Finite Group Databasebeta

← Group #13167563

Character table — Group #13167563

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112224444444888888888181818183636363636363636363636363636367272112224444444888888888181818183636363636363636363636363636367272
order122363366666336666666226624444461212121212121212612222666666666666666666226624444461212121212121212612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-111-1-111111-1-1-1-1-1-11111111111111111111111111-1-111-1-111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1111-1-1-1-11111-1-11111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1
χ511-11111-11-11-111-111-1-1-1-11-1-1-11-1i−ii−i1ii−i−iii−i−i1-111-11111-11-11-111-111-1-1-1-11-1-1-11-1i−ii−i1ii−i−iii−i−i1-1
χ611-11111-11-11-111-111-1-1-1-11-1-1-11-1−ii−ii1−i−iii−i−iii1-111-11111-11-11-111-111-1-1-1-11-1-1-11-1−ii−ii1−i−iii−i−iii1-1
χ711-11111-11-11-111-111-1-1-1-11-1-1-1-11i−i−ii1ii−i−i−i−iii-1111-11111-11-11-111-111-1-1-1-11-1-1-1-11i−i−ii1ii−i−i−i−iii-11
χ811-11111-11-11-111-111-1-1-1-11-1-1-1-11−iii−i1−i−iiiii−i−i-1111-11111-11-11-111-111-1-1-1-11-1-1-1-11−iii−i1−i−iiiii−i−i-11
χ9222222222222222222222-2-2-2-2000000-20000000000222222222222222222222-2-2-2-2000000-20000000000
χ10222-1-122-12222-1-12-1-1-1-1-1-122-1-1000022-10000-1-1-1-100222-1-122-12222-1-12-1-1-1-1-1-122-1-1000022-10000-1-1-1-100
χ11222-1-122-12222-1-12-1-1-1-1-1-122-1-10000-2-2-10000111100222-1-122-12222-1-12-1-1-1-1-1-122-1-10000-2-2-10000111100
χ12222-1-122-12222-1-12-1-1-1-1-1-1-2-211000000100003−33−300222-1-122-12222-1-12-1-1-1-1-1-1-2-211000000100003−33−300
χ13222-1-122-12222-1-12-1-1-1-1-1-1-2-21100000010000−33−3300222-1-122-12222-1-12-1-1-1-1-1-1-2-21100000010000−33−3300
χ1422-22222-22-22-222-222-2-2-2-2-2222000000-2000000000022-22222-22-22-222-222-2-2-2-2-2222000000-20000000000
χ1522-2-1-12212-22-2-1-1-2-1-111112-21100002i−2i-10000−i−iii0022-2-1-12212-22-2-1-1-2-1-111112-21100002i−2i-10000−i−iii00
χ1622-2-1-12212-22-2-1-1-2-1-111112-2110000−2i2i-10000ii−i−i0022-2-1-12212-22-2-1-1-2-1-111112-2110000−2i2i-10000ii−i−i00
χ1722-2-1-12212-22-2-1-1-2-1-11111-22-1-100000010000−i3i3i3−i30022-2-1-12212-22-2-1-1-2-1-11111-22-1-100000010000−i3i3i3−i300
χ1822-2-1-12212-22-2-1-1-2-1-11111-22-1-100000010000i3−i3−i3i30022-2-1-12212-22-2-1-1-2-1-11111-22-1-100000010000i3−i3−i3i300
χ19444441-2411-211-2-21-211-2-200000022000-1-1-1-1000000444441-2411-211-2-21-211-2-200000022000-1-1-1-1000000
χ20444441-2411-211-2-21-211-2-2000000-2-20001111000000444441-2411-211-2-21-211-2-2000000-2-20001111000000
χ2144444-214-2-21-2-211-21-2-2110000220000000000000-1-144444-214-2-21-2-211-21-2-2110000220000000000000-1-1
χ2244444-214-2-21-2-211-21-2-2110000-2-200000000000001144444-214-2-21-2-211-21-2-2110000-2-2000000000000011
χ2344-4441-2-41-1-2-11-221-2-1-1220000002i−2i000−i−iii00000044-4441-2-41-1-2-11-221-2-1-1220000002i−2i000−i−iii000000
χ2444-4441-2-41-1-2-11-221-2-1-122000000−2i2i000ii−i−i00000044-4441-2-41-1-2-11-221-2-1-122000000−2i2i000ii−i−i000000
χ2544-444-21-4-2212-21-1-2122-1-100002-20000000000000-1144-444-21-4-2212-21-1-2122-1-100002-20000000000000-11
χ2644-444-21-4-2212-21-1-2122-1-10000-2200000000000001-144-444-21-4-2212-21-1-2122-1-10000-2200000000000001-1
