Finite Group Databasebeta

← Group #13180847

Character table — Group #13180847

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222223333444466666666888812121212161616161616161616161616161616161818363636363636363636363636363636363636363636363636545472727272
order124433661212121222443612126666121212123612126612123333666612121212121212122422444444666612121212121212121212121224661212
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
χ31111111111111111111111111111111111111111111111111111-1-11-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1
χ511-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-11-1-111-11-111-1-1-1-11111-1-111-1-11-111-1-1
χ611-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-111-1-11-11-1-11111-1-1-1-111-1-1111-111-1-1
χ711-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1111-1-11-1-111111-1-1-1-111-1-1-1-111-11-1-111
χ811-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-11-1-111-111-1-1-1-1-11111-1-11111-1-1-11-1-111
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
χ102222222222222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000000000000000000000-2-21111
χ1122222-12-122-1-12222-1-1-1-122-1-122-1-12222-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1000202002200-1-100-1-10000-1-1-1-1000000
χ1222222-12-122-1-12222-1-1-1-122-1-122-1-12222-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1000-20-200-2-20011001100001111000000
χ132222-12-12-1-1222222-1-1-1-1-1-122-1-1222222-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-10020202200-1-100-1-100-1-1-1-10000000000
χ142222-12-12-1-1222222-1-1-1-1-1-122-1-1222222-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-100-20-20-2-2001100110011110000000000
χ1522-2-22222-2-2-2-222-2-222-2-22222-2-2-2-2-1-11122-2-2-1-1-1-1-1-1-1-1111111112-20000000000000000000000002-2-1-111
χ1622-2-22222-2-2-2-222-2-222-2-22222-2-2-2-2-1-11122-2-2-1-1-1-1-1-1-1-111111111-22000000000000000000000000-2211-1-1
χ1722-2-22-12-1-2-21122-2-2-1-11122-1-1-2-21122-2-2-1-1112-1-1-12-1-1-1-2-211111100020-200-2200-1-10011000011-1-1000000
χ1822-2-22-12-1-2-21122-2-2-1-11122-1-1-2-21122-2-2-1-1112-1-1-12-1-1-1-2-2111111000-202002-2001100-1-10000-1-111000000
χ1922-2-2-12-1211-2-222-2-2-1-111-1-12211-2-222-2-2-1-111-12-1-1-12-1-111-2-211110020-202-200-1-1001100-1-1110000000000
χ2022-2-2-12-1211-2-222-2-2-1-111-1-12211-2-222-2-2-1-111-12-1-1-12-1-111-2-2111100-2020-22001100-1-10011-1-10000000000
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χ222-22i−2i22-2-22i−2i2i−2i2-22i−2i2-22i−2i2-22-22i−2i2i−2i-11−ii2-22i−2i-1-1-1-11111−ii−ii−i−iii0000000000000000000000000000−i3i33−3
χ232-22i−2i22-2-22i−2i2i−2i2-22i−2i2-22i−2i2-22-22i−2i2i−2i-11−ii2-22i−2i-1-1-1-11111−ii−ii−i−iii0000000000000000000000000000i3−i3−33
χ242-22i−2i2-1-212i−2i−ii2-22i−2i-11−ii2-2-112i−2i−ii2-22i−2i-11−ii2-1-1-1-21112i−2i−ii−i−iii000000000000−i3i3003−300003−3−i3i3000000
χ252-22i−2i2-1-212i−2i−ii2-22i−2i-11−ii2-2-112i−2i−ii2-22i−2i-11−ii2-1-1-1-21112i−2i−ii−i−iii000000000000i3−i300−330000−33i3−i3000000
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χ272-22i−2i-121-2−ii2i−2i2-22i−2i-11−ii-112-2−ii2i−2i2-22i−2i-11−ii-12-1-11-211−ii2i−2i−i−iii0000000000i3−i300−3300i3−i3−330000000000
