Finite Group Databasebeta

← Group #13166045

Character table — Group #13166045

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222224444666666668888888888881212121216161616161616161616161618182424242424242424242424242424363636363636363636367272108108108108
order12443366121212123612122488242424243336661212121212126612123336661212121212128861224242424242424242424242424882424242424246124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-11111-1-1-1-111-1-1-11i−iii−i−i111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1i−i-11iiiiii−i−i−i−i−i−i1-11-1i−i11-1-11-1i−ii−i
χ611-1-11111-1-1-1-111-1-1-11i−iii−i−i111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1i−i-11iiiiii−i−i−i−i−i−i-11-11i−i-1-111-11−ii−ii
χ711-1-11111-1-1-1-111-1-1-11−ii−i−iii111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−ii-11−i−i−i−i−i−iiiiiii1-11-1−ii11-1-11-1−ii−ii
χ811-1-11111-1-1-1-111-1-1-11−ii−i−iii111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−ii-11−i−i−i−i−i−iiiiiii-11-11−ii-1-111-11i−ii−i
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000220000000000
χ10222222222222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2221111111111110000-2-20000000000
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χ1222222-12-1-1-122-1-1-1-1220000002222222222222-12-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000-2-2-2-2001111110000
χ132222-12-1222-1-1-1-1-1-12222-1-1-1-12-1-12-1-122-1-1-1-1-12-122-1-12-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-10000-1-10000000000
χ142222-12-1222-1-1-1-1-1-12222-1-1-1-1-12-1-12-1-1-122-1-1-12-12-12-1-12-1-1-122-1-122-1-1-1-122-1-1-1-122-1-10000-1-10000000000
χ152222-12-1222-1-1-1-1-1-12222-1-1-1-1-1-12-1-12-1-1-1-122-12-12-1-12-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1220000-1-10000000000
χ162222-12-1222-1-1-1-1-1-122-2-211112-1-12-1-122-1-1-1-1-12-122-1-12-1-122-1-1-1-1-2-2-1-1-2-21111-2-211110000110000000000
χ172222-12-1222-1-1-1-1-1-122-2-21111-12-1-12-1-1-122-1-1-12-12-12-1-12-1-1-122-1-1-2-2-1-111-2-21111-2-2110000110000000000
χ182222-12-1222-1-1-1-1-1-122-2-21111-1-12-1-12-1-1-1-122-12-12-1-12-1-12-1-1-1-122-2-2-1-11111-2-21111-2-20000110000000000
χ1922-2-22222-2-2-2-222-2-2-222i−2i2i2i−2i−2i-1-1-1-1-1-1111111-2-222-1-1-1-1-1-11111112i−2i-22−i−i−i−i−i−iiiiiii00002i−2i0000000000
χ2022-2-22222-2-2-2-222-2-2-22−2i2i−2i−2i2i2i-1-1-1-1-1-1111111-2-222-1-1-1-1-1-1111111−2i2i-22iiiiii−i−i−i−i−i−i0000−2i2i0000000000
χ2122-2-22-12-111-2-2-1-111-22000000222222-2-2-2-2-2-2-212-1-1-1-1-1-1-1111111001-10000000000002-22-200-1-111-110000
χ2222-2-22-12-111-2-2-1-111-22000000222222-2-2-2-2-2-2-212-1-1-1-1-1-1-1111111001-1000000000000-22-220011-1-11-10000
χ2322-2-2-12-12-2-211-1-111-222i−2i−i−iii2-1-12-1-1-2-211111-2-122-1-12-1-1-2-211112i−2i1-12i2i−i−i−i−i−2i−2iiiii0000−ii0000000000
χ2422-2-2-12-12-2-211-1-111-222i−2i−i−iii-12-1-12-111-2-2111-2-12-12-1-12-111-2-2112i−2i1-1−i−i2i2i−i−iii−2i−2iii0000−ii0000000000
χ2522-2-2-12-12-2-211-1-111-222i−2i−i−iii-1-12-1-121111-2-21-2-12-1-12-1-121111-2-22i−2i1-1−i−i−i−i2i2iiiii−2i−2i0000−ii0000000000
χ2622-2-2-12-12-2-211-1-111-22−2i2iii−i−i2-1-12-1-1-2-211111-2-122-1-12-1-1-2-21111−2i2i1-1−2i−2iiiii2i2i−i−i−i−i0000i−i0000000000
χ2722-2-2-12-12-2-211-1-111-22−2i2iii−i−i-12-1-12-111-2-2111-2-12-12-1-12-111-2-211−2i2i1-1ii−2i−2iii−i−i2i2i−i−i0000i−i0000000000
χ2822-2-2-12-12-2-211-1-111-22−2i2iii−i−i-1-12-1-121111-2-21-2-12-1-12-1-121111-2-2−2i2i1-1iiii−2i−2i−i−i−i−i2i2i0000i−i0000000000
χ293333333333333333-1-1333333000000000000-1-1-1-1000000000000-1-1-1-100000000000011-1-1-1-1-1-1-1-111-1-111
