Finite Group Databasebeta

← Group #13178777

Character table — Group #13178777

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1122222222222444444444444444444444444444444444488888888888888888888888888888888889918181818181818363636363636363636363636363636367272727272727272
order1223334466612122333334666666666612121212121212121212121212121212126666666666666666612121212121212121212121212121212122224466121224444466688881212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-111-1-111
χ51111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-11-1-11111-1-1-1-1
χ61111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111
χ71111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-11111-1-1-1-111
χ81111111111111-111111-1111-1-111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11111-1-1-111-1-11111-1-1
χ911-1111-11111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-111-11-111-1-11-11-11-1-1111-11-11-1-11-11-11-11-1
χ1011-1111-11111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-111-11-111-1-11-1-11-11-111-11-111-1-1-11-11-11-11
χ1111-1111-11111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-111-1-111-1-11-1-11-1111-1-111-1-11
χ1211-1111-11111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-111-11-1-1-111-1-111-111-1-111-1
χ1311-1111-11111-1-1-1111111-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-11-111-1-1-111-11-1-1-1-1-11-111111-11-1-11-11
χ1411-1111-11111-1-1-1111111-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-11-111-1-1-11-11-11-1-1-11-11-1111-11-111-11-1
χ1511-1111-11111-1-1-1111111-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-11-1-1111-11-1-11111-111-1-1-1-11-1-11-111-1
χ1611-1111-11111-1-1-1111111-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-11-1-1111-1-111-11111-1-11-1-1-1-111-11-1-11
χ17222222-2-2222-2-202222202220022222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-20000000000222-2-222-2-20000002000000-20000000000
χ18222222-2-2222-2-202222202220022222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-20000000000-2-2-222-2-222000000-200000020000000000
χ1922222-12222-1-1-122-1-1-1-1222-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-1220000-1-1-10000-1-1-100000000
χ2022222-12222-1-1-122-1-1-1-1222-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-21111-2-20000111000011100000000
χ2122222-12222-1-1-1-22-1-1-1-1-222-1112-1-1-1-1-1221122-1-1-1-1-1-1-1-122-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-21111111122222-1-1-1-1-2-20000-1110000-11100000000
χ2222222-12222-1-1-1-22-1-1-1-1-222-1112-1-1-1-1-1221122-1-1-1-1-1-1-1-122-2-22-1-1-1-1-2-211111111-2-22-1-1-1-1-2-211111111-2-2-2-2-211112200001-1-100001-1-100000000
χ2322222-1-2-222-11102-1-1-1-1022-1−i3i32-1-1-1-11-2-2−i3i3-2-211111111-2-2002-1-1-1-100−i3−i3−i3−i3i3i3i3i300-2111100−i3−i3−i3−i3i3i3i3i3222-2-2-1-111000000-1−i3i300001−i3i300000000
χ2422222-1-2-222-11102-1-1-1-1022-1−i3i32-1-1-1-11-2-2−i3i3-2-211111111-2-2002-1-1-1-100−i3−i3−i3−i3i3i3i3i300-2111100−i3−i3−i3−i3i3i3i3i3-2-2-22211-1-10000001i3−i30000-1i3−i300000000
χ2522222-1-2-222-11102-1-1-1-1022-1i3−i32-1-1-1-11-2-2i3−i3-2-211111111-2-2002-1-1-1-100i3i3i3i3−i3−i3−i3−i300-2111100i3i3i3i3−i3−i3−i3−i3222-2-2-1-111000000-1i3−i300001i3−i300000000
χ2622222-1-2-222-11102-1-1-1-1022-1i3−i32-1-1-1-11-2-2i3−i3-2-211111111-2-2002-1-1-1-100i3i3i3i3−i3−i3−i3−i300-2111100i3i3i3i3−i3−i3−i3−i3-2-2-22211-1-10000001−i3i30000-1−i3i300000000
χ272222-12222-12222-12-1-1-122-1222-12-1-1-122-122-1-122-1-1-1-1-1-12-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-1-1000000000000022000002200000-1-100-1-1
