-1-1-122-1-1-1-1-1-12-1-12-12-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-10000000000000000-2000-2110011
χ172222-122222-122-2-12-1-1-1-22-1-2-22-12-1-1-122-2-2-1-1-122-1-1-1-1-1-12-11-2-12-1-1-111-2-2111111-21-12-1-1-111-2-211111100000000000000002000-2-1-10011
χ182222-122222-122-2-12-1-1-1-22-1-2-22-12-1-1-122-2-2-1-1-122-1-1-1-1-1-12-11-2-12-1-1-111-2-2111111-21-12-1-1-111-2-21111110000000000000000-200021100-1-1
χ19222-12222-122-1-12-1-12-1-12-12-1-12-1-12-1-1-12-1-12-1-1-1-122-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-1000000000000
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χ21222-12222-122-1-1-2-1-12-1-1-2-12112-1-12-1-1-12112-1-1-1-122-1-1-1-122-2-2-1-12-1-11111-2-21111-2-2-1-12-1-11111-2-2111122-1-1-1-12-2-2-1-11111000000000000
χ22222-12222-122-1-1-2-1-12-1-1-2-12112-1-12-1-1-12112-1-1-1-122-1-1-1-122-2-2-1-12-1-11111-2-21111-2-2-1-12-1-11111-2-21111-2-21111-22211-1-1-1-1000000000000
χ23222-122-2-2-122110-1-12-1-10-12−i3i32-1-12-1-11-2−i3i3-21111-2-21111-2-200-1-12-1-1−i3i3−i3i300−i3−i3i3i30011-211−i3i3−i3i300−i3−i3i3i30033−3−302i−2i3−3−i−iii000000000000
χ24222-122-2-2-122110-1-12-1-10-12−i3i32-1-12-1-11-2−i3i3-21111-2-21111-2-200-1-12-1-1−i3i3−i3i300−i3−i3i3i30011-211−i3i3−i3i300−i3−i3i3i300−3−3330−2i2i−33ii−i−i000000000000
χ25222-122-2-2-122110-1-12-1-10-12i3−i32-1-12-1-11-2i3−i3-21111-2-21111-2-200-1-12-1-1i3−i3i3−i300i3i3−i3−i30011-211i3−i3i3−i300i3i3−i3−i30033−3−30−2i2i3−3ii−i−i000000000000
χ26222-122-2-2-122110-1-12-1-10-12i3−i32-1-12-1-11-2i3−i3-21111-2-21111-2-200-1-12-1-1i3−i3i3−i300i3i3−i3−i30011-211i3−i3i3−i300i3i3−i3−i300−3−33302i−2i−33−i−iii000000000000
χ2722-22222-2222220222220-2-200-222222-220022222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-20000000000222222-200-2-20000000000000000
χ2822-22222-2222220222220-2-200-222222-220022222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-20000000000-2-2-2-2-2-2200220000000000000000
χ2922-2222-22222-2-2222222-2-2-222-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-22222222222-2-222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000
χ3022-2222-22222-2-2-2222222-2-2-2-2-2222222-222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222000000000000000000000000000
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χ3322-222-1-222-12-2-2-22-1-1-1-12-2-2-2-212-1-1-1-12122-2-2-211111111-12-21-21111-2-211111111-122-1-1-1-122-1-1-1-1-1-1-1-100000000000000000−i3i30000i3−i300
χ3422-222-1-222-12-2-2-22-1-1-1-12-2-2-2-212-1-1-1-12122-2-2-211111111-12-21-21111-2-211111111-122-1-1-1-122-1-1-1-1-1-1-1-100000000000000000i3−i30000−i3i300
χ3522-22-12-2222-1-2-22-12-1-1-1-2-2122-2-12-1-1-12-2-2-2111-2-21111112-1-121-2111-1-122-1-1-1-1-1-1-21-12-1-1-111-2-2111111000000000000000000000−i3i300−i3i3
χ3622-22-12-2222-1-2-22-12-1-1-1-2-2122-2-12-1-1-12-2-2-2111-2-21111112-1-121-2111-1-122-1-1-1-1-1-1-21-12-1-1-111-2-2111111000000000000000000000i3−i300i3−i3