χ282-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i2-22-2−2i2i−2i2i2-2−2i2i2-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000
χ292-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i2-22-2−2i2i−2i2i-11i−i2-2−2i2i-1-1-1-11111i−ii−iii−i−i0000000000000000000000000000−i3i3−33
χ302-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i2-22-2−2i2i−2i2i-11i−i2-2−2i2i-1-1-1-11111i−ii−iii−i−i0000000000000000000000000000i3−i33−3
χ312-2−2i2i2-1-21−2i2ii−i2-2−2i2i-11i−i2-2-11−2i2ii−i2-2−2i2i-11i−i2-1-1-1-2111−2i2ii−iii−i−i000000000000−i3i300−330000−33−i3i3000000
χ322-2−2i2i2-1-21−2i2ii−i2-2−2i2i-11i−i2-2-11−2i2ii−i2-2−2i2i-11i−i2-1-1-1-2111−2i2ii−iii−i−i000000000000i3−i3003−300003−3i3−i3000000
χ332-2−2i2i-121-2i−i−2i2i2-2−2i2i-11i−i-112-2i−i−2i2i2-2−2i2i-11i−i-12-1-11-211i−i−2i2iii−i−i0000000000−i3i300−3300−i3i3−330000000000
χ342-2−2i2i-121-2i−i−2i2i2-2−2i2i-11i−i-112-2i−i−2i2i2-2−2i2i-11i−i-12-1-11-211i−i−2i2iii−i−i0000000000i3−i3003−300i3−i33−30000000000
χ35333333333333-1-1-1-13333-1-1-1-1-1-1-1-10000-1-1-1-10000000000000000331111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-10000
χ36333333333333-1-1-1-13333-1-1-1-1-1-1-1-10000-1-1-1-1000000000000000033-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-10000
χ37333333333333-1-1-1-13333-1-1-1-1-1-1-1-10000-1-1-1-10000000000000000-3-31-11-1-1-11111-1-111-1-1-1-1-1-11111110000
χ38333333333333-1-1-1-13333-1-1-1-1-1-1-1-10000-1-1-1-10000000000000000-3-3-11-1111-1-1-1-111-1-1111111-1-1-1-1110000
χ3933-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-11100000000000000003-31-1-11-11-1111-1-1-1-111-1-111-1-111-110000
χ4033-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-11100000000000000003-3-111-11-11-1-1-11111-1-111-1-111-1-1-110000
χ4133-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-1110000000000000000-3311-1-1-111-11111-1-1-1-1-1-11111-1-11-10000
χ4233-3-33333-3-3-3-3-1-11133-3-3-1-1-1-111110000-1-1110000000000000000-33-1-1111-1-11-1-1-1-1111111-1-1-1-1111-10000
χ4344444-24-244-2-24444-2-2-2-244-2-244-2-2-2-2-2-2-2-2-2-2-2111-2111-2-211111100000000000000000000000000000000
χ444444-24-24-2-2444444-2-2-2-2-2-244-2-244-2-2-2-2-2-2-2-21-2111-21111-2-2111100000000000000000000000000000000
χ454444-2-2-2-2-2-2-2-244441111-2-2-2-2-2-2-2-244441111-2-211-2-211-2-2-2-2111100000000000000000000000000000000
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
χ4844-4-44-24-2-4-42244-4-4-2-22244-2-2-4-422-2-222-2-222-2111-211122-1-1-1-1-1-100000000000000000000000000000000
χ4944-4-4-24-2422-4-444-4-4-2-222-2-24422-4-4-2-222-2-2221-2111-211-1-122-1-1-1-100000000000000000000000000000000
χ5044-4-4-2-2-2-2222244-4-411-1-1-2-2-2-2222244-4-411-1-1-2-211-2-2112222-1-1-1-100000000000000000000000000000000
χ5144-4-4-2-2-2-2222244-4-411-1-1-2-2-2-22222-2-22211-1-111−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321−3i321+3i321−3i3200000000000000000000000000000000
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−4i4-2-424i−4i−2i2i4-44i−4i-22−2i2i4-4-224i−4i−2i2i-22−2i2i-22−2i2i-21112-1-1-1−2i2ii−iii−i−i00000000000000000000000000000000
χ544-44i−4i-242-4−2i2i4i−4i4-44i−4i-22−2i2i-224-4−2i2i4i−4i-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−ζ7+2ζ112ζ7−ζ11ζ7−2ζ11−2ζ7+ζ1100000000000000000000000000000000
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−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ1100000000000000000000000000000000
