Finite Group Databasebeta

← Group #13162044

Character table — Group #13162044

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222244444444444444444444444444444444448888888888888888888888888888888888363636363636363636363636363636363636727272727272727272
order12233344666121223333346666666666121212121212121212121212121212121266666666666666666121212121212121212121212121212121224444466121212121212121212122668824242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-111
χ51111111111111-111111-11-1-111111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-1-111
χ61111111111111-111111-11-1-111111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1
χ71111111111111-111111-11-1-111111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1
χ81111111111111-111111-11-1-111111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111
χ9222222-2-2222-2-202222202002222222-2-2-2-200-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-20000000000002-200000022-2-20000000000000
χ10222222-2-2222-2-202222202002222222-2-2-2-200-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-2000000000000-22000000-2-2220000000000000
χ1122222-1222-122222-1-1-1-12222-12-1-1-1-122-1222222-1-1-1-1-1-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000002-1-10200-1-1
χ1222222-1222-122222-1-1-1-12222-12-1-1-1-122-1222222-1-1-1-1-1-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000-2110-20011
χ1322222-1222-1222-22-1-1-1-1-22-2-2-12-1-1-1-122-122-2-222-1-1-1-1-1-1-1-1-1-212-1-1-1-1-2-211111111-212-1-1-1-1-2-2111111110000000000000000002-1-10-20011
χ1422222-1222-1222-22-1-1-1-1-22-2-2-12-1-1-1-122-122-2-222-1-1-1-1-1-1-1-1-1-212-1-1-1-1-2-211111111-212-1-1-1-1-2-211111111000000000000000000-2110200-1-1
χ152222-122222-1222-12-1-1-12-1-1-12-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-122-1-1-1-1-1-1222200-1-1-1-1-1-1-1-10000000000000
χ162222-122222-1222-12-1-1-12-1-1-12-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200111111110000000000000
χ172222-122222-122-2-12-1-1-1-2-1112-12-1-1-1222-1-111-1-122-1-1-1-1-1-12-2-2-12-1-1-111-2-2111111-2-2-12-1-1-111-2-211111122-2-200-1-1-1-111110000000000000
χ182222-122222-122-2-12-1-1-1-2-1112-12-1-1-1222-1-111-1-122-1-1-1-1-1-12-2-2-12-1-1-111-2-2111111-2-2-12-1-1-111-2-2111111-2-222001111-1-1-1-10000000000000
χ192222-12-2-222-1-2-20-12-1-1-10-1−i3i32-12-1-1-12-2-211−i3i311-2-2111111-200-12-1-1-1−i3i300−i3−i3−i3i3i3i3001-2111−i3i300−i3−i3−i3i3i3i3002-200−i3i3−i3i3-1-1110000000000000
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χ222222-12-2-222-1-2-20-12-1-1-10-1i3−i32-12-1-1-12-2-211i3−i311-2-2111111-200-12-1-1-1i3−i300i3i3i3−i3−i3−i3001-2111i3−i300i3i3i3−i3−i3−i300-2200−i3i3−i3i311-1-10000000000000
χ23222-12222-122-1-12-1-12-1-122222-1-12-1-1-1-122222-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-1-12-1-12-1-1-12-1-12-1-1-1-1-1-12-1-12-1-100002200000000-1-1-1-100020-1-100