χ303333333333333333-1-1333333000000000000-1-1-1-1000000000000-1-1-1-1000000000000-1-111-1-11111-1-111-1-1
χ313333333333333333-1-1-3-3-3-3-3-3000000000000-1-1-1-100000000000011-1-100000000000011-1-111-1-1-1-11111-1-1
χ323333333333333333-1-1-3-3-3-3-3-3000000000000-1-1-1-100000000000011-1-1000000000000-1-111111111-1-1-1-111
χ3333-3-33333-3-3-3-333-3-31-13i−3i3i3i−3i−3i00000000000011-1-1000000000000−ii1-10000000000001-1-11−ii-1-1111-1−iii−i
χ3433-3-33333-3-3-3-333-3-31-13i−3i3i3i−3i−3i00000000000011-1-1000000000000−ii1-1000000000000-111-1−ii11-1-1-11i−i−ii
χ3533-3-33333-3-3-3-333-3-31-1−3i3i−3i−3i3i3i00000000000011-1-1000000000000i−i1-10000000000001-1-11i−i-1-1111-1i−i−ii
χ3633-3-33333-3-3-3-333-3-31-1−3i3i−3i−3i3i3i00000000000011-1-1000000000000i−i1-1000000000000-111-1i−i11-1-1-11−iii−i
χ3744444-24-2-2-244-2-2-2-244000000-2-2-2-2-2-2-2-2-2-2-2-24-24-211111111111100-2-20000000000000000000000000000
χ384444-2-2-2-2-2-2-2-21111440000004-2-24-2-244-2-2-2-2-2-2-2-2-211-211-2-2111100110000000000000000000000000000
χ394444-2-2-2-2-2-2-2-2111144000000-24-2-24-2-2-244-2-2-2-2-2-21-211-2111-2-21100110000000000000000000000000000
χ404444-2-2-2-2-2-2-2-2111144000000-2-24-2-24-2-2-2-244-2-2-2-211-211-21111-2-200110000000000000000000000000000
χ4144-4-44-24-222-4-4-2-222-44000000-2-2-2-2-2-2222222-424-2111111-1-1-1-1-1-1002-20000000000000000000000000000
χ4244-4-4-2-2-2-2222211-1-1-440000004-2-24-2-2-4-4222222-2-2-211-21122-1-1-1-100-110000000000000000000000000000
χ4344-4-4-2-2-2-2222211-1-1-44000000-24-2-24-222-4-42222-2-21-211-21-1-122-1-100-110000000000000000000000000000
χ4444-4-4-2-2-2-2222211-1-1-44000000-2-24-2-242222-4-422-2-211-211-2-1-1-1-12200-110000000000000000000000000000
χ454-44i−4i44-4-44i−4i4i−4i4-44i−4i00000000111-1-1-1i−ii−ii−i0000111-1-1-1i−ii−ii−i0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ464-44i−4i44-4-44i−4i4i−4i4-44i−4i00000000111-1-1-1i−ii−ii−i0000111-1-1-1i−ii−ii−i0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ474-44i−4i44-4-44i−4i4i−4i4-44i−4i00000000-2-2-2222−2i2i−2i2i−2i2i0000-2-2-2222−2i2i−2i2i−2i2i00000000000000000000000000000000
χ484-44i−4i4-2-42−2i2i4i−4i-22−2i2i00000000-2-2-2222−2i2i−2i2i−2i2i0000111-1-1-1i−ii−ii−i00000000000000000000006−6i6−i6000000
χ494-44i−4i4-2-42−2i2i4i−4i-22−2i2i00000000-2-2-2222−2i2i−2i2i−2i2i0000111-1-1-1i−ii−ii−i0000000000000000000000−66−i6i6000000
χ504-44i−4i-242-44i−4i−2i2i-22−2i2i0000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ1311-2-1-12i−ii−i−2i2i000011-2-1-12i−ii−i−2i2i0000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ514-44i−4i-242-44i−4i−2i2i-22−2i2i0000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ131-21-12-1i−i−2i2ii−i00001-21-12-1i−i−2i2ii−i0000ζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ130000000000000000
χ524-44i−4i-242-44i−4i−2i2i-22−2i2i0000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13-2112-1-1−2i2ii−ii−i0000-2112-1-1−2i2ii−ii−i000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ534-44i−4i-242-44i−4i−2i2i-22−2i2i00002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ1311-2-1-12i−ii−i−2i2i000011-2-1-12i−ii−i−2i2i0000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ544-44i−4i-242-44i−4i−2i2i-22−2i2i00002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ131-21-12-1i−i−2i2ii−i00001-21-12-1i−i−2i2ii−i0000−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ130000000000000000