χ274-404-41-20-132-31-20-123-30000000000000−i3i3−i3i30000004-404-41-20-132-31-20-123-30000000000000−i3i3−i3i3000000
χ284-404-41-20-132-31-20-123-30000000000000i3−i3i3−i30000004-404-41-20-132-31-20-123-30000000000000i3−i3i3−i3000000
χ294-404-41-20-1-3231-20-12-3300000000000003−3−330000004-404-41-20-1-3231-20-12-3300000000000003−3−33000000
χ304-404-41-20-1-3231-20-12-330000000000000−333−30000004-404-41-20-1-3231-20-12-330000000000000−333−3000000
χ314-404-4440-40-40440-4-400000000000000000000000004-404-4440-40-40440-4-40000000000000000000000000
χ324-40-22440-40-40-2-2022000000−2i32i3000000000000000004-40-22440-40-40-2-2022000000−2i32i300000000000000000
χ334-40-22440-40-40-2-20220000002i3−2i3000000000000000004-40-22440-40-40-2-20220000002i3−2i300000000000000000
χ34888-4-42-4-422-42-12-4-12-1-122000000000000000000000888-4-42-4-422-42-12-4-12-1-122000000000000000000000
χ35888-4-4-42-4-4-42-42-122-122-1-1000000000000000000000888-4-4-42-4-4-42-42-122-122-1-1000000000000000000000
χ3688-8-4-42-442-2-4-2-124-1211-2-200000000000000000000088-8-4-42-442-2-4-2-124-1211-2-2000000000000000000000
χ3788-8-4-4-424-44242-1-22-1-2-21100000000000000000000088-8-4-4-424-44242-1-22-1-2-211000000000000000000000
χ388-808-8-42040-20-4204-200000000000000000000000008-808-8-42040-20-4204-20000000000000000000000000
χ398-80-442-40-264-6-1201-2-33000000000000000000000008-80-442-40-264-6-1201-2-3300000000000000000000000
χ408-80-442-40-2-646-1201-23-3000000000000000000000008-80-442-40-2-646-1201-23-300000000000000000000000
χ418-80-44-42040-202-10-2100−3i33i30000000000000000000008-80-44-42040-202-10-2100−3i33i3000000000000000000000
χ428-80-44-42040-202-10-21003i3−3i30000000000000000000008-80-44-42040-202-10-21003i3−3i3000000000000000000000
χ43111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ44111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1
χ451111111111111111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1111111
χ461111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-111
χ4711-11111-11-11-111-111-1-1-1-11-1-1-11-1i−ii−i1ii−i−iii−i−i1-1-1-11-1-1-1-11-11-11-1-11-1-11111-1111-11−ii−ii-1−i−iii−i−iii-11
χ4811-11111-11-11-111-111-1-1-1-11-1-1-11-1−ii−ii1−i−iii−i−iii1-1-1-11-1-1-1-11-11-11-1-11-1-11111-1111-11i−ii−i-1ii−i−iii−i−i-11
χ4911-11111-11-11-111-111-1-1-1-11-1-1-1-11i−i−ii1ii−i−i−i−iii-11-1-11-1-1-1-11-11-11-1-11-1-11111-11111-1−iii−i-1−i−iiiii−i−i1-1
χ5011-11111-11-11-111-111-1-1-1-11-1-1-1-11−iii−i1−i−iiiii−i−i-11-1-11-1-1-1-11-11-11-1-11-1-11111-11111-1i−i−ii-1ii−i−i−i−iii1-1
χ51222222222222222222222-2-2-2-2000000-20000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000020000000000
χ52222-1-122-12222-1-12-1-1-1-1-1-122-1-1000022-10000-1-1-1-100-2-2-211-2-21-2-2-2-211-2111111-2-2110000-2-210000111100
χ53222-1-122-12222-1-12-1-1-1-1-1-122-1-10000-2-2-10000111100-2-2-211-2-21-2-2-2-211-2111111-2-21100002210000-1-1-1-100
χ54222-1-122-12222-1-12-1-1-1-1-1-1-2-211000000100003−33−300-2-2-211-2-21-2-2-2-211-211111122-1-1000000-10000−33−3300
χ55222-1-122-12222-1-12-1-1-1-1-1-1-2-21100000010000−33−3300-2-2-211-2-21-2-2-2-211-211111122-1-1000000-100003−33−300
χ5622-22222-22-22-222-222-2-2-2-2-2222000000-20000000000-2-22-2-2-2-22-22-22-2-22-2-222222-2-2-200000020000000000