χ24222-12222-122-1-12-1-12-1-122222-1-12-1-1-1-122222-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-1-12-1-12-1-1-12-1-12-1-1-1-1-1-12-1-12-1-10000-2-2000000001111000-201100
χ25222-12222-122-1-1-2-1-12-1-1-22-2-22-1-12-1-1-1-1222-2-2-1-1-1-122-1-1-1-121-2-1-12-1-11111-211-2111-2-1-12-1-11111-211-21100002200000000-1-1-1-1000-201100
χ26222-12222-122-1-1-2-1-12-1-1-22-2-22-1-12-1-1-1-1222-2-2-1-1-1-122-1-1-1-121-2-1-12-1-11111-211-2111-2-1-12-1-11111-211-2110000-2-200000000111100020-1-100
χ2722-22222-2222220222220-200-222222-2-222-2002222222222-200-2-2-2-2-2000000000000-2-2-2-2-200000000002-2000022-2-200000000000000000
χ2822-22222-2222220222220-200-222222-2-222-2002222222222-200-2-2-2-2-2000000000000-2-2-2-2-20000000000-220000-2-22200000000000000000
χ2922-2222-22222-2-2222222-2-222-222222-22-2-22-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-22222222222-2-222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000
χ3022-2222-22222-2-2-2222222-2-2-2-222222-22-2-2222-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222000000000000000000000000000
χ3122-222-1-222-12-2-222-1-1-1-1-2-22212-1-1-1-1-221-22-2-2-2-211111111-12-1-2111122-1-1-1-1-1-1-1-1-212-1-1-1-1-2-2111111110000000000000000000−i3i30000−i3i3
χ3222-222-1-222-12-2-222-1-1-1-1-2-22212-1-1-1-1-221-22-2-2-2-211111111-12-1-2111122-1-1-1-1-1-1-1-1-212-1-1-1-1-2-2111111110000000000000000000i3−i30000i3−i3
χ3322-222-1-222-12-2-2-22-1-1-1-12-2-2-212-1-1-1-1-221-2222-2-211111111-1-21-21111-2-2111111112-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000−i3i30000i3−i3
χ3422-222-1-222-12-2-2-22-1-1-1-12-2-2-212-1-1-1-1-221-2222-2-211111111-1-21-21111-2-2111111112-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000i3−i30000−i3i3
χ3522-22-122-222-1220-12-1-1-101−i3i3-2-12-1-1-1-2-22-11i3−i3-1-122-1-1-1-1-1-1-2001-2111−i3i300−i3−i3−i3i3i3i3001-2111i3−i300i3i3i3−i3−i3−i32-20000-1-111−i3i3−i3i30000000000000
χ3622-22-122-222-1220-12-1-1-101−i3i3-2-12-1-1-1-2-22-11i3−i3-1-122-1-1-1-1-1-1-2001-2111−i3i300−i3−i3−i3i3i3i3001-2111i3−i300i3i3i3−i3−i3−i3-22000011-1-1i3−i3i3−i30000000000000
χ3722-22-122-222-1220-12-1-1-101i3−i3-2-12-1-1-1-2-22-11−i3i3-1-122-1-1-1-1-1-1-2001-2111i3−i300i3i3i3−i3−i3−i3001-2111−i3i300−i3−i3−i3i3i3i32-20000-1-111i3−i3i3−i30000000000000
χ3822-22-122-222-1220-12-1-1-101i3−i3-2-12-1-1-1-2-22-11−i3i3-1-122-1-1-1-1-1-1-2001-2111i3−i300i3i3i3−i3−i3−i3001-2111−i3i300−i3−i3−i3i3i3i3-22000011-1-1−i3i3−i3i30000000000000
χ3922-22-12-2222-1-2-22-12-1-1-1-21-1-1-2-12-1-1-1-22-21-11111-2-21111112221-2111-1-122-1-1-1-1-1-1-2-2-12-1-1-111-2-2111111000000−i3i3i3−i3−i3i3i3−i30000000000000
χ4022-22-12-2222-1-2-22-12-1-1-1-21-1-1-2-12-1-1-1-22-21-11111-2-21111112221-2111-1-122-1-1-1-1-1-1-2-2-12-1-1-111-2-2111111000000i3−i3−i3i3i3−i3−i3i30000000000000
