Finite Group Databasebeta

← Group #13167411

Character table — Group #13167411

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444444444888888888888888888181818181818181836363636363636363636363636363636363636363636363636363636363672727272
order122234466633666666121212121212336666661212121212121212121222441212121222224444668888121212121212121224242424242424246666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
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
χ911-1-111-1-1-1111-1-111-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-11-111-1-11-11-1i−ii−i1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011-1-111-1-1-1111-1-111-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-11-111-1-11-11-1−ii−ii1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-1
χ1111-1-111-1-1-1111-1-111-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-11-111-1-1-11-11i−ii−i1-1−ii−iiii−i−iii−i−i−i−iii−i−iii-11-11
χ1211-1-111-1-1-1111-1-111-1-11-111-1-111-1-1-1-1111-11111-1-1-1-11-11-111-1-1-11-11−ii−ii1-1i−ii−i−i−iii−i−iiiii−i−iii−i−i-11-11
χ1311-1-11-11-1-1111-1-111-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-111-111-1-11-1-11i−i−ii-11i−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411-1-11-11-1-1111-1-111-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-111-111-1-11-1-11−iii−i-11−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1511-1-11-11-1-1111-1-111-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-111-111-1-1-111-1i−i−ii-11−iii−iii−i−i−i−iii−i−iiiii−i−i-111-1
χ1611-1-11-11-1-1111-1-111-1-1-11-1-11111-1-1-1-111-11-1-1-1-11111-111-111-1-1-111-1−iii−i-11i−i−ii−i−iiiii−i−iii−i−i−i−iii-111-1
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
χ2722-2-222-2-2-2222-2-222-2-22-222-2-222-2-2-2-2222-22222-2-2-2-2-22-22-2-22200000000-22000000000000000000000000
χ2822-2-22-22-2-2222-2-222-2-2-22-2-22222-2-2-2-222-22-2-2-2-222222-2-22-2-222000000002-2000000000000000000000000
χ2922-2-2-12-211-122-2-222-2-2-1122-2-2-1-11111-1-12-2-1-1-1-111112-22-2-1-11100000000-112i−2i2i−2i00000000−i−iii−i−iii0000
χ3022-2-2-12-211-122-2-222-2-2-1122-2-2-1-11111-1-12-2-1-1-1-111112-22-2-1-11100000000-11−2i2i−2i2i00000000ii−i−iii−i−i0000
χ3122-2-2-12-211-122-2-222-2-2-1122-2-2-1-11111-1-12-2-1-1-1-11111-22-2211-1-1000000001-1000000000000−i3i3i3−i3−i3i3i3−i30000
χ3222-2-2-12-211-122-2-222-2-2-1122-2-2-1-11111-1-12-2-1-1-1-11111-22-2211-1-1000000001-1000000000000i3−i3−i3i3i3−i3−i3i30000
χ3322-2-2-1-2211-122-2-222-2-21-1-2-222-1-11111-1-1-221111-1-1-1-12-2-2211-1-100000000-11000000000000−i3i3i3−i3i3−i3−i3i30000
χ3422-2-2-1-2211-122-2-222-2-21-1-2-222-1-11111-1-1-221111-1-1-1-12-2-2211-1-100000000-11000000000000i3−i3−i3i3−i3i3i3−i30000
χ3522-2-2-1-2211-122-2-222-2-21-1-2-222-1-11111-1-1-221111-1-1-1-1-222-2-1-111000000001-12i−2i−2i2i00000000−i−iiiii−i−i0000
χ3622-2-2-1-2211-122-2-222-2-21-1-2-222-1-11111-1-1-221111-1-1-1-1-222-2-1-111000000001-1−2i2i2i−2i00000000ii−i−i−i−iii0000
χ3744444444441-2-2-21-2114411111-211-2-21-2-2-211-2-211-2-20000000000002222000000-1-1-1-1-1-1-1-1000000000000
χ3844444444441-2-2-21-2114411111-211-2-21-2-2-211-2-211-2-2000000000000-2-2-2-200000011111111000000000000
χ394444444444-2111-21-2-244-2-2-2-2-21-2-211-2111-2-211-2-21100000000222200000000000000000000000000-1-1-1-1
χ404444444444-2111-21-2-244-2-2-2-2-21-2-211-2111-2-211-2-21100000000-2-2-2-2000000000000000000000000001111
χ4144444-4-44441-2-2-21-211-4-4-1-1-1-11-211-2-21-222-1-122-1-12200000000000022-2-2000000-1-1-1-11111000000000000
χ4244444-4-44441-2-2-21-211-4-4-1-1-1-11-211-2-21-222-1-122-1-122000000000000-2-2220000001111-1-1-1-1000000000000
χ4344444-4-4444-2111-21-2-2-4-42222-21-2-211-21-1-122-1-122-1-10000000022-2-200000000000000000000000000-1-111
χ4444444-4-4444-2111-21-2-2-4-42222-21-2-211-21-1-122-1-122-1-100000000-2-2220000000000000000000000000011-1-1
χ4544-4-444-4-4-441-2221-2-1-14-411-1-11-2-1-1221-2-2211-2-2-1-1220000000000002i−2i2i−2i000000−i−iii−i−iii000000000000
χ4644-4-444-4-4-441-2221-2-1-14-411-1-11-2-1-1221-2-2211-2-2-1-122000000000000−2i2i−2i2i000000ii−i−iii−i−i000000000000
χ4744-4-444-4-4-44-21-1-1-21224-4-2-222-2122-1-1-211-1-2-21122-1-1000000002-22-200000000000000000000000000-11-11
