Finite Group Databasebeta

← Group #13167575

Character table — Group #13167575

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222444444488888888899181818181818183636363636363636363636363672721122244444448888888889918181818181818363636363636363636363636367272
order122363366666336666666444444412122488121212121224242424612222666666666666666666444444412122488121212121224242424612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-111-1-1111-1-1-1-11111-1-1111111111111111111111111-1-1-1-111-1-1111-1-1-1-11111-1-1
χ511-11111-11-11-111-111-1-1-1-1-1-11ii−i−i-1-11-1i−i1ii−i−iii−i−i1-111-11111-11-11-111-111-1-1-1-1-1-11ii−i−i-1-11-1i−i1ii−i−iii−i−i1-1
χ611-11111-11-11-111-111-1-1-1-1-1-11ii−i−i-1-1-11−ii1ii−i−i−i−iii-1111-11111-11-11-111-111-1-1-1-1-1-11ii−i−i-1-1-11−ii1ii−i−i−i−iii-11
χ711-11111-11-11-111-111-1-1-1-1-1-11−i−iii-1-11-1−ii1−i−iii−i−iii1-111-11111-11-11-111-111-1-1-1-1-1-11−i−iii-1-11-1−ii1−i−iii−i−iii1-1
χ811-11111-11-11-111-111-1-1-1-1-1-11−i−iii-1-1-11i−i1−i−iiiii−i−i-1111-11111-11-11-111-111-1-1-1-1-1-11−i−iii-1-1-11i−i1−i−iiiii−i−i-11
χ9222222222222222222222-2-2-20000-2-20000-20000000000222222222222222222222-2-2-20000-2-20000-20000000000
χ10222-1-122-12222-1-12-1-1-1-1-1-12220000-1-10022-10000-1-1-1-100222-1-122-12222-1-12-1-1-1-1-1-12220000-1-10022-10000-1-1-1-100
χ11222-1-122-12222-1-12-1-1-1-1-1-12220000-1-100-2-2-10000111100222-1-122-12222-1-12-1-1-1-1-1-12220000-1-100-2-2-10000111100
χ12222-1-122-12222-1-12-1-1-1-1-1-1-2-2-20000110000100003−33−300222-1-122-12222-1-12-1-1-1-1-1-1-2-2-20000110000100003−33−300
χ13222-1-122-12222-1-12-1-1-1-1-1-1-2-2-2000011000010000−33−3300222-1-122-12222-1-12-1-1-1-1-1-1-2-2-2000011000010000−33−3300
χ1422-22222-22-22-222-222-2-2-2-222-20000220000-2000000000022-22222-22-22-222-222-2-2-2-222-20000220000-20000000000
χ1522-2-1-12212-22-2-1-1-2-1-1111122-20000-1-1000010000−i3i3i3−i30022-2-1-12212-22-2-1-1-2-1-1111122-20000-1-1000010000−i3i3i3−i300
χ1622-2-1-12212-22-2-1-1-2-1-1111122-20000-1-1000010000i3−i3−i3i30022-2-1-12212-22-2-1-1-2-1-1111122-20000-1-1000010000i3−i3−i3i300
χ1722-2-1-12212-22-2-1-1-2-1-11111-2-22000011002i−2i-10000−i−iii0022-2-1-12212-22-2-1-1-2-1-11111-2-22000011002i−2i-10000−i−iii00
χ1822-2-1-12212-22-2-1-1-2-1-11111-2-2200001100−2i2i-10000ii−i−i0022-2-1-12212-22-2-1-1-2-1-11111-2-2200001100−2i2i-10000ii−i−i00
χ192-202-2220-20-20220-2-200002i−2i01+i−1−i1−i−1+i2i−2i000001+i−1−i1−i−1+i0000002-202-2220-20-20220-2-200002i−2i01+i−1−i1−i−1+i2i−2i000001+i−1−i1−i−1+i000000
χ202-202-2220-20-20220-2-200002i−2i0−1−i1+i−1+i1−i2i−2i00000−1−i1+i−1+i1−i0000002-202-2220-20-20220-2-200002i−2i0−1−i1+i−1+i1−i2i−2i00000−1−i1+i−1+i1−i000000
χ212-202-2220-20-20220-2-20000−2i2i01−i−1+i1+i−1−i−2i2i000001−i−1+i1+i−1−i0000002-202-2220-20-20220-2-20000−2i2i01−i−1+i1+i−1−i−2i2i000001−i−1+i1+i−1−i000000
