Finite Group Databasebeta

← Group #13146549

Character table — Group #13146549

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222441212121212121212121212121818181818181818242436363636363636363636363636363636363636363636363636363636363672727272
order122234466612123366666612121212224412121212121222224444668888121212121212121224242424242424246666
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-1111-1-111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111-1-1111-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ711111-1-1111-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ811111-1-1111-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-111-1-1-111-111-1-111-1-111-1-11-11-111-1-11-11-11-1i−ii−i1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011-1-111-1-1-111-111-1-111-1-111-1-11-11-111-1-11-11-11-1−ii−ii1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-1
χ1111-1-111-1-1-111-111-1-111-1-111-1-11-11-111-1-11-1-11-11i−ii−i1-1−ii−iiii−i−iii−i−i−i−iii−i−iii-11-11
χ1211-1-111-1-1-111-111-1-111-1-111-1-11-11-111-1-11-1-11-11−ii−ii1-1i−ii−i−i−iii−i−iiiii−i−iii−i−i-11-11
χ1311-1-11-11-1-11-1111-1-111-1-1-1-111-111-111-1-1-111-1-11i−i−ii-11i−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411-1-11-11-1-11-1111-1-111-1-1-1-111-111-111-1-1-111-1-11−iii−i-11−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1511-1-11-11-1-11-1111-1-111-1-1-1-111-111-111-1-1-11-111-1i−i−ii-11−iii−iii−i−i−i−iii−i−iiiii−i−i-111-1
χ1611-1-11-11-1-11-1111-1-111-1-1-1-111-111-111-1-1-11-111-1−iii−i-11i−i−ii−i−iiiii−i−iii−i−i−i−iii-111-1
χ17222222222222222222222222-2-2-2-2-2-2-2-22200000000-2-2000000000000000000000000
χ1822222-2-2222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-20000000022000000000000000000000000
χ1922-2-222-2-2-222-222-2-222-2-222-2-2-22-22-2-2222-200000000-22000000000000000000000000
χ2022-2-22-22-2-22-2222-2-222-2-2-2-2222-2-22-2-222-22000000002-2000000000000000000000000
χ214444444444441-2-2-21-211111100000000-2-200002222000000-1-1-1-1-1-1-1-1000000000000
χ224444444444441-2-2-21-211111100000000-2-20000-2-2-2-200000011111111000000000000
χ23444444444444-2111-21-2-2-2-2-2-20000000011222200000000000000000000000000-1-1-1-1
χ24444444444444-2111-21-2-2-2-2-2-20000000011-2-2-2-2000000000000000000000000001111
χ2544444-4-4444-4-41-2-2-21-211-1-1-1-10000000022000022-2-2000000-1-1-1-11111000000000000
χ2644444-4-4444-4-41-2-2-21-211-1-1-1-100000000220000-2-2220000001111-1-1-1-1000000000000
χ2744444-4-4444-4-4-2111-21-2-2222200000000-1-122-2-200000000000000000000000000-1-111
χ2844444-4-4444-4-4-2111-21-2-2222200000000-1-1-2-2220000000000000000000000000011-1-1
χ2944-4-444-4-4-444-41-2221-2-1-111-1-100000000-2200002i−2i2i−2i000000−i−iii−i−iii000000000000
χ3044-4-444-4-4-444-41-2221-2-1-111-1-100000000-220000−2i2i−2i2i000000ii−i−iii−i−i000000000000
χ3144-4-444-4-4-444-4-21-1-1-2122-2-222000000001-12-22-200000000000000000000000000-11-11
χ3244-4-444-4-4-444-4-21-1-1-2122-2-222000000001-1-22-22000000000000000000000000001-11-1
χ3344-4-44-44-4-44-441-2221-2-1-1-1-111000000002-200002i−2i−2i2i000000−i−iiiii−i−i000000000000
