Finite Group Databasebeta

← Group #13167449

Character table — Group #13167449

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444444444888888888888888888181818181818181836363636363636363636363636363636363636363636363636363636363672727272
order1222344666336666661212121212123366666612121212121212121212224412121212444444446688881212121212121212242424242424242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-111-1-1-1111-111-1-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-1-11-1-111i−ii−ii−ii−i1-11-11-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-111-1-1-1111-111-1-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-1-11-1-111i−ii−i−ii−ii1-1-11-11ii−i−iii−i−i-1-111-1-111−ii−ii
χ1111-1-111-1-1-1111-111-1-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-1-11-1-111−ii−iii−ii−i1-1-11-11−i−iii−i−iii-1-111-1-111i−ii−i
χ1211-1-111-1-1-1111-111-1-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-1-11-1-111−ii−ii−ii−ii1-11-11-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ1311-1-11-11-1-1111-111-1-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-11-11-1-111i−i−iii−i−ii-111-1-11ii−i−i−i−iii11-1-1-1-111i−i−ii
χ1411-1-11-11-1-1111-111-1-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-11-11-1-111i−i−ii−iii−i-11-111-1ii−i−i−i−iii-1-11111-1-1−iii−i
χ1511-1-11-11-1-1111-111-1-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-11-11-1-111−iii−ii−i−ii-11-111-1−i−iiiii−i−i-1-11111-1-1i−i−ii
χ1611-1-11-11-1-1111-111-1-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-11-11-1-111−iii−i−iii−i-111-1-11−i−iiiii−i−i11-1-1-1-111−iii−i
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000-2-2000000000000000000000000
χ1822222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-20000000022000000000000000000000000
χ192222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-100000000-1-1222200000000-1-1-1-1-1-1-1-10000
χ202222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-100000000-1-1-2-2-2-200000000111111110000
χ212222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2111100000000110000000000003−33−33−33−30000
χ222222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211110000000011000000000000−33−33−33−330000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-2-2111100000000-1-10000000000003−33−3−33−330000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-2-2111100000000-1-1000000000000−33−333−33−30000
χ252222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-222-1-1-1-1000000001122-2-200000000-1-1-1-111110000
χ262222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-222-1-1-1-10000000011-2-222000000001111-1-1-1-10000
χ2722-2-222-2-2-2222-222-2-2-22-222-2-222-2-2-2-2222-22222-2-2-2-2-222-222-2-200000000-22000000000000000000000000
χ2822-2-22-22-2-2222-222-2-2-2-22-2-22222-2-2-2-222-22-2-2-2-222222-22-222-2-2000000002-2000000000000000000000000
χ2922-2-2-12-211-122-222-2-2-2-1122-2-2-1-11111-1-12-2-1-1-1-111112-2-2211-1-100000000-112-22-200000000-1-111-1-1110000
χ3022-2-2-12-211-122-222-2-2-2-1122-2-2-1-11111-1-12-2-1-1-1-111112-2-2211-1-100000000-11-22-220000000011-1-111-1-10000