χ222-202-2220-20-20220-2-20000−2i2i0−1+i1−i−1−i1+i−2i2i00000−1+i1−i−1−i1+i0000002-202-2220-20-20220-2-20000−2i2i0−1+i1−i−1−i1+i−2i2i00000−1+i1−i−1−i1+i000000
χ23444441-2411-211-2-21-211-2-200022220000000-1-1-1-1000000444441-2411-211-2-21-211-2-200022220000000-1-1-1-1000000
χ24444441-2411-211-2-21-211-2-2000-2-2-2-200000001111000000444441-2411-211-2-21-211-2-2000-2-2-2-200000001111000000
χ2544444-214-2-21-2-211-21-2-2110000000002200000000000-1-144444-214-2-21-2-211-21-2-2110000000002200000000000-1-1
χ2644444-214-2-21-2-211-21-2-211000000000-2-2000000000001144444-214-2-21-2-211-21-2-211000000000-2-20000000000011
χ2744-4441-2-41-1-2-11-221-2-1-1220002i2i−2i−2i0000000−i−iii00000044-4441-2-41-1-2-11-221-2-1-1220002i2i−2i−2i0000000−i−iii000000
χ2844-4441-2-41-1-2-11-221-2-1-122000−2i−2i2i2i0000000ii−i−i00000044-4441-2-41-1-2-11-221-2-1-122000−2i−2i2i2i0000000ii−i−i000000
χ2944-444-21-4-2212-21-1-2122-1-10000000002-200000000000-1144-444-21-4-2212-21-1-2122-1-10000000002-200000000000-11
χ3044-444-21-4-2212-21-1-2122-1-1000000000-22000000000001-144-444-21-4-2212-21-1-2122-1-1000000000-22000000000001-1
χ314-404-41-20-132-31-20-123-3000002-22-20000000-11-110000004-404-41-20-132-31-20-123-3000002-22-20000000-11-11000000
χ324-404-41-20-132-31-20-123-300000-22-2200000001-11-10000004-404-41-20-132-31-20-123-300000-22-2200000001-11-1000000
χ334-404-41-20-1-3231-20-12-33000002i−2i−2i2i0000000−iii−i0000004-404-41-20-1-3231-20-12-33000002i−2i−2i2i0000000−iii−i000000
χ344-404-41-20-1-3231-20-12-3300000−2i2i2i−2i0000000i−i−ii0000004-404-41-20-1-3231-20-12-3300000−2i2i2i−2i0000000i−i−ii000000
χ354-40-22440-40-40-2-202200004i−4i00000−2i2i0000000000000004-40-22440-40-40-2-202200004i−4i00000−2i2i000000000000000
χ364-40-22440-40-40-2-20220000−4i4i000002i−2i0000000000000004-40-22440-40-40-2-20220000−4i4i000002i−2i000000000000000
χ37888-4-42-4-422-42-12-4-12-1-122000000000000000000000000888-4-42-4-422-42-12-4-12-1-122000000000000000000000000
χ38888-4-4-42-4-4-42-42-122-122-1-1000000000000000000000000888-4-4-42-4-4-42-42-122-122-1-1000000000000000000000000
χ3988-8-4-42-442-2-4-2-124-1211-2-200000000000000000000000088-8-4-42-442-2-4-2-124-1211-2-2000000000000000000000000
χ4088-8-4-4-424-44242-1-22-1-2-21100000000000000000000000088-8-4-4-424-44242-1-22-1-2-211000000000000000000000000
χ418-808-8-42040-20-4204-200000000000000000000000000008-808-8-42040-20-4204-20000000000000000000000000000
χ428-80-442-40-264-6-1201-2-33000000000000000000000000008-80-442-40-264-6-1201-2-3300000000000000000000000000
χ438-80-442-40-2-646-1201-23-3000000000000000000000000008-80-442-40-2-646-1201-23-300000000000000000000000000
χ448-80-44-42040-202-10-2100−3i33i30000000000000000000000008-80-44-42040-202-10-2100−3i33i3000000000000000000000000
χ458-80-44-42040-202-10-21003i3−3i30000000000000000000000008-80-44-42040-202-10-21003i3−3i3000000000000000000000000
