Finite Group Databasebeta

← Group #13162046

Character table — Group #13162046

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222244444444444444444444444444444444448888888888888888888888888888888888363636363636363636363636363636363636727272727272727272
order1223334466612122333334666666666612121212121212121212121212121212126666666666666666612121212121212121212121212121212122444446612121212121212121212488121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111
χ51111111111111-111111-111-1-11111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-11-1-1-1-111
χ61111111111111-111111-111-1-11111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-11111-1-1
χ71111111111111-111111-111-1-11111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1-1
χ81111111111111-111111-111-1-11111111111-1-111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-11111
χ9222222-2-2222-2-202222202200222222-2-2-2-200-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-20000000000002-200000022-2-20000000000000
χ10222222-2-2222-2-202222202200222222-2-2-2-200-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-2000000000000-22000000-2-2220000000000000
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χ1222222-12222-12222-1-1-1-122-1-1-12-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200111111110000000000000
χ1322222-12222-122-22-1-1-1-1-22-1112-1-1-1-1222-1-11122-1-1-1-1-1-1-1-12-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-21111111122-2-200-1-1-1-111110000000000000
χ1422222-12222-122-22-1-1-1-1-22-1112-1-1-1-1222-1-11122-1-1-1-1-1-1-1-12-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-211111111-2-222001111-1-1-1-10000000000000
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χ1622222-1-2-222-1-2-202-1-1-1-102-1−i3i32-1-1-1-12-2-211−i3i3-2-211111111-2002-1-1-1-100−i3−i3−i3−i3i3i3i3i300-2111100−i3−i3−i3−i3i3i3i3i300-2200i3−i3i3−i311-1-10000000000000
χ1722222-1-2-222-1-2-202-1-1-1-102-1i3−i32-1-1-1-12-2-211i3−i3-2-211111111-2002-1-1-1-100i3i3i3i3−i3−i3−i3−i300-2111100i3i3i3i3−i3−i3−i3−i3002-200i3−i3i3−i3-1-1110000000000000
χ1822222-1-2-222-1-2-202-1-1-1-102-1i3−i32-1-1-1-12-2-211i3−i3-2-211111111-2002-1-1-1-100i3i3i3i3−i3−i3−i3−i300-2111100i3i3i3i3−i3−i3−i3−i300-2200−i3i3−i3i311-1-10000000000000
χ192222-12222-12222-12-1-1-12-1222-12-1-1-122-12222-1-122-1-1-1-1-1-1-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-1-1000000000000000000202-1-100-1-1
χ202222-12222-12222-12-1-1-12-1222-12-1-1-122-12222-1-122-1-1-1-1-1-1-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-1-1000000000000000000-20-2110011
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χ23222-12222-122-1-12-1-12-1-122222-1-12-1-1-1-122222-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-100002200000000-1-1-1-102000-1-100
χ24222-12222-122-1-12-1-12-1-122222-1-12-1-1-1-122222-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-10000-2-20000000011110-20001100
χ25222-12222-122-1-1-2-1-12-1-1-222-2-2-1-12-1-1-1-1222-2-2-1-1-1-122-1-1-1-121-2-1-12-1-1111-2111-2111-2-1-12-1-1111-2111-21100002200000000-1-1-1-10-20001100
χ26222-12222-122-1-1-2-1-12-1-1-222-2-2-1-12-1-1-1-1222-2-2-1-1-1-122-1-1-1-121-2-1-12-1-1111-2111-2111-2-1-12-1-1111-2111-2110000-2-200000000111102000-1-100
χ2722-22222-2222220222220-2-20022222-2-222-2002222222222-200-2-2-2-2-2000000000000-2-2-2-2-200000000002-2000022-2-200000000000000000
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χ2922-2222-22222-2-2222222-2-2-22222222-22-2-22-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-22222222222-2-222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000
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
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χ3322-222-12-222-12202-1-1-1-10-21i3−i32-1-1-1-1-2-22-11−i3i322-1-1-1-1-1-1-1-1-200-2111100i3i3i3i3−i3−i3−i3−i300-2111100−i3−i3−i3−i3i3i3i3i32-20000-1-111i3−i3i3−i30000000000000
χ3422-222-12-222-12202-1-1-1-10-21i3−i32-1-1-1-1-2-22-11−i3i322-1-1-1-1-1-1-1-1-200-2111100i3i3i3i3−i3−i3−i3−i300-2111100−i3−i3−i3−i3i3i3i3i3-22000011-1-1−i3i3−i3i30000000000000
χ3522-222-1-2222-1-2-222-1-1-1-1-2-21-1-12-1-1-1-1-22-21-111-2-211111111222-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-211111111000000−i3i3i3−i3−i3i3i3−i30000000000000
χ3622-222-1-2222-1-2-222-1-1-1-1-2-21-1-12-1-1-1-1-22-21-111-2-211111111222-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-211111111000000i3−i3−i3i3i3−i3−i3i30000000000000
