Finite Group Databasebeta

← Group #13167214

Character table — Group #13167214

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222244444444444444444888888888888888881212121212121818242424242424242424242424242424363636363636367272727272216216
order1223666333346666666666121236666121212121212121212121212441212121244412121212121212121212121212122244412126612121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-11-1-111-1-11-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-111
χ511111111111-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-11-1-11-1111-1-11-11-1
χ611111111111-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-11-1-1111-11-1-11-11
χ711111111111-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-11-1111-1-11-1-11
χ811111111111-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-11-1-1111-11-1-111-1
χ922222222222222222222222222222222222222222000000-2-200000000000000000-200-2-200-20000
χ1022222222222-22222222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-2000000-2-200000000000000000200-2-20020000
χ11222-1-1-1-12-1-1222-1-12-1-12-1-1222-12-1-1-1-122-1-1-1-12-1-1-1-100−i3−i3i3i3-2-20−i3i300−i3−i3i3i300−i3−i3i3i300-200110010000
χ12222-1-1-1-12-1-1222-1-12-1-12-1-1222-12-1-1-1-122-1-1-1-12-1-1-1-100i3i3−i3−i3-2-20i3−i300i3i3−i3−i300i3i3−i3−i300-200110010000
χ13222-1-1-1-12-1-1222-1-12-1-12-1-1222-12-1-1-1-122-1-1-1-12-1-1-1-122-1-1-1-1222-1-122-1-1-1-122-1-1-1-100200-1-100-10000
χ14222-1-1-1-12-1-1222-1-12-1-12-1-1222-12-1-1-1-122-1-1-1-12-1-1-1-1-2-2111122-211-2-21111-2-2111100200-1-100-10000
χ15222-1-1-1-12-1-12-22-1-12-1-12-1-12-2-2-12-1-1-11-2-21111-2111100−i3−i3i3i3-2-20i3−i300−i3−i3i3i300i3i3−i3−i3002001100-10000
χ16222-1-1-1-12-1-12-22-1-12-1-12-1-12-2-2-12-1-1-11-2-21111-2111100i3i3−i3−i3-2-20−i3i300i3i3−i3−i300−i3−i3i3i3002001100-10000
χ17222-1-1-1-12-1-12-22-1-12-1-12-1-12-2-2-12-1-1-11-2-21111-2111122-1-1-1-122-21122-1-1-1-1-2-2111100-200-1-10010000
χ18222-1-1-1-12-1-12-22-1-12-1-12-1-12-2-2-12-1-1-11-2-21111-21111-2-21111222-1-1-2-2111122-1-1-1-100-200-1-10010000
χ1922-22-2-2222220-2-2-2-2-2-22222002-2-2-220000000000000000002-20000000000000000200-22-20200-200
χ2022-22-2-2222220-2-2-2-2-2-22222002-2-2-220000000000000000002-20000000000000000-20022-20-200200
χ2122-22-2-2222220-2-2-2-2-2-22222002-2-2-22000000000000000000-22000000000000000200-20-22200-2000
χ2222-22-2-2222220-2-2-2-2-2-22222002-2-2-22000000000000000000-22000000000000000-20020-22-2002000
χ234444444111-24111111111-2-2-2-2-2-2-2-24111111-2-2-2-2-222222200222-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ244444444111-24111111111-2-2-2-2-2-2-2-24111111-2-2-2-2-2-2-2-2-2-2-200-2-2-211111111111100000000000000
χ254444444111-2-4111111111-222-2-2-2-2-2-4-1-1-1-1-1-12222222222200-2-2-2-1-1-1-1-1-111111100000000000000
χ264444444111-2-4111111111-222-2-2-2-2-2-4-1-1-1-1-1-122222-2-2-2-2-2-200222111111-1-1-1-1-1-100000000000000
χ274444444-2-2-214-2-2-2-2-2-2-2-2-2111111114-2-2-2-2-2-211111000000000000000000000002202200-1-10-1-100
χ284444444-2-2-214-2-2-2-2-2-2-2-2-2111111114-2-2-2-2-2-21111100000000000000000000000-2-20-2-2001101100
χ294444444-2-2-21-4-2-2-2-2-2-2-2-2-21-1-111111-4222222-1-1-1-1-1000000000000000000000002-202-200-110-1100
χ304444444-2-2-21-4-2-2-2-2-2-2-2-2-21-1-111111-4222222-1-1-1-1-100000000000000000000000-220-22001-101-100
χ31444-2-2-2-21−1−3i32−1+3i32-241−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21-2111-211−1−3i32−1−3i32−1+3i32−1+3i32-2111122−1−i3−1−i3−1+i3−1+i3002−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000