χ3722-22-12-2222-1-2-2-2-12-1-1-12-21-2-2-2-12-1-1-12-222111-2-21111112-11-21-211111-2-21111112-1-12-1-1-1-1-122-1-1-1-1-1-1000000000000000000000−i3i300i3−i3
χ3822-22-12-2222-1-2-2-2-12-1-1-12-21-2-2-2-12-1-1-12-222111-2-21111112-11-21-211111-2-21111112-1-12-1-1-1-1-122-1-1-1-1-1-1000000000000000000000i3−i300−i3i3
χ3922-2-1222-2-122-1-10-1-12-1-101-2−i3i3-2-1-12-1-112i3−i32-1-1-1-122-1-1-1-1-2-20011-211−i3i3−i3i300−i3−i3i3i30011-211i3−i3i3−i300i3i3−i3−i322-1-1-1-1-20011−i3i3−i3i3000000000000
χ4022-2-1222-2-122-1-10-1-12-1-101-2−i3i3-2-1-12-1-112i3−i32-1-1-1-122-1-1-1-1-2-20011-211−i3i3−i3i300−i3−i3i3i30011-211i3−i3i3−i300i3i3−i3−i3-2-21111200-1-1i3−i3i3−i3000000000000
χ4122-2-1222-2-122-1-10-1-12-1-101-2i3−i3-2-1-12-1-112−i3i32-1-1-1-122-1-1-1-1-2-20011-211i3−i3i3−i300i3i3−i3−i30011-211−i3i3−i3i300−i3−i3i3i322-1-1-1-1-20011i3−i3i3−i3000000000000
χ4222-2-1222-2-122-1-10-1-12-1-101-2i3−i3-2-1-12-1-112−i3i32-1-1-1-122-1-1-1-1-2-20011-211i3−i3i3−i300i3i3−i3−i30011-211−i3i3−i3i300−i3−i3i3i3-2-21111200-1-1−i3i3−i3i3000000000000
χ4322-2-122-22-122112-1-12-1-1-21-2-1-1-2-1-12-1-1-1-211-21111-2-21111222211-211-1-1-1-122-1-1-1-1-2-2-1-12-1-11111-2-211110033−3−3000−333−3−33000000000000
χ4422-2-122-22-122112-1-12-1-1-21-2-1-1-2-1-12-1-1-1-211-21111-2-21111222211-211-1-1-1-122-1-1-1-1-2-2-1-12-1-11111-2-2111100−3−3330003−3−333−3000000000000
χ4522-2-122-22-12211-2-1-12-1-121-211-2-1-12-1-1-1-2-1-1-21111-2-2111122-2-211-2111111-2-2111122-1-12-1-1-1-1-1-122-1-1-1-10033−3−3000−33−333−3000000000000
χ4622-2-122-22-12211-2-1-12-1-121-211-2-1-12-1-1-1-2-1-1-21111-2-2111122-2-211-2111111-2-2111122-1-12-1-1-1-1-1-122-1-1-1-100−3−3330003−33−3−33000000000000
χ4744444-2-4-44-24-4-404-2-2-2-204400-24-2-2-2-2-4200-4-4-4222222222-4004-2-2-2-2000000000000-422220000000000000000000000000000000000000
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χ494444-2-2444-2-2444-2-211144-244-2-2-21114-244-2-2-2-2-2111111-2-2-2-2-2-2111-2-2-2-2111111-2-2-2-2111-2-2-2-2111111000000000000000000000000000
χ504444-2-2444-2-244-4-2-2111-44-2-4-4-2-2-21114-2-4-4-2-2-2-2-2111111-2-222-2-21112222-1-1-1-1-1-122-2-21112222-1-1-1-1-1-1000000000000000000000000000
χ514444-2-2-4-44-2-2-4-40-2-211104-200-2-2-2111-420022222-1-1-1-1-1-12200-2-211100003-33-33-30022-1-1-100003-33-33-3000000000000000000000000000
χ524444-2-2-4-44-2-2-4-40-2-211104-200-2-2-2111-420022222-1-1-1-1-1-12200-2-21110000-33-33-330022-1-1-10000-33-33-33000000000000000000000000000
χ53444-24-244-2-24-2-24-21-2114-24-2-2-2-21-211-2-2-2-24-2-211-2-21111-244-2-21-211-2-211-2-21111-24-21-211-2-211-2-21111000000000000000000000000000
χ54444-24-244-2-24-2-2-4-21-211-4-2422-2-21-211-2-2224-2-211-2-21111-24-42-21-21122-1-122-1-1-1-12-4-21-21122-1-122-1-1-1-1000000000000000000000000000
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χ56444-24-2-4-4-2-24220-21-2110-242i3−2i3-2-21-211222i3−2i3-422-1-122-1-1-1-12-400-21-2112i3−2i3−i3i300−i3−i3i3i3002-12-1-12i3−2i3−i3i300−i3−i3i3i3000000000000000000000000000