χ282222-12222-12222-12-1-1-122-1222-12-1-1-122-122-1-122-1-1-1-1-1-12-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-1-10000000000000-2-200000-2-200000110011
χ292222-12222-1222-2-12-1-1-1-22-12-2-2-12-1-1-122-1-2-2-1-122-1-1-1-1-1-12-1-21-12-1-1-111-2111-2111-21-12-1-1-111-2111-211100000000000002200000-2-200000-1-10011
χ302222-12222-1222-2-12-1-1-1-22-12-2-2-12-1-1-122-1-2-2-1-122-1-1-1-1-1-12-1-21-12-1-1-111-2111-2111-21-12-1-1-111-2111-21110000000000000-2-20000022000001100-1-1
χ31222-12222-122222-1-12-1-12-12222-1-12-1-12-1222-1-1-1-122-1-1-1-1-12-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-10000000000022000002200000-1-100-1-100
χ32222-12222-122222-1-12-1-12-12222-1-12-1-12-1222-1-1-1-122-1-1-1-1-12-12-1-12-1-1-1-1-12-1-1-12-1-1-12-1-12-1-1-1-1-12-1-1-12-1-100000000000-2-200000-2-20000011001100
χ33222-12222-12222-2-1-12-1-1-2-122-2-2-1-12-1-12-12-2-2-1-1-1-122-1-1-1-1-121-2-1-12-1-1111-2111-2111-2-1-12-1-1111-2111-211000000000002200000-2-200000-1-1001100
χ34222-12222-12222-2-1-12-1-1-2-122-2-2-1-12-1-12-12-2-2-1-1-1-122-1-1-1-1-121-2-1-12-1-1111-2111-2111-2-1-12-1-1111-2111-21100000000000-2-20000022000001100-1-100
χ3522-22222-2222220222220-2-2-20022222-222002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-2000000000022-2-222222000000-2000000-20000000000
χ3622-22222-2222220222220-2-2-20022222-222002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-20000000000-2-222-2-2-2-2-2000000200000020000000000
χ3722-222-12-222-1-1-102-1-1-1-10-2-21−i3i32-1-1-1-1122i3−i322-1-1-1-1-1-1-1-1-2-200-2111100−i3−i3−i3−i3i3i3i3i300-2111100i3i3i3i3−i3−i3−i3−i322-2-22-1-1-1-10000001−i3i300001i3−i300000000
χ3822-222-12-222-1-1-102-1-1-1-10-2-21−i3i32-1-1-1-1122i3−i322-1-1-1-1-1-1-1-1-2-200-2111100−i3−i3−i3−i3i3i3i3i300-2111100i3i3i3i3−i3−i3−i3−i3-2-222-21111000000-1i3−i30000-1−i3i300000000
χ3922-222-12-222-1-1-102-1-1-1-10-2-21i3−i32-1-1-1-1122−i3i322-1-1-1-1-1-1-1-1-2-200-2111100i3i3i3i3−i3−i3−i3−i300-2111100−i3−i3−i3−i3i3i3i3i322-2-22-1-1-1-10000001i3−i300001−i3i300000000
χ4022-222-12-222-1-1-102-1-1-1-10-2-21i3−i32-1-1-1-1122−i3i322-1-1-1-1-1-1-1-1-2-200-2111100i3i3i3i3−i3−i3−i3−i300-2111100−i3−i3−i3−i3i3i3i3i3-2-222-21111000000-1−i3i30000-1i3−i300000000
χ4122-222-1-2222-11122-1-1-1-1-2-2-21-1-12-1-1-1-1-1-2-211-2-2111111112222-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-21111111122-22-2-1-1112-200001-1-10000-11100000000
χ4222-222-1-2222-11122-1-1-1-1-2-2-21-1-12-1-1-1-1-1-2-211-2-2111111112222-2111122-1-1-1-1-1-1-1-1-2-22-1-1-1-1-2-211111111-2-22-2211-1-1-220000-11100001-1-100000000
χ4322-222-1-2222-111-22-1-1-1-12-2-21112-1-1-1-1-1-2-2-1-1-2-21111111122-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-122-22-2-1-111-2200001110000-1-1-100000000
χ4422-222-1-2222-111-22-1-1-1-12-2-21112-1-1-1-1-1-2-2-1-1-2-21111111122-2-2-21111-2-211111111222-1-1-1-122-1-1-1-1-1-1-1-1-2-22-2211-1-12-20000-1-1-1000011100000000
χ4522-22-12-222-12-2-22-12-1-1-1-2-21-222-12-1-1-12-21-2-211-2-21111112-12-11-2111-1-12-1-1-12-1-1-1-21-12-1-1-111-2111-211100000000000002-2000002-200000-1100-11
χ4622-22-12-222-12-2-22-12-1-1-1-2-21-222-12-1-1-12-21-2-211-2-21111112-12-11-2111-1-12-1-1-12-1-1-1-21-12-1-1-111-2111-21110000000000000-2200000-22000001-1001-1
χ4722-22-12-222-12-2-2-2-12-1-1-12-21-2-2-2-12-1-1-12-212211-2-21111112-1-211-211111-2111-21112-1-12-1-1-1-1-12-1-1-12-1-1-100000000000002-200000-2200000-11001-1