χ3722-222-1-2222-1-2-2-22-1-1-1-12-21112-1-1-1-1-22-21-1-1-1-2-2111111112-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-1000000−i3i3i3−i3i3−i3−i3i30000000000000
χ3822-222-1-2222-1-2-2-22-1-1-1-12-21112-1-1-1-1-22-21-1-1-1-2-2111111112-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-1000000i3−i3−i3i3−i3i3i3−i30000000000000
χ3922-22-12-222-12-2-22-12-1-1-1-21-222-12-1-1-1-221-22-2-211-2-2111111-12-11-2111-1-12-1-1-12-1-1-1-21-12-1-1-111-2111-2111000000000000000000000−i3i300−i3i3
χ4022-22-12-222-12-2-22-12-1-1-1-21-222-12-1-1-1-221-22-2-211-2-2111111-12-11-2111-1-12-1-1-12-1-1-1-21-12-1-1-111-2111-2111000000000000000000000i3−i300i3−i3
χ4122-22-12-222-12-2-2-2-12-1-1-121-2-2-2-12-1-1-1-221-222211-2-2111111-1-211-211111-2111-21112-1-12-1-1-1-1-12-1-1-12-1-1-1000000000000000000000−i3i300i3−i3
χ4222-22-12-222-12-2-2-2-12-1-1-121-2-2-2-12-1-1-1-221-222211-2-2111111-1-211-211111-2111-21112-1-12-1-1-1-1-12-1-1-12-1-1-1000000000000000000000i3−i300−i3i3
χ4322-2-122-22-122112-1-12-1-1-2-2-222-1-12-1-11-1-2-22-2-21111-2-211112-1211-211-1-1-12-1-1-12-1-11-2-1-12-1-1111-2111-2110000000000000033−3−3000003−300
χ4422-2-122-22-122112-1-12-1-1-2-2-222-1-12-1-11-1-2-22-2-21111-2-211112-1211-211-1-1-12-1-1-12-1-11-2-1-12-1-1111-2111-21100000000000000−3−33300000−3300
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χ4622-2-122-22-12211-2-1-12-1-12-2-2-2-2-1-12-1-11-1-2-22221111-2-2111121-211-211111-2111-211-12-1-12-1-1-1-1-12-1-1-12-1-100000000000000−3−333000003−300
χ474444-24-4-44-24-4-40-24-2-2-20-2400-24-2-2-24-42-4-40022-4-4222222200-24-2-2-20000000000002-42220000000000000000000000000000000000000
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χ494444-2-2444-2-244-4-2-2111-4-2-222-2-211144-2-2-222-2-2-2-2111111-2-42-2-2111222-1-1-12-1-1-1-42-2-2111222-1-1-12-1-1-1000000000000000000000000000
χ504444-2-2-4-44-2-2-4-40-2-21110-2-2−2i32i3-2-21114-4222−2i32i32222-1-1-1-1-1-1200-2-211100−2i3i3i3i32i3−i3−i3−i30022-1-1-100−2i3i3i3i32i3−i3−i3−i3000000000000000000000000000
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χ54444-24-244-24-2-2-2-4-21-211-44-222-21-211-2-24-2-222-2-211-2-2111142-4-21-21122-12-1-1-12-1-12-4-21-21122-12-1-1-12-1-1000000000000000000000000000
χ55444-24-2-4-4-24-2220-21-21104-2−2i32i3-21-211-22-422−2i32i322-1-122-1-1-1-1-400-21-21100i3−2i3i3i3−i32i3−i3−i3002-12-1-100i3−2i3i3i3−i32i3−i3−i3000000000000000000000000000
χ56444-24-2-4-4-24-2220-21-21104-22i3−2i3-21-211-22-4222i3−2i322-1-122-1-1-1-1-400-21-21100−i32i3−i3−i3i3−2i3i3i3002-12-1-100−i32i3−i3−i3i3−2i3i3i3000000000000000000000000000
χ57444-2-2444-2-24-2-241-2-2114-24441-2-211-2-2-2444411-2-2-2-21111-2-2-21-2-21111-2-211-2-211-2-21-2-21111-2-211-2-211000000000000000000000000000
χ58444-2-2444-2-24-2-2-41-2-211-4-24-4-41-2-211-2-2-244-4-411-2-2-2-21111-2221-2-211-1-122-1-122-1-1221-2-211-1-122-1-122-1-1000000000000000000000000000
χ59444-2-24-4-4-2-242201-2-2110-24001-2-211-222-4-400-1-12222-1-1-1-12001-2-2113-3003-3003-300-122-1-13-3003-3003-3000000000000000000000000000
χ60444-2-24-4-4-2-242201-2-2110-24001-2-211-222-4-400-1-12222-1-1-1-12001-2-211-3300-3300-3300-122-1-1-3300-3300-33000000000000000000000000000
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χ65444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-2-2−2i32i3111−1−3i32−1+3i32-22222−2i32i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32200111−1−3i32−1+3i323-3i3i3−3−i323−i32−i3−i3−3+i323+i3200-1-1-11+3i321−3i323-3i3i3−3−i323−i32−i3−i3−3+i323+i32000000000000000000000000000
χ66444-2-2-2-4-4-2-2-2220111−1−3i32−1+3i320-2-22i3−2i3111−1−3i32−1+3i32-222222i3−2i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32200111−1−3i32−1+3i32-33−i3−i33+i32−3+i32i3i33−i32−3−i3200-1-1-11+3i321−3i32-33−i3−i33+i32−3+i32i3i33−i32−3−i32000000000000000000000000000
χ67444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-2-2−2i32i3111−1+3i32−1−3i32-22222−2i32i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32200111−1+3i32−1−3i32-33i3i33−i32−3−i32−i3−i33+i32−3+i3200-1-1-11−3i321+3i32-33i3i33−i32−3−i32−i3−i33+i32−3+i32000000000000000000000000000
χ68444-2-2-2-4-4-2-2-2220111−1+3i32−1−3i320-2-22i3−2i3111−1+3i32−1−3i32-222222i3−2i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32200111−1+3i32−1−3i323-3−i3−i3−3+i323+i32i3i3−3−i323−i3200-1-1-11−3i321+3i323-3−i3−i3−3+i323+i32i3i3−3−i323−i32000000000000000000000000000
χ6944-44-244-44-24440-24-2-2-202-400-24-2-2-2-4-4-24-400-2-244-2-2-2-2-2-22002-42220000000000002-42220000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.