χ32444-2-2-2-21−1−3i32−1+3i32-241−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21-2111-211−1−3i32−1−3i32−1+3i32−1+3i32-21111-2-21+i31+i31−i31−i300-21+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000
χ33444-2-2-2-21−1−3i32−1+3i32-2-41−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2221-21112-1-11+3i321+3i321−3i321−3i322-1-1-1-122−1−i3−1−i3−1+i3−1+i300-21+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3200000000000000
χ34444-2-2-2-21−1−3i32−1+3i32-2-41−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2221-21112-1-11+3i321+3i321−3i321−3i322-1-1-1-1-2-21+i31+i31−i31−i3002−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3200000000000000
χ35444-2-2-2-21−1+3i32−1−3i32-241−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21-2111-211−1+3i32−1+3i32−1−3i32−1−3i32-2111122−1+i3−1+i3−1−i3−1−i3002−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000
χ36444-2-2-2-21−1+3i32−1−3i32-241−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21-2111-211−1+3i32−1+3i32−1−3i32−1−3i32-21111-2-21−i31−i31+i31+i300-21−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000
χ37444-2-2-2-21−1+3i32−1−3i32-2-41−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2221-21112-1-11−3i321−3i321+3i321+3i322-1-1-1-122−1+i3−1+i3−1−i3−1−i300-21−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3200000000000000
χ38444-2-2-2-21−1+3i32−1−3i32-2-41−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2221-21112-1-11−3i321−3i321+3i321+3i322-1-1-1-1-2-21−i31−i31+i31+i3002−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3200000000000000
χ3944-44-4-44-2-2-210222222-2-2-21331-1-1-110000000-333-3-300000000000000000000000220-2-200-1-101100
χ4044-44-4-44-2-2-210222222-2-2-21331-1-1-110000000-333-3-300000000000000000000000-2-202200110-1-100
χ4144-44-4-44-2-2-210222222-2-2-21-3-31-1-1-1100000003-3-333000000000000000000000002-20-2200-1101-100
χ4244-44-4-44-2-2-210222222-2-2-21-3-31-1-1-1100000003-3-33300000000000000000000000-2202-2001-10-1100
χ4344-4-222-24-2-240-422-4224-2-2400-2-422-20000000000000000004-400000000000000000000-220000000
χ4444-4-222-24-2-240-422-4224-2-2400-2-422-2000000000000000000-44000000000000000000002-20000000
χ454-40400-4111-20333-3-3-3-1-1-1223−23-2000203−33−33−3023−23002-22-22-2000001-11-11-13−33−33−300000000000000
χ464-40400-4111-20333-3-3-3-1-1-1223−23-2000203−33−33−3023−2300-22-22-2200000-11-11-11−33−33−3300000000000000
χ474-40400-4111-20333-3-3-3-1-1-12−2323-200020−33−33−330−2323002-22-22-2000001-11-11-1−33−33−3300000000000000
χ484-40400-4111-20333-3-3-3-1-1-12−2323-200020−33−33−330−232300-22-22-2200000-11-11-113−33−33−300000000000000
χ494-40400-444440000000-4-4-4-4004000-40000000000002-22-22-200000-22-22-2200000000000000000000
χ504-40400-444440000000-4-4-4-4004000-4000000000000-22-22-22000002-22-22-200000000000000000000
χ514-40-2−2i32i321−1−3i32−1+3i32-203−3−i32−3+i32-33+i323−i32-11+3i321−3i32223−2310−i3i3-103−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ110−333i−3i2-2−1−i31+i3−1+i31−i3000001-1−1−i321+i32−1+i321−i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000
χ524-40-2−2i32i321−1−3i32−1+3i32-203−3−i32−3+i32-33+i323−i32-11+3i321−3i32223−2310−i3i3-103−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ110−333i−3i-221+i3−1−i31−i3−1+i300000-111+i32−1−i321−i32−1+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000
χ534-40-2−2i32i321−1−3i32−1+3i32-203−3−i32−3+i32-33+i323−i32-11+3i321−3i322−232310−i3i3-10−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1103−3−3i3i2-2−1−i31+i3−1+i31−i3000001-1−1−i321+i32−1+i321−i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000
χ544-40-2−2i32i321−1−3i32−1+3i32-203−3−i32−3+i32-33+i323−i32-11+3i321−3i322−232310−i3i3-10−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1103−3−3i3i-221+i3−1−i31−i3−1+i300000-111+i32−1−i321−i32−1+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000