χ57444-2-2444-24-2-2-241-2-2114-2-2-2-241-2-211-24-2-2-211-2-2-2-211114-2-241-2-21111-2-2-2-211114-21-2-21111-2-2-2-21111000000000000000000000000000
χ58444-2-2444-24-2-2-2-41-2-211-4-2-22241-2-211-2422-211-2-2-2-211114-22-41-2-211-1-12222-1-1-1-1-421-2-211-1-12222-1-1-1-1000000000000000000000000000
χ59444-2-24-4-4-24-22201-2-2110-2-2−2i32i341-2-2112-4−2i32i32-1-12222-1-1-1-1-42001-2-211i3−i3−2i32i300i3i3−i3−i300-122-1-1i3−i3−2i32i300i3i3−i3−i3000000000000000000000000000
χ60444-2-24-4-4-24-22201-2-2110-2-22i3−2i341-2-2112-42i3−2i32-1-12222-1-1-1-1-42001-2-211−i3i32i3−2i300−i3−i3i3i300-122-1-1−i3i32i3−2i300−i3−i3i3i3000000000000000000000000000
χ61444-2-2-244-2-2-2-2-24111−1−3i32−1+3i324-2-2-2-2-2111−1−3i32−1+3i32-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1+3i32−1−3i32-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1+3i32−1−3i32000000000000000000000000000
χ62444-2-2-244-2-2-2-2-24111−1+3i32−1−3i324-2-2-2-2-2111−1+3i32−1−3i32-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1−3i32−1+3i32-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1−3i32−1+3i32000000000000000000000000000
χ63444-2-2-244-2-2-2-2-2-4111−1−3i32−1+3i32-4-2-222-2111−1−3i32−1+3i32-2-222-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321−3i321+3i3222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321−3i321+3i32000000000000000000000000000
χ64444-2-2-244-2-2-2-2-2-4111−1+3i32−1−3i32-4-2-222-2111−1+3i32−1−3i32-2-222-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321+3i321−3i3222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321+3i321−3i32000000000000000000000000000
χ65444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-2-2−2i32i3-2111−1−3i32−1+3i3222−2i32i32-1-1-1-1-1-11+3i321+3i321−3i321−3i322200111−1−3i32−1+3i32i3−i3i3−i33-3−3−i323−i32−3+i323+i3200-1-1-11+3i321−3i32i3−i3i3−i33-3−3−i323−i32−3+i323+i32000000000000000000000000000
χ66444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-2-22i3−2i3-2111−1−3i32−1+3i32222i3−2i32-1-1-1-1-1-11+3i321+3i321−3i321−3i322200111−1−3i32−1+3i32−i3i3−i3i3-333+i32−3+i323−i32−3−i3200-1-1-11+3i321−3i32−i3i3−i3i3-333+i32−3+i323−i32−3−i32000000000000000000000000000
χ67444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-2-2−2i32i3-2111−1+3i32−1−3i3222−2i32i32-1-1-1-1-1-11−3i321−3i321+3i321+3i322200111−1+3i32−1−3i32i3−i3i3−i3-333−i32−3−i323+i32−3+i3200-1-1-11−3i321+3i32i3−i3i3−i3-333−i32−3−i323+i32−3+i32000000000000000000000000000
χ68444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-2-22i3−2i3-2111−1+3i32−1−3i32222i3−2i32-1-1-1-1-1-11−3i321−3i321+3i321+3i322200111−1+3i32−1−3i32−i3i3−i3i33-3−3+i323+i32−3−i323−i3200-1-1-11−3i321+3i32−i3i3−i3i33-3−3+i323+i32−3−i323−i32000000000000000000000000000
χ6944-444-24-44-244404-2-2-2-20-4-40024-2-2-2-2-4-200444-2-2-2-2-2-2-2-22-400-42222000000000000-422220000000000000000000000000000000000000
χ7044-44-244-444-2440-24-2-2-20-4200-4-24-2-2-2-4400-2-2-244-2-2-2-2-2-2-42002-42220000000000002-42220000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.