χ3444-4-44-44-4-44-441-2221-2-1-1-1-111000000002-20000−2i2i2i−2i000000ii−i−i−i−iii000000000000
χ3544-4-44-44-4-44-44-21-1-1-212222-2-200000000-112-2-2200000000000000000000000000-111-1
χ3644-4-44-44-4-44-44-21-1-1-212222-2-200000000-11-222-2000000000000000000000000001-1-11
χ374-44-44004-4-4001-22-2-121-13i−3i3i−3i000000000000000000000000−i3i3−i3i33−33−3000000000000
χ384-44-44004-4-4001-22-2-121-13i−3i3i−3i000000000000000000000000i3−i3i3−i3−33−33000000000000
χ394-44-44004-4-4001-22-2-121-1−3i3i−3i3i000000000000000000000000−i3i3−i3i3−33−33000000000000
χ404-44-44004-4-4001-22-2-121-1−3i3i−3i3i000000000000000000000000i3−i3i3−i33−33−3000000000000
χ414-44-44004-4-40044-44-4-44-4000000000000000000000000000000000000000000000000
χ424-4-44400-44-4001-2-22-12-113i−3i−3i3i0000000000000000000000003−3−33i3−i3−i3i3000000000000
χ434-4-44400-44-4001-2-22-12-113i−3i−3i3i000000000000000000000000−333−3−i3i3i3−i3000000000000
χ444-4-44400-44-4001-2-22-12-11−3i3i3i−3i0000000000000000000000003−3−33−i3i3i3−i3000000000000
χ454-4-44400-44-4001-2-22-12-11−3i3i3i−3i000000000000000000000000−333−3i3−i3−i3i3000000000000
χ464-4-44400-44-400444-4-4-4-44000000000000000000000000000000000000000000000000
χ476666-366-3-3-3-3-30000000000002222-1-1-1-10000000000-1-10000000000003−33−33−33−30000
χ486666-366-3-3-3-3-30000000000002222-1-1-1-10000000000-1-1000000000000−33−33−33−330000
χ496666-366-3-3-3-3-3000000000000-2-2-2-21111000000000011222200000000-1-1-1-1-1-1-1-10000
χ506666-366-3-3-3-3-3000000000000-2-2-2-21111000000000011-2-2-2-200000000111111110000
χ516666-3-6-6-3-3-33300000000000022-2-211110000000000-1-122-2-200000000-1-1-1-111110000
χ526666-3-6-6-3-3-33300000000000022-2-211110000000000-1-1-2-222000000001111-1-1-1-10000
χ536666-3-6-6-3-3-333000000000000-2-222-1-1-1-10000000000110000000000003−33−3−33−330000
χ546666-3-6-6-3-3-333000000000000-2-222-1-1-1-1000000000011000000000000−33−333−33−30000
χ5566-6-6-36-633-3-330000000000002-22-2-1-1110000000000-11000000000000−i3i3i3−i3−i3i3i3−i30000
χ5666-6-6-36-633-3-330000000000002-22-2-1-1110000000000-11000000000000i3−i3−i3i3i3−i3−i3i30000
χ5766-6-6-36-633-3-33000000000000-22-2211-1-100000000001-12i−2i2i−2i00000000−i−iii−i−iii0000
χ5866-6-6-36-633-3-33000000000000-22-2211-1-100000000001-1−2i2i−2i2i00000000ii−i−iii−i−i0000
χ5966-6-6-3-6633-33-30000000000002-2-2211-1-10000000000-112i−2i−2i2i00000000−i−iiiii−i−i0000
χ6066-6-6-3-6633-33-30000000000002-2-2211-1-10000000000-11−2i2i2i−2i00000000ii−i−i−i−iii0000
χ6166-6-6-3-6633-33-3000000000000-222-2-1-11100000000001-1000000000000−i3i3i3−i3i3−i3−i3i30000
χ6266-6-6-3-6633-33-3000000000000-222-2-1-11100000000001-1000000000000i3−i3−i3i3−i3i3i3−i30000
χ638-88-88008-8-800-42-224-2-44000000000000000000000000000000000000000000000000
χ648-8-88800-88-800-422-24-24-4000000000000000000000000000000000000000000000000
χ6512-1212-12-600-66600000000000000000023−2323−23000000000000000000000000000000000000
χ6612-1212-12-600-666000000000000000000−2323−2323000000000000000000000000000000000000
χ6712-12-1212-6006-6600000000000000000023−23−2323000000000000000000000000000000000000
χ6812-12-1212-6006-66000000000000000000−232323−23000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).