χ584-4−4i4i4-2-42−4i4i2i−2i4-4−4i4i-222i−2i4-4-22−4i4i2i−2i-222i−2i-222i−2i-21112-1-1-12i−2i−ii−i−iii00000000000000000000000000000000
χ594-4−4i4i-242-42i−2i−4i4i4-4−4i4i-222i−2i-224-42i−2i−4i4i-222i−2i-222i−2i1-211-12-1-1−ii2i−2i−i−iii00000000000000000000000000000000
χ604-4−4i4i-2-2222i−2i2i−2i4-4−4i4i1-1−ii-22-222i−2i2i−2i4-4−4i4i1-1−ii-2-21122-1-12i−2i2i−2i−i−iii00000000000000000000000000000000
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−iiζ7−2ζ11−2ζ7+ζ11−ζ7+2ζ112ζ7−ζ1100000000000000000000000000000000
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−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ1100000000000000000000000000000000
χ6366666-36-366-3-3-2-2-2-2-3-3-3-3-2-211-2-21100001111000000000000000000020200-2-200-1-100-1-100001111000000
χ6466666-36-366-3-3-2-2-2-2-3-3-3-3-2-211-2-211000011110000000000000000000-20-20022001100110000-1-1-1-1000000
χ656666-36-36-3-366-2-2-2-2-3-3-3-311-2-211-2-2000011110000000000000000002020-2-200-1-100-1-10011110000000000
χ666666-36-36-3-366-2-2-2-2-3-3-3-311-2-211-2-200001111000000000000000000-20-20220011001100-1-1-1-10000000000
χ6766-6-66-36-3-6-633-2-222-3-333-2-21122-1-1000011-1-1000000000000000000020-2002-200-1-100110000-1-111000000
χ6866-6-66-36-3-6-633-2-222-3-333-2-21122-1-1000011-1-10000000000000000000-20200-22001100-1-1000011-1-1000000
χ6966-6-6-36-3633-6-6-2-222-3-33311-2-2-1-122000011-1-100000000000000000020-20-2200-1-100110011-1-10000000000
χ7066-6-6-36-3633-6-6-2-222-3-33311-2-2-1-122000011-1-1000000000000000000-20202-2001100-1-100-1-1110000000000
χ716-66i−6i66-6-66i−6i6i−6i-22−2i2i6-66i−6i-22-22−2i2i−2i2i0000-22−2i2i000000000000000000000000000000000000000000000000
χ726-66i−6i6-3-636i−6i−3i3i-22−2i2i-33−3i3i-221-1−2i2ii−i00001-1i−i0000000000000000000000000000−i3i3003−30000−33i3−i3000000
χ736-66i−6i6-3-636i−6i−3i3i-22−2i2i-33−3i3i-221-1−2i2ii−i00001-1i−i0000000000000000000000000000i3−i300−3300003−3−i3i3000000
χ746-66i−6i-363-6−3i3i6i−6i-22−2i2i-33−3i3i1-1-22i−i−2i2i00001-1i−i00000000000000000000000000−i3i3003−300i3−i3−330000000000
χ756-66i−6i-363-6−3i3i6i−6i-22−2i2i-33−3i3i1-1-22i−i−2i2i00001-1i−i00000000000000000000000000i3−i300−3300−i3i33−30000000000
χ766-6−6i6i66-6-6−6i6i−6i6i-222i−2i6-6−6i6i-22-222i−2i2i−2i0000-222i−2i000000000000000000000000000000000000000000000000
χ776-6−6i6i6-3-63−6i6i3i−3i-222i−2i-333i−3i-221-12i−2i−ii00001-1−ii0000000000000000000000000000−i3i300−3300003−3i3−i3000000
χ786-6−6i6i6-3-63−6i6i3i−3i-222i−2i-333i−3i-221-12i−2i−ii00001-1−ii0000000000000000000000000000i3−i3003−30000−33−i3i3000000
χ796-6−6i6i-363-63i−3i−6i6i-222i−2i-333i−3i1-1-22−ii2i−2i00001-1−ii00000000000000000000000000−i3i300−3300i3−i33−30000000000
χ806-6−6i6i-363-63i−3i−6i6i-222i−2i-333i−3i1-1-22−ii2i−2i00001-1−ii00000000000000000000000000i3−i3003−300−i3i3−330000000000
χ8112121212-6-6-6-6-6-6-6-6-4-4-4-43333222222220000-1-1-1-1000000000000000000000000000000000000000000000000
χ821212-12-12-6-6-6-66666-4-44433-3-32222-2-2-2-20000-1-111000000000000000000000000000000000000000000000000
χ8312-1212i−12i-6-666−6i6i−6i6i-44−4i4i3-33i−3i2-22-22i−2i2i−2i0000-11−ii000000000000000000000000000000000000000000000000
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 12 (ζ12 = 1); i = ζ3.