χ46111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ47111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111
χ48111111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111111111-1-1
χ49111111111111111111111111-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11111-1-1-1-111
χ5011-11111-11-11-111-111-1-1-1-1-1-11ii−i−i-1-11-1i−i1ii−i−iii−i−i1-1-1-11-1-1-1-11-11-11-1-11-1-1111111-1−i−iii11-11−ii-1−i−iii−i−iii-11
χ5111-11111-11-11-111-111-1-1-1-1-1-11ii−i−i-1-1-11−ii1ii−i−i−i−iii-11-1-11-1-1-1-11-11-11-1-11-1-1111111-1−i−iii111-1i−i-1−i−iiiii−i−i1-1
χ5211-11111-11-11-111-111-1-1-1-1-1-11−i−iii-1-11-1−ii1−i−iii−i−iii1-1-1-11-1-1-1-11-11-11-1-11-1-1111111-1ii−i−i11-11i−i-1ii−i−iii−i−i-11
χ5311-11111-11-11-111-111-1-1-1-1-1-11−i−iii-1-1-11i−i1−i−iiiii−i−i-11-1-11-1-1-1-11-11-11-1-11-1-1111111-1ii−i−i111-1−ii-1ii−i−i−i−iii1-1
χ54222222222222222222222-2-2-20000-2-20000-20000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222000022000020000000000
χ55222-1-122-12222-1-12-1-1-1-1-1-12220000-1-10022-10000-1-1-1-100-2-2-211-2-21-2-2-2-211-2111111-2-2-200001100-2-210000111100
χ56222-1-122-12222-1-12-1-1-1-1-1-12220000-1-100-2-2-10000111100-2-2-211-2-21-2-2-2-211-2111111-2-2-2000011002210000-1-1-1-100
χ57222-1-122-12222-1-12-1-1-1-1-1-1-2-2-20000110000100003−33−300-2-2-211-2-21-2-2-2-211-21111112220000-1-10000-10000−33−3300
χ58222-1-122-12222-1-12-1-1-1-1-1-1-2-2-2000011000010000−33−3300-2-2-211-2-21-2-2-2-211-21111112220000-1-10000-100003−33−300
χ5922-22222-22-22-222-222-2-2-2-222-20000220000-20000000000-2-22-2-2-2-22-22-22-2-22-2-22222-2-220000-2-2000020000000000
χ6022-2-1-12212-22-2-1-1-2-1-1111122-20000-1-1000010000−i3i3i3−i300-2-2211-2-2-1-22-2211211-1-1-1-1-2-220000110000-10000i3−i3−i3i300
χ6122-2-1-12212-22-2-1-1-2-1-1111122-20000-1-1000010000i3−i3−i3i300-2-2211-2-2-1-22-2211211-1-1-1-1-2-220000110000-10000−i3i3i3−i300
χ6222-2-1-12212-22-2-1-1-2-1-11111-2-22000011002i−2i-10000−i−iii00-2-2211-2-2-1-22-2211211-1-1-1-122-20000-1-100−2i2i10000ii−i−i00
χ6322-2-1-12212-22-2-1-1-2-1-11111-2-2200001100−2i2i-10000ii−i−i00-2-2211-2-2-1-22-2211211-1-1-1-122-20000-1-1002i−2i10000−i−iii00
χ642-202-2220-20-20220-2-200002i−2i01+i−1−i1−i−1+i2i−2i000001+i−1−i1−i−1+i000000-220-22-2-202020-2-20220000−2i2i0−1−i1+i−1+i1−i−2i2i00000−1−i1+i−1+i1−i000000
χ652-202-2220-20-20220-2-200002i−2i0−1−i1+i−1+i1−i2i−2i00000−1−i1+i−1+i1−i000000-220-22-2-202020-2-20220000−2i2i01+i−1−i1−i−1+i−2i2i000001+i−1−i1−i−1+i000000
χ662-202-2220-20-20220-2-20000−2i2i01−i−1+i1+i−1−i−2i2i000001−i−1+i1+i−1−i000000-220-22-2-202020-2-202200002i−2i0−1+i1−i−1−i1+i2i−2i00000−1+i1−i−1−i1+i000000
χ672-202-2220-20-20220-2-20000−2i2i0−1+i1−i−1−i1+i−2i2i00000−1+i1−i−1−i1+i000000-220-22-2-202020-2-202200002i−2i01−i−1+i1+i−1−i2i−2i000001−i−1+i1+i−1−i000000