χ4822-22-12-222-12-2-2-2-12-1-1-12-21-2-2-2-12-1-1-12-212211-2-21111112-1-211-211111-2111-21112-1-12-1-1-1-1-12-1-1-12-1-1-10000000000000-22000002-2000001-100-11
χ4922-2-122-22-122-2-22-1-12-1-1-21-2-222-1-12-1-121-2-2-21111-2-21111-12-1211-211-1-1-12-1-1-12-1-11-2-1-12-1-1111-2111-211000000000002-2000002-200000-1100-1100
χ5022-2-122-22-122-2-22-1-12-1-1-21-2-222-1-12-1-121-2-2-21111-2-21111-12-1211-211-1-1-12-1-1-12-1-11-2-1-12-1-1111-2111-21100000000000-2200000-22000001-1001-100
χ5122-2-122-22-122-2-2-2-1-12-1-121-2-2-2-2-1-12-1-121-2221111-2-21111-121-211-211111-2111-211-12-1-12-1-1-1-1-12-1-1-12-1-1000000000002-200000-2200000-11001-100
χ5222-2-122-22-122-2-2-2-1-12-1-121-2-2-2-2-1-12-1-121-2221111-2-21111-121-211-211111-2111-211-12-1-12-1-1-1-1-12-1-1-12-1-100000000000-22000002-2000001-100-1100
χ534444-24-4-44-24-4-40-24-2-2-204-2400-24-2-2-2-4-420022-4-4222222-4200-24-2-2-20000000000002-42220000000000000000000000000000000000000000000
χ544444-2-2444-2-2-2-24-2-211144-2-2-2-2-2-2111-24-2-2-2-2-2-2-21111114-24-2-2-2111-2-2-2111-21114-2-2-2111-2-2-2111-2111000000000000000000000000000000000
χ554444-2-2444-2-2-2-2-4-2-2111-44-2-222-2-2111-24-222-2-2-2-21111114-2-42-2-2111222-1-1-12-1-1-1-42-2-2111222-1-1-12-1-1-1000000000000000000000000000000000
χ564444-2-2-4-44-2-2220-2-211104-2-2−2i32i3-2-21112-42−2i32i32222-1-1-1-1-1-1-4200-2-211100−2i3i3i3i32i3−i3−i3−i30022-1-1-100−2i3i3i3i32i3−i3−i3−i3000000000000000000000000000000000
χ574444-2-2-4-44-2-2220-2-211104-2-22i3−2i3-2-21112-422i3−2i32222-1-1-1-1-1-1-4200-2-2111002i3−i3−i3−i3−2i3i3i3i30022-1-1-1002i3−i3−i3−i3−2i3i3i3i3000000000000000000000000000000000
χ58444-244-4-4-244-4-40-2-24-2-20-24400-2-24-2-2-42-4002222-4-422222-400-2-24-2-200000000000022-4220000000000000000000000000000000000000000000
χ59444-24-244-24-2-2-24-21-2114-24-2-2-2-21-211-2-24-2-2-2-211-2-21111-24-24-21-211-2-21-2111-211-24-21-211-2-21-2111-211000000000000000000000000000000000
χ60444-24-244-24-2-2-2-4-21-211-4-24-222-21-211-2-2422-2-211-2-21111-242-4-21-21122-12-1-1-12-1-12-4-21-21122-12-1-1-12-1-1000000000000000000000000000000000
χ61444-24-2-4-4-24-2220-21-2110-24-2−2i32i3-21-21122-4−2i32i322-1-122-1-1-1-12-400-21-21100i3−2i3i3i3−i32i3−i3−i3002-12-1-100i3−2i3i3i3−i32i3−i3−i3000000000000000000000000000000000
χ62444-24-2-4-4-24-2220-21-2110-24-22i3−2i3-21-21122-42i3−2i322-1-122-1-1-1-12-400-21-21100−i32i3−i3−i3i3−2i3i3i3002-12-1-100−i32i3−i3−i3i3−2i3i3i3000000000000000000000000000000000
χ63444-2-2444-2-244441-2-2114-2-24441-2-2114-2-24411-2-2-2-21111-2-2-2-21-2-21111-2-211-2-211-2-21-2-21111-2-211-2-211000000000000000000000000000000000
χ64444-2-2444-2-2444-41-2-211-4-2-24-4-41-2-2114-2-2-4-411-2-2-2-21111-2-2221-2-211-1-122-1-122-1-1221-2-211-1-122-1-122-1-1000000000000000000000000000000000
χ65444-2-24-4-4-2-24-4-401-2-2110-2-24001-2-211-42200-1-12222-1-1-1-122001-2-2113-3003-3003-300-122-1-13-3003-3003-3000000000000000000000000000000000
χ66444-2-24-4-4-2-24-4-401-2-2110-2-24001-2-211-42200-1-12222-1-1-1-122001-2-211-3300-3300-3300-122-1-1-3300-3300-33000000000000000000000000000000000
χ67444-2-2-244-2-2-2-2-24111−1−3i32−1+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+3i321111−1−3i32−1+3i3211−1+3i32−1−3i32-2-2111−1−3i32−1+3i321111−1−3i32−1+3i3211−1+3i32−1−3i32000000000000000000000000000000000
χ68444-2-2-244-2-2-2-2-24111−1+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+3i32−1−3i321111−1+3i32−1−3i3211−1−3i32−1+3i32-2-2111−1+3i32−1−3i321111−1+3i32−1−3i3211−1−3i32−1+3i32000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.