χ4122-22-12-2222-1-2-2-2-12-1-1-12111-2-12-1-1-1-22-21-1-1-111-2-21111112-2-21-211111-2-211111122-12-1-1-1-1-122-1-1-1-1-1-1000000−i3i3i3−i3i3−i3−i3i30000000000000
χ4222-22-12-2222-1-2-2-2-12-1-1-12111-2-12-1-1-1-22-21-1-1-111-2-21111112-2-21-211111-2-211111122-12-1-1-1-1-122-1-1-1-1-1-1000000i3−i3−i3i3−i3i3i3−i30000000000000
χ4322-2-122-22-122112-1-12-1-1-2-222-2-1-12-1-11-1-2-22-2-21111-2-211112-1211-211-1-1-1-12-1-12-1-11-2-1-12-1-11111-211-2110000000000000033−3−3000003−300
χ4422-2-122-22-122112-1-12-1-1-2-222-2-1-12-1-11-1-2-22-2-21111-2-211112-1211-211-1-1-1-12-1-12-1-11-2-1-12-1-11111-211-21100000000000000−3−33300000−3300
χ4522-2-122-22-12211-2-1-12-1-12-2-2-2-2-1-12-1-11-1-2-22221111-2-2111121-211-2111111-211-211-12-1-12-1-1-1-1-1-12-1-12-1-10000000000000033−3−300000−3300
χ4622-2-122-22-12211-2-1-12-1-12-2-2-2-2-1-12-1-11-1-2-22221111-2-2111121-211-2111111-211-211-12-1-12-1-1-1-1-1-12-1-12-1-100000000000000−3−333000003−300
χ4744444-2-4-44-24-4-404-2-2-2-20400-24-2-2-2-24-42-4-400-4-4222222222004-2-2-2-2000000000000-422220000000000000000000000000000000000000
χ484444-2-2444-2-2444-2-21114-2-2-2-2-2-211144-2-2-2-2-2-2-2-2-2111111-24-2-2-2111-2-2-2-21111114-2-2-2111-2-2-2-2111111000000000000000000000000000
χ494444-2-2444-2-244-4-2-2111-4-222-2-2-211144-2-2-222-2-2-2-2111111-2-42-2-21112222-1-1-1-1-1-1-42-2-21112222-1-1-1-1-1-1000000000000000000000000000
χ504444-2-2-4-44-2-2-4-40-2-21110-2−2i32i3-2-2-21114-4222−2i32i32222-1-1-1-1-1-1200-2-2111−2i32i300i3i3i3−i3−i3−i30022-1-1-1−2i32i300i3i3i3−i3−i3−i3000000000000000000000000000
χ514444-2-2-4-44-2-2-4-40-2-21110-22i3−2i3-2-2-21114-42222i3−2i32222-1-1-1-1-1-1200-2-21112i3−2i300−i3−i3−i3i3i3i30022-1-1-12i3−2i300−i3−i3−i3i3i3i3000000000000000000000000000
χ52444-244-4-4-244220-2-24-2-204004-2-24-2-2-22-4-4-4002222-4-42222-400-2-24-2-200000000000022-4220000000000000000000000000000000000000
χ53444-24-244-2-24-2-24-21-2114444-2-21-211-2-2-24444-2-211-2-21111-2-2-2-21-211-2-211-211-211-2-2-21-211-2-211-211-211000000000000000000000000000
χ54444-24-244-2-24-2-2-4-21-211-44-4-4-2-21-211-2-2-244-4-4-2-211-2-21111-222-21-21122-1-12-1-12-1-122-21-21122-1-12-1-12-1-1000000000000000000000000000
χ55444-24-2-4-4-2-24220-21-2110400-2-21-211-222-4-40022-1-122-1-1-1-1200-21-211003-303-303-3002-12-1-1003-303-303-3000000000000000000000000000
χ56444-24-2-4-4-2-24220-21-2110400-2-21-211-222-4-40022-1-122-1-1-1-1200-21-21100-330-330-33002-12-1-100-330-330-33000000000000000000000000000
χ57444-2-2444-24-2-2-241-2-2114-2-2-241-2-211-2-24-2-2-2-211-2-2-2-211114-241-2-21111-2-2-211-211-241-2-21111-2-2-211-211000000000000000000000000000
χ58444-2-2444-24-2-2-2-41-2-211-4-22241-2-211-2-24-2-22211-2-2-2-2111142-41-2-211-1-1222-1-12-1-12-41-2-211-1-1222-1-12-1-1000000000000000000000000000