χ68444441-2411-211-2-21-211-2-200022220000000-1-1-1-1000000-4-4-4-4-4-12-4-1-12-1-122-12-1-122000-2-2-2-200000001111000000
χ69444441-2411-211-2-21-211-2-2000-2-2-2-200000001111000000-4-4-4-4-4-12-4-1-12-1-122-12-1-12200022220000000-1-1-1-1000000
χ7044444-214-2-21-2-211-21-2-2110000000002200000000000-1-1-4-4-4-4-42-1-422-122-1-12-122-1-1000000000-2-20000000000011
χ7144444-214-2-21-2-211-21-2-211000000000-2-20000000000011-4-4-4-4-42-1-422-122-1-12-122-1-10000000002200000000000-1-1
χ7244-4441-2-41-1-2-11-221-2-1-1220002i2i−2i−2i0000000−i−iii000000-4-44-4-4-124-1121-12-2-1211-2-2000−2i−2i2i2i0000000ii−i−i000000
χ7344-4441-2-41-1-2-11-221-2-1-122000−2i−2i2i2i0000000ii−i−i000000-4-44-4-4-124-1121-12-2-1211-2-20002i2i−2i−2i0000000−i−iii000000
χ7444-444-21-4-2212-21-1-2122-1-10000000002-200000000000-11-4-44-4-42-142-2-1-22-112-1-2-211000000000-22000000000001-1
χ7544-444-21-4-2212-21-1-2122-1-1000000000-22000000000001-1-4-44-4-42-142-2-1-22-112-1-2-2110000000002-200000000000-11
χ764-404-41-20-132-31-20-123-3000002-22-20000000-11-11000000-440-44-1201-3-23-1201-2-3300000-22-2200000001-11-1000000
χ774-404-41-20-132-31-20-123-300000-22-2200000001-11-1000000-440-44-1201-3-23-1201-2-33000002-22-20000000-11-11000000
χ784-404-41-20-1-3231-20-12-33000002i−2i−2i2i0000000−iii−i000000-440-44-12013-2-3-1201-23-300000−2i2i2i−2i0000000i−i−ii000000
χ794-404-41-20-1-3231-20-12-3300000−2i2i2i−2i0000000i−i−ii000000-440-44-12013-2-3-1201-23-3000002i−2i−2i2i0000000−iii−i000000
χ804-40-22440-40-40-2-202200004i−4i00000−2i2i000000000000000-4402-2-4-404040220-2-20000−4i4i000002i−2i000000000000000
χ814-40-22440-40-40-2-20220000−4i4i000002i−2i000000000000000-4402-2-4-404040220-2-200004i−4i00000−2i2i000000000000000
χ82888-4-42-4-422-42-12-4-12-1-122000000000000000000000000-8-8-844-244-2-24-21-241-211-2-2000000000000000000000000
χ83888-4-4-42-4-4-42-42-122-122-1-1000000000000000000000000-8-8-8444-2444-24-21-2-21-2-211000000000000000000000000
χ8488-8-4-42-442-2-4-2-124-1211-2-2000000000000000000000000-8-8844-24-4-22421-2-41-2-1-122000000000000000000000000
χ8588-8-4-4-424-44242-1-22-1-2-211000000000000000000000000-8-88444-2-44-4-2-4-212-2122-1-1000000000000000000000000
χ868-808-8-42040-20-4204-20000000000000000000000000000-880-884-20-40204-20-420000000000000000000000000000
χ878-80-442-40-264-6-1201-2-3300000000000000000000000000-8804-4-2402-6-461-20-123-300000000000000000000000000
χ888-80-442-40-2-646-1201-23-300000000000000000000000000-8804-4-24026-4-61-20-12-3300000000000000000000000000
χ898-80-44-42040-202-10-2100−3i33i3000000000000000000000000-8804-44-20-4020-2102-1003i3−3i3000000000000000000000000
χ908-80-44-42040-202-10-21003i3−3i3000000000000000000000000-8804-44-20-4020-2102-100−3i33i3000000000000000000000000

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