χ5722-2-1-12212-22-2-1-1-2-1-111112-21100002i−2i-10000−i−iii00-2-2211-2-2-1-22-2211211-1-1-1-1-22-1-10000−2i2i10000ii−i−i00
χ5822-2-1-12212-22-2-1-1-2-1-111112-2110000−2i2i-10000ii−i−i00-2-2211-2-2-1-22-2211211-1-1-1-1-22-1-100002i−2i10000−i−iii00
χ5922-2-1-12212-22-2-1-1-2-1-11111-22-1-100000010000−i3i3i3−i300-2-2211-2-2-1-22-2211211-1-1-1-12-211000000-10000i3−i3−i3i300
χ6022-2-1-12212-22-2-1-1-2-1-11111-22-1-100000010000i3−i3−i3i300-2-2211-2-2-1-22-2211211-1-1-1-12-211000000-10000−i3i3i3−i300
χ61444441-2411-211-2-21-211-2-200000022000-1-1-1-1000000-4-4-4-4-4-12-4-1-12-1-122-12-1-122000000-2-20001111000000
χ62444441-2411-211-2-21-211-2-2000000-2-20001111000000-4-4-4-4-4-12-4-1-12-1-122-12-1-12200000022000-1-1-1-1000000
χ6344444-214-2-21-2-211-21-2-2110000220000000000000-1-1-4-4-4-4-42-1-422-122-1-12-122-1-10000-2-2000000000000011
χ6444444-214-2-21-2-211-21-2-2110000-2-2000000000000011-4-4-4-4-42-1-422-122-1-12-122-1-10000220000000000000-1-1
χ6544-4441-2-41-1-2-11-221-2-1-1220000002i−2i000−i−iii000000-4-44-4-4-124-1121-12-2-1211-2-2000000−2i2i000ii−i−i000000
χ6644-4441-2-41-1-2-11-221-2-1-122000000−2i2i000ii−i−i000000-4-44-4-4-124-1121-12-2-1211-2-20000002i−2i000−i−iii000000
χ6744-444-21-4-2212-21-1-2122-1-100002-20000000000000-11-4-44-4-42-142-2-1-22-112-1-2-2110000-2200000000000001-1
χ6844-444-21-4-2212-21-1-2122-1-10000-2200000000000001-1-4-44-4-42-142-2-1-22-112-1-2-21100002-20000000000000-11
χ694-404-41-20-132-31-20-123-30000000000000−i3i3−i3i3000000-440-44-1201-3-23-1201-2-330000000000000i3−i3i3−i3000000
χ704-404-41-20-132-31-20-123-30000000000000i3−i3i3−i3000000-440-44-1201-3-23-1201-2-330000000000000−i3i3−i3i3000000
χ714-404-41-20-1-3231-20-12-3300000000000003−3−33000000-440-44-12013-2-3-1201-23-30000000000000−333−3000000
χ724-404-41-20-1-3231-20-12-330000000000000−333−3000000-440-44-12013-2-3-1201-23-300000000000003−3−33000000
χ734-404-4440-40-40440-4-40000000000000000000000000-440-44-4-404040-4-40440000000000000000000000000
χ744-40-22440-40-40-2-2022000000−2i32i300000000000000000-4402-2-4-404040220-2-20000002i3−2i300000000000000000
χ754-40-22440-40-40-2-20220000002i3−2i300000000000000000-4402-2-4-404040220-2-2000000−2i32i300000000000000000
χ76888-4-42-4-422-42-12-4-12-1-122000000000000000000000-8-8-844-244-2-24-21-241-211-2-2000000000000000000000
χ77888-4-4-42-4-4-42-42-122-122-1-1000000000000000000000-8-8-8444-2444-24-21-2-21-2-211000000000000000000000
χ7888-8-4-42-442-2-4-2-124-1211-2-2000000000000000000000-8-8844-24-4-22421-2-41-2-1-122000000000000000000000
χ7988-8-4-4-424-44242-1-22-1-2-211000000000000000000000-8-88444-2-44-4-2-4-212-2122-1-1000000000000000000000
χ808-808-8-42040-20-4204-20000000000000000000000000-880-884-20-40204-20-420000000000000000000000000
χ818-80-442-40-264-6-1201-2-3300000000000000000000000-8804-4-2402-6-461-20-123-300000000000000000000000
χ828-80-442-40-2-646-1201-23-300000000000000000000000-8804-4-24026-4-61-20-12-3300000000000000000000000
χ838-80-44-42040-202-10-2100−3i33i3000000000000000000000-8804-44-20-4020-2102-1003i3−3i3000000000000000000000
χ848-80-44-42040-202-10-21003i3−3i3000000000000000000000-8804-44-20-4020-2102-100−3i33i3000000000000000000000

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