χ59444-2-24-4-4-24-22201-2-2110-2−2i32i341-2-211-22-422−2i32i3-1-12222-1-1-1-1-4001-2-211i3−i300−2i3i3i32i3−i3−i300-122-1-1i3−i300−2i3i3i32i3−i3−i3000000000000000000000000000
χ60444-2-24-4-4-24-22201-2-2110-22i3−2i341-2-211-22-4222i3−2i3-1-12222-1-1-1-1-4001-2-211−i3i3002i3−i3−i3−2i3i3i300-122-1-1−i3i3002i3−i3−i3−2i3i3i3000000000000000000000000000
χ61444-2-2-244-2-2-2-2-24111−1−3i32−1+3i324-2-2-2-2111−1−3i32−1+3i32-2-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2111−1−3i32−1+3i3211111−1−3i32−1+3i321−1+3i32−1−3i32-2-2111−1−3i32−1+3i3211111−1−3i32−1+3i321−1+3i32−1−3i32000000000000000000000000000
χ62444-2-2-244-2-2-2-2-24111−1+3i32−1−3i324-2-2-2-2111−1+3i32−1−3i32-2-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2111−1+3i32−1−3i3211111−1+3i32−1−3i321−1−3i32−1+3i32-2-2111−1+3i32−1−3i3211111−1+3i32−1−3i321−1−3i32−1+3i32000000000000000000000000000
χ63444-2-2-244-2-2-2-2-2-4111−1−3i32−1+3i32-4-222-2111−1−3i32−1+3i32-2-2-2-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32-222111−1−3i32−1+3i32-1-1-1-1-11+3i321−3i32-11−3i321+3i3222111−1−3i32−1+3i32-1-1-1-1-11+3i321−3i32-11−3i321+3i32000000000000000000000000000
χ64444-2-2-244-2-2-2-2-2-4111−1+3i32−1−3i32-4-222-2111−1+3i32−1−3i32-2-2-2-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32-222111−1+3i32−1−3i32-1-1-1-1-11−3i321+3i32-11+3i321−3i3222111−1+3i32−1−3i32-1-1-1-1-11−3i321+3i32-11+3i321−3i32000000000000000000000000000
χ65444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-2−2i32i3-2111−1−3i32−1+3i32-22222−2i32i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32200111−1−3i32−1+3i32i3−i33-3i3−3−i323−i32−i3−3+i323+i3200-1-1-11+3i321−3i32i3−i33-3i3−3−i323−i32−i3−3+i323+i32000000000000000000000000000
χ66444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-22i3−2i3-2111−1−3i32−1+3i32-222222i3−2i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32200111−1−3i32−1+3i32−i3i3-33−i33+i32−3+i32i33−i32−3−i3200-1-1-11+3i321−3i32−i3i3-33−i33+i32−3+i32i33−i32−3−i32000000000000000000000000000
χ67444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-2−2i32i3-2111−1+3i32−1−3i32-22222−2i32i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32200111−1+3i32−1−3i32i3−i3-33i33−i32−3−i32−i33+i32−3+i3200-1-1-11−3i321+3i32i3−i3-33i33−i32−3−i32−i33+i32−3+i32000000000000000000000000000
χ68444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-22i3−2i3-2111−1+3i32−1−3i32-222222i3−2i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32200111−1+3i32−1−3i32−i3i33-3−i3−3+i323+i32i3−3−i323−i3200-1-1-11−3i321+3i32−i3i33-3−i3−3+i323+i32i3−3−i323−i32000000000000000000000000000
χ6944-444-24-44-244404-2-2-2-20-40024-2-2-2-2-4-4-24-40044-2-2-2-2-2-2-2-2200-42222000000000000-422220000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.