χ554-44i−4i-242-44i−4i−2i2i-22−2i2i00002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13-2112-1-1−2i2ii−ii−i0000-2112-1-1−2i2ii−ii−i000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ564-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i00000000111-1-1-1−ii−ii−ii0000111-1-1-1−ii−ii−ii0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ574-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i00000000111-1-1-1−ii−ii−ii0000111-1-1-1−ii−ii−ii0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ584-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i00000000-2-2-22222i−2i2i−2i2i−2i0000-2-2-22222i−2i2i−2i2i−2i00000000000000000000000000000000
χ594-4−4i4i4-2-422i−2i−4i4i-222i−2i00000000-2-2-22222i−2i2i−2i2i−2i0000111-1-1-1−ii−ii−ii00000000000000000000006−6−i6i6000000
χ604-4−4i4i4-2-422i−2i−4i4i-222i−2i00000000-2-2-22222i−2i2i−2i2i−2i0000111-1-1-1−ii−ii−ii0000000000000000000000−66i6−i6000000
χ614-4−4i4i-242-4−4i4i2i−2i-222i−2i00002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ2311-2-1-12−ii−ii2i−2i000011-2-1-12−ii−ii2i−2i0000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ624-4−4i4i-242-4−4i4i2i−2i-222i−2i00002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ231-21-12-1−ii2i−2i−ii00001-21-12-1−ii2i−2i−ii0000−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ230000000000000000
χ634-4−4i4i-242-4−4i4i2i−2i-222i−2i00002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23-2112-1-12i−2i−ii−ii0000-2112-1-12i−2i−ii−ii000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ644-4−4i4i-242-4−4i4i2i−2i-222i−2i0000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ2311-2-1-12−ii−ii2i−2i000011-2-1-12−ii−ii2i−2i0000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ654-4−4i4i-242-4−4i4i2i−2i-222i−2i0000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ231-21-12-1−ii2i−2i−ii00001-21-12-1−ii2i−2i−ii0000ζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ230000000000000000
χ664-4−4i4i-242-4−4i4i2i−2i-222i−2i0000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23-2112-1-12i−2i−ii−ii0000-2112-1-12i−2i−ii−ii000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ6766666-36-3-3-366-3-3-3-3-2-2000000000000000000-21-21000000000000001100000000000022-2-2001111-1-10000
χ6866666-36-3-3-366-3-3-3-3-2-2000000000000000000-21-210000000000000011000000000000-2-22200-1-1-1-1110000
χ696666-36-3666-3-3-3-3-3-3-2-266-3-3-3-30000000000001-21-2000000000000-2-2110000000000000000110000000000
χ706666-36-3666-3-3-3-3-3-3-2-2-6-633330000000000001-21-200000000000022110000000000000000-1-10000000000
χ7166-6-66-36-333-6-6-3-3332-20000000000000000002-1-2100000000000000-110000000000002-2-220011-1-1-110000
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χ768-88i−8i-4-444−4i4i−4i4i2-22i−2i0000000022-4-2-242i−2i2i−2i−4i4i0000-1-1211-2−ii−ii2i−2i00000000000000000000000000000000
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χ788-88i−8i-4-444−4i4i−4i4i2-22i−2i00000000-4224-2-2−4i4i2i−2i2i−2i00002-1-1-2112i−2i−ii−ii00000000000000000000000000000000
χ798-8−8i8i8-4-844i−4i−8i8i-444i−4i00000000222-2-2-2−2i2i−2i2i−2i2i0000-1-1-1111i−ii−ii−i00000000000000000000000000000000
χ808-8−8i8i-4-4444i−4i4i−4i2-2−2i2i0000000022-4-2-24−2i2i−2i2i4i−4i0000-1-1211-2i−ii−i−2i2i00000000000000000000000000000000
χ818-8−8i8i-4-4444i−4i4i−4i2-2−2i2i000000002-42-24-2−2i2i4i−4i−2i2i0000-12-11-21i−i−2i2ii−i00000000000000000000000000000000
χ828-8−8i8i-4-4444i−4i4i−4i2-2−2i2i00000000-4224-2-24i−4i−2i2i−2i2i00002-1-1-211−2i2ii−ii−i00000000000000000000000000000000
χ8312121212-6-6-6-6-6-6-6-63333-4-4000000000000000000222200000000000000-1-10000000000000000000000000000
χ841212-12-12-6-6-6-6666633-3-34-4000000000000000000-2-222000000000000001-10000000000000000000000000000

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