Finite Group Databasebeta

← Group #13166072

Character table — Group #13166072

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222223333444466666666888812121212161616161616161616161616161616161818363636363636363636363636363636363636363636363636545472727272
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ31111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ511-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1i−i1-11-111i−ii−i-1-111-1-1ii−i−iii−i−ii−iii−i−i
χ611-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1i−i-11-11-1-1−ii−ii11-1-111−i−iii−i−iiii−iii−i−i
χ711-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−ii1-11-111−ii−ii-1-111-1-1−i−iii−i−iii−ii−i−iii
χ811-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−ii-11-11-1-1i−ii−i11-1-111ii−i−iii−i−i−ii−i−iii
χ92222222222222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200000000000000000000000022-1-1-1-1
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χ142222-12-1222-1-12222-1-1-1-1-1-12222-1-12222-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-100000000-2-2-2-200000011111111000000
χ1522-2-22222-2-2-2-222-2-222-2-22222-2-2-2-2-1-11122-2-2-1-1-1-1-1-1-1-1111111112i−2i0000000000000000000000002i−2i−i−iii
χ1622-2-22222-2-2-2-222-2-222-2-22222-2-2-2-2-1-11122-2-2-1-1-1-1-1-1-1-111111111−2i2i000000000000000000000000−2i2iii−i−i
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χ332-2−2i2i-121-2−2i2ii−i2-2−2i2i-11i−i-112-2−2i2ii−i2-2−2i2i-11i−i-12-1-11-211i−i−2i2iii−i−i000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
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χ38333333333333-1-1-1-13333-1-1-1-1-1-1-1-10000-1-1-1-10000000000000000-3-3-1-111-1-111-1-1-1-111111111-1-1-1-1110000
χ3933-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-11100000000000000003i−3i1-1-1111i−i−ii-1-1-1-111ii−i−i−i−iii−ii0000
χ4033-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-11100000000000000003i−3i-111-1-1-1−iii−i1111-1-1−i−iiiii−i−i−ii0000
χ4133-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-1110000000000000000−3i3i1-1-1111−iii−i-1-1-1-111−i−iiiii−i−ii−i0000
χ4233-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-1110000000000000000−3i3i-111-1-1-1i−i−ii1111-1-1ii−i−i−i−iiii−i0000
χ4344444-24-2-2-2444444-2-2-2-244-2-2-2-244-2-2-2-2-2-2-2-2-2111-2111-2-211111100000000000000000000000000000000
χ444444-24-2444-2-24444-2-2-2-2-2-24444-2-2-2-2-2-2-2-2-2-21-2111-21111-2-2111100000000000000000000000000000000
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χ464444-2-2-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1+3i32−1−3i32−1+3i3200000000000000000000000000000000
χ474444-2-2-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1−3i32−1+3i32−1−3i3200000000000000000000000000000000
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χ5244-4-4-2-2-2-2222244-4-411-1-1-2-2-2-22222-2-22211-1-111−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321+3i321−3i321+3i3200000000000000000000000000000000
χ534-44i−4i4-2-42−2i2i4i−4i4-44i−4i-22−2i2i4-4-22−2i2i4i−4i-22−2i2i-22−2i2i-21112-1-1-1−2i2ii−iii−i−i00000000000000000000000000000000
χ544-44i−4i-242-44i−4i−2i2i4-44i−4i-22−2i2i-224-44i−4i−2i2i-22−2i2i-22−2i2i1-211-12-1-1i−i−2i2iii−i−i00000000000000000000000000000000
χ554-44i−4i-2-222−2i2i−2i2i4-44i−4i1-1i−i-22-22−2i2i−2i2i4-44i−4i1-1i−i-2-21122-1-1−2i2i−2i2iii−i−i00000000000000000000000000000000
χ564-44i−4i-2-222−2i2i−2i2i4-44i−4i1-1i−i-22-22−2i2i−2i2i-22−2i2i1-1i−i11−1−3i32−1+3i32-1-11+3i321−3i32i−ii−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ2200000000000000000000000000000000
χ574-44i−4i-2-222−2i2i−2i2i4-44i−4i1-1i−i-22-22−2i2i−2i2i-22−2i2i1-1i−i11−1+3i32−1−3i32-1-11−3i321+3i32i−ii−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ2200000000000000000000000000000000
χ584-4−4i4i4-2-422i−2i−4i4i4-4−4i4i-222i−2i4-4-222i−2i−4i4i-222i−2i-222i−2i-21112-1-1-12i−2i−ii−i−iii00000000000000000000000000000000
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χ614-4−4i4i-2-2222i−2i2i−2i4-4−4i4i1-1−ii-22-222i−2i2i−2i-222i−2i1-1−ii11−1−3i32−1+3i32-1-11+3i321−3i32−ii−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ2200000000000000000000000000000000
χ624-4−4i4i-2-2222i−2i2i−2i4-4−4i4i1-1−ii-22-222i−2i2i−2i-222i−2i1-1−ii11−1+3i32−1−3i32-1-11−3i321+3i32−ii−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ2200000000000000000000000000000000
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χ821212-12-12-6-6-6-66666-4-44433-3-32222-2-2-2-20000-1-111000000000000000000000000000000000000000000000000
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χ8412-12−12i12i-6-6666i−6i6i−6i-444i−4i3-3−3i3i2-22-2−2i2i−2i2i0000-11i−i000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.