χ4844-4-444-4-4-44-21-1-1-21224-4-2-222-2122-1-1-211-1-2-21122-1-100000000-22-22000000000000000000000000001-11-1
χ4944-4-44-44-4-441-2221-2-1-1-44-1-1111-2-1-1221-22-2-1-12211-2-20000000000002i−2i−2i2i000000−i−iiiii−i−i000000000000
χ5044-4-44-44-4-441-2221-2-1-1-44-1-1111-2-1-1221-22-2-1-12211-2-2000000000000−2i2i2i−2i000000ii−i−i−i−iii000000000000
χ5144-4-44-44-4-44-21-1-1-2122-4422-2-2-2122-1-1-21-1122-1-1-2-211000000002-2-2200000000000000000000000000-111-1
χ5244-4-44-44-4-44-21-1-1-2122-4422-2-2-2122-1-1-21-1122-1-1-2-21100000000-222-2000000000000000000000000001-1-11
χ534-44-44004-4-41-22-2-121-1003i−3i3i−3i1-21-12-2-12003i−3i003i−3i000000000000000000000000−i3i3−i3i33−33−3000000000000
χ544-44-44004-4-41-22-2-121-1003i−3i3i−3i1-21-12-2-12003i−3i003i−3i000000000000000000000000i3−i3i3−i3−33−33000000000000
χ554-44-44004-4-41-22-2-121-100−3i3i−3i3i1-21-12-2-1200−3i3i00−3i3i000000000000000000000000−i3i3−i3i3−33−33000000000000
χ564-44-44004-4-41-22-2-121-100−3i3i−3i3i1-21-12-2-1200−3i3i00−3i3i000000000000000000000000i3−i3i3−i33−33−3000000000000
χ574-44-44004-4-444-44-4-44-4000000444-4-44-4-40000000000000000000000000000000000000000000000000000
χ584-44-4-200-22244-44-4-44-4000000-2-2-222-2220000000000000023−2323−230000000000000000000000000000000000
χ594-44-4-200-22244-44-4-44-4000000-2-2-222-22200000000000000−2323−23230000000000000000000000000000000000
χ604-4-44400-44-41-2-22-12-11003i−3i−3i3i1-2-11-22-12003i−3i00−3i3i0000000000000000000000003−3−33i3−i3−i3i3000000000000
χ614-4-44400-44-41-2-22-12-11003i−3i−3i3i1-2-11-22-12003i−3i00−3i3i000000000000000000000000−333−3−i3i3i3−i3000000000000
χ624-4-44400-44-41-2-22-12-1100−3i3i3i−3i1-2-11-22-1200−3i3i003i−3i0000000000000000000000003−3−33−i3i3i3−i3000000000000
χ634-4-44400-44-41-2-22-12-1100−3i3i3i−3i1-2-11-22-1200−3i3i003i−3i000000000000000000000000−333−3i3−i3−i3i3000000000000
χ644-4-44400-44-4444-4-4-4-4400000044-444-4-4-40000000000000000000000000000000000000000000000000000
χ654-4-44-2002-22444-4-4-4-44000000-2-22-2-22220000000000000023−23−23230000000000000000000000000000000000
χ664-4-44-2002-22444-4-4-4-44000000-2-22-2-222200000000000000−232323−230000000000000000000000000000000000
χ678888-488-4-4-42-4-4-42-422-4-42222-12-1-122-12-4-4-1-122-1-122000000000000000000000000000000000000000000
χ688888-488-4-4-4-4222-42-4-4-4-4-4-4-4-42-122-1-12-12222-1-122-1-1000000000000000000000000000000000000000000
χ698888-4-8-8-4-4-42-4-4-42-42244-2-2-2-2-12-1-122-124411-2-211-2-2000000000000000000000000000000000000000000
χ708888-4-8-8-4-4-4-4222-42-4-44444442-122-1-12-1-2-2-2-211-2-211000000000000000000000000000000000000000000
χ7188-8-8-48-844-42-4442-4-2-2-4422-2-2-1211-2-2-12-44-1-12211-2-2000000000000000000000000000000000000000000
χ7288-8-8-48-844-4-42-2-2-4244-44-4-4442-1-2-2112-12-222-1-1-2-211000000000000000000000000000000000000000000
χ7388-8-8-4-8844-42-4442-4-2-24-4-2-222-1211-2-2-124-411-2-2-1-122000000000000000000000000000000000000000000
χ7488-8-8-4-8844-4-42-2-2-42444-444-4-42-1-2-2112-1-22-2-21122-1-1000000000000000000000000000000000000000000
χ758-88-88008-8-8-42-224-2-44000000-42-44-224-20000000000000000000000000000000000000000000000000000
χ768-88-8-400-4442-44-4-242-2006i−6i6i−6i-12-11-221-200−3i3i00−3i3i00000000000000000000000000000000000000000000
χ778-88-8-400-4442-44-4-242-200−6i6i−6i6i-12-11-221-2003i−3i003i−3i00000000000000000000000000000000000000000000
χ788-88-8-400-444-42-224-2-440000002-12-21-1-21000033−330033−33000000000000000000000000000000000000000000
χ798-88-8-400-444-42-224-2-440000002-12-21-1-210000−333300−3333000000000000000000000000000000000000000000
χ808-8-88800-88-8-422-24-24-4000000-424-42-24-20000000000000000000000000000000000000000000000000000
χ818-8-88-4004-442-4-44-24-22006i−6i−6i6i-121-12-21-200−3i3i003i−3i00000000000000000000000000000000000000000000
χ828-8-88-4004-442-4-44-24-2200−6i6i6i−6i-121-12-21-2003i−3i00−3i3i00000000000000000000000000000000000000000000
χ838-8-88-4004-44-422-24-24-40000002-1-22-11-21000033−3300−3333000000000000000000000000000000000000000000
χ848-8-88-4004-44-422-24-24-40000002-1-22-11-210000−33330033−33000000000000000000000000000000000000000000

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