χ3122-2-2-12-211-122-222-2-2-2-1122-2-2-1-11111-1-12-2-1-1-1-11111-222-2-1-111000000001-10000000000003−3−333−3−330000
χ3222-2-2-12-211-122-222-2-2-2-1122-2-2-1-11111-1-12-2-1-1-1-11111-222-2-1-111000000001-1000000000000−333−3−333−30000
χ3322-2-2-1-2211-122-222-2-2-21-1-2-222-1-11111-1-1-221111-1-1-1-12-22-2-1-11100000000-110000000000003−3−33−333−30000
χ3422-2-2-1-2211-122-222-2-2-21-1-2-222-1-11111-1-1-221111-1-1-1-12-22-2-1-11100000000-11000000000000−333−33−3−330000
χ3522-2-2-1-2211-122-222-2-2-21-1-2-222-1-11111-1-1-221111-1-1-1-1-22-2211-1-1000000001-12-2-2200000000-1-11111-1-10000
χ3622-2-2-1-2211-122-222-2-2-21-1-2-222-1-11111-1-1-221111-1-1-1-1-22-2211-1-1000000001-1-222-20000000011-1-1-1-1110000
χ3744444444441-211-2-2-2144-2-2-2-21-211-2-21-21111-2-211-2-200000000000022220000000000000000000000-1-1-1-1
χ3844444444441-211-2-2-2144-2-2-2-21-211-2-21-21111-2-211-2-2000000000000-2-2-2-200000000000000000000001111
χ394444444444-21-2-2111-2441111-21-2-211-21-2-2-2-211-2-2110000000022220000000000-1-1-1-1-1-1-1-1000000000000
χ404444444444-21-2-2111-2441111-21-2-211-21-2-2-2-211-2-21100000000-2-2-2-2000000000011111111000000000000
χ4144444-4-44441-211-2-2-21-4-422221-211-2-21-2-1-1-1-122-1-12200000000000022-2-20000000000000000000000-1-111
χ4244444-4-44441-211-2-2-21-4-422221-211-2-21-2-1-1-1-122-1-122000000000000-2-222000000000000000000000011-1-1
χ4344444-4-4444-21-2-2111-2-4-4-1-1-1-1-21-2-211-212222-1-122-1-10000000022-2-20000000000-1-1-1-11111000000000000
χ4444444-4-4444-21-2-2111-2-4-4-1-1-1-1-21-2-211-212222-1-122-1-100000000-2-22200000000001111-1-1-1-1000000000000
χ4544-4-444-4-4-441-2-11-222-14-4-2-2221-2-1-1221-21-111-2-2-1-1220000000000002i−2i2i−2i0000000000000000000000−ii−ii
χ4644-4-444-4-4-441-2-11-222-14-4-2-2221-2-1-1221-21-111-2-2-1-122000000000000−2i2i−2i2i0000000000000000000000i−ii−i
χ4744-4-444-4-4-44-212-21-1-124-411-1-1-2122-1-1-21-22-2-21122-1-1000000002i−2i2i−2i0000000000−i−iii−i−iii000000000000
χ4844-4-444-4-4-44-212-21-1-124-411-1-1-2122-1-1-21-22-2-21122-1-100000000−2i2i−2i2i0000000000ii−i−iii−i−i000000000000
χ4944-4-44-44-4-441-2-11-222-1-4422-2-21-2-1-1221-2-11-1-12211-2-20000000000002i−2i−2i2i0000000000000000000000−iii−i
χ5044-4-44-44-4-441-2-11-222-1-4422-2-21-2-1-1221-2-11-1-12211-2-2000000000000−2i2i2i−2i0000000000000000000000i−i−ii
χ5144-4-44-44-4-44-212-21-1-12-44-1-111-2122-1-1-212-222-1-1-2-211000000002i−2i−2i2i0000000000−i−iiiii−i−i000000000000
χ5244-4-44-44-4-44-212-21-1-12-44-1-111-2122-1-1-212-222-1-1-2-21100000000−2i2i2i−2i0000000000ii−i−i−i−iii000000000000
χ534-44-44004-4-4444-4-44-4-4000000444-44-4-4-40000000000000000000000000000000000000000000000000000
χ544-44-44004-4-4-21-22-11-12003i−3i3i−3i-21-221-12-100003i−3i003i−3i0000000000000000000000−i3i3−i3i33−33−3000000000000
χ554-44-44004-4-4-21-22-11-12003i−3i3i−3i-21-221-12-100003i−3i003i−3i0000000000000000000000i3−i3i3−i3−33−33000000000000
χ564-44-44004-4-4-21-22-11-1200−3i3i−3i3i-21-221-12-10000−3i3i00−3i3i0000000000000000000000−i3i3−i3i3−33−33000000000000
χ574-44-44004-4-4-21-22-11-1200−3i3i−3i3i-21-221-12-10000−3i3i00−3i3i0000000000000000000000i3−i3i3−i33−33−3000000000000
χ584-44-4-200-222444-4-44-4-4000000-2-2-22-22220000000000000023−2323−230000000000000000000000000000000000
χ594-44-4-200-222444-4-44-4-4000000-2-2-22-222200000000000000−2323−23230000000000000000000000000000000000
χ604-4-44400-44-444-4-4-4-44400000044-44-44-4-40000000000000000000000000000000000000000000000000000
χ614-4-44400-44-4-2122-1-11-2003i−3i−3i3i-212-2-112-100003i−3i00−3i3i00000000000000000000003−3−33i3−i3−i3i3000000000000
χ624-4-44400-44-4-2122-1-11-2003i−3i−3i3i-212-2-112-100003i−3i00−3i3i0000000000000000000000−333−3−i3i3i3−i3000000000000
χ634-4-44400-44-4-2122-1-11-200−3i3i3i−3i-212-2-112-10000−3i3i003i−3i00000000000000000000003−3−33−i3i3i3−i3000000000000
χ644-4-44400-44-4-2122-1-11-200−3i3i3i−3i-212-2-112-10000−3i3i003i−3i0000000000000000000000−333−3i3−i3−i3i3000000000000
χ654-4-44-2002-2244-4-4-4-444000000-2-22-22-2220000000000000023−23−23230000000000000000000000000000000000
χ664-4-44-2002-2244-4-4-4-444000000-2-22-22-22200000000000000−232323−230000000000000000000000000000000000
χ678888-488-4-4-42-422-4-4-42-4-4-4-4-4-4-12-1-122-1222-1-122-1-122000000000000000000000000000000000000000000
χ688888-488-4-4-4-42-4-4222-4-4-422222-122-1-12-1-4-422-1-122-1-1000000000000000000000000000000000000000000
χ698888-4-8-8-4-4-42-422-4-4-42444444-12-1-122-12-2-211-2-211-2-2000000000000000000000000000000000000000000
χ708888-4-8-8-4-4-4-42-4-4222-444-2-2-2-22-122-1-12-144-2-211-2-211000000000000000000000000000000000000000000
χ7188-8-8-48-844-42-4-22-444-2-44-4-444-1211-2-2-122-2-1-12211-2-2000000000000000000000000000000000000000000
χ7288-8-8-48-844-4-424-42-2-24-4422-2-22-1-2-2112-1-4422-1-1-2-211000000000000000000000000000000000000000000
χ7388-8-8-4-8844-42-4-22-444-24-444-4-4-1211-2-2-12-2211-2-2-1-122000000000000000000000000000000000000000000
χ7488-8-8-4-8844-4-424-42-2-244-4-2-2222-1-2-2112-14-4-2-21122-1-1000000000000000000000000000000000000000000
χ758-88-88008-8-82-42-24-44-20000002-42-2-44-240000000000000000000000000000000000000000000000000000
χ768-88-8-400-4442-42-24-44-2000000-12-112-21-20033−330033−3300000000000000000000000000000000000000000000
χ778-88-8-400-4442-42-24-44-2000000-12-112-21-200−333300−333300000000000000000000000000000000000000000000
χ788-88-8-400-444-42-44-22-24006i−6i6i−6i2-12-2-11-210000−3i3i00−3i3i000000000000000000000000000000000000000000
χ798-88-8-400-444-42-44-22-2400−6i6i−6i6i2-12-2-11-2100003i−3i003i−3i000000000000000000000000000000000000000000
χ808-8-88800-88-82-4-2-244-420000002-4-224-4-240000000000000000000000000000000000000000000000000000
χ818-8-88-4004-442-4-2-244-42000000-121-1-221-20033−3300−333300000000000000000000000000000000000000000000
χ828-8-88-4004-442-4-2-244-42000000-121-1-221-200−33330033−3300000000000000000000000000000000000000000000
χ838-8-88-4004-44-4244-2-22-4006i−6i−6i6i2-1-221-1-210000−3i3i003i−3i000000000000000000000000000000000000000000
χ848-8-88-4004-44-4244-2-22-400−6i6i6i−6i2-1-221-1-2100003i−3i00−3i3i000000000000000000000000000000000000000000

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