χ554-40-2−2i32i324-2-2400−2i32i302i3−2i3-422-400-202i3−2i320000000000002-2−1−i31+i3−1+i31−i300000-221+i3−1−i31−i3−1+i300000000000000000000
χ564-40-2−2i32i324-2-2400−2i32i302i3−2i3-422-400-202i3−2i32000000000000-221+i3−1−i31−i3−1+i3000002-2−1−i31+i3−1+i31−i300000000000000000000
χ574-40-22i3−2i321−1+3i32−1−3i32-203−3+i32−3−i32-33−i323+i32-11−3i321+3i32223−2310i3−i3-103−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ110−33−3i3i2-2−1+i31−i3−1−i31+i3000001-1−1+i321−i32−1−i321+i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000000000
χ584-40-22i3−2i321−1+3i32−1−3i32-203−3+i32−3−i32-33−i323+i32-11−3i321+3i32223−2310i3−i3-103−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ110−33−3i3i-221−i3−1+i31+i3−1−i300000-111−i32−1+i321+i32−1−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000000000
χ594-40-22i3−2i321−1+3i32−1−3i32-203−3+i32−3−i32-33−i323+i32-11−3i321+3i322−232310i3−i3-10−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1103−33i−3i2-2−1+i31−i3−1−i31+i3000001-1−1+i321−i32−1−i321+i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000000000
χ604-40-22i3−2i321−1+3i32−1−3i32-203−3+i32−3−i32-33−i323+i32-11−3i321+3i322−232310i3−i3-10−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1103−33i−3i-221−i3−1+i31+i3−1−i300000-111−i32−1+i321+i32−1−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000000000
χ614-40-22i3−2i324-2-24002i3−2i30−2i32i3-422-400-20−2i32i320000000000002-2−1+i31−i3−1−i31+i300000-221−i3−1+i31+i3−1−i300000000000000000000
χ624-40-22i3−2i324-2-24002i3−2i30−2i32i3-422-400-20−2i32i32000000000000-221−i3−1+i31+i3−1−i3000002-2−1+i31−i3−1−i31+i300000000000000000000
χ63888-4-4-4-4-42228-422-422-422222-12-1-1-1-4-4-422222-1-1-1-10000000000000000000000000000000000000
χ64888-4-4-4-4-4222-8-422-422-4222-2-2-12-1-1-1444-2-2-2-2-211110000000000000000000000000000000000000
χ6588-88-8-88222-40-2-2-2-2-2-2222-400-4444-40000000000000000000000000000000000000000000000000
χ6688-8-444-42−1−3i3−1+3i3-40-21+3i31−3i3-21+3i31−3i32−1−3i3−1+3i3-40024-2-220000000000000000000000000000000000000000000000000
χ6788-8-444-42−1+3i3−1−3i3-40-21−3i31+3i3-21−3i31+3i32−1+3i3−1−3i3-40024-2-220000000000000000000000000000000000000000000000000
χ6888-8-444-4-422204-2-24-2-2-422266-1-211-10000000-6-3-3330000000000000000000000000000000000000
χ6988-8-444-4-422204-2-24-2-2-4222-6-6-1-211-10000000633-3-30000000000000000000000000000000000000
χ708-80800-8222-40-6-6-6666-2-2-2400-400040000000000000000000000000000000000000000000000000
χ718-80800-8-4-4-420000000444-223−232000-20−2323−2323−2323023−23000000000000000000000000000000000000000
χ728-80800-8-4-4-420000000444-2−23232000-2023−2323−2323−230−2323000000000000000000000000000000000000000
χ738-80-4−4i34i342−1+3i3−1−3i3-40-63−i33+i36−3+i3−3−i3-21−3i31+3i340020−2i32i3-20000000000000000000000000000000000000000000000000
χ748-80-4−4i34i34-4222002i3−2i30−2i32i34-2-2-223−23-10i3−i310−23232ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ110−333i−3i0000000000000000000000000000000000000
χ758-80-4−4i34i34-4222002i3−2i30−2i32i34-2-2-2−2323-10i3−i31023−23−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ1103−3−3i3i0000000000000000000000000000000000000
χ768-80-44i3−4i342−1−3i3−1+3i3-40-63+i33−i36−3−i3−3+i3-21+3i31−3i3400202i3−2i3-20000000000000000000000000000000000000000000000000
χ778-80-44i3−4i34-422200−2i32i302i3−2i34-2-2-223−23-10−i3i310−2323−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ110−33−3i3i0000000000000000000000000000000000000
χ788-80-44i3−4i34-422200−2i32i302i3−2i34-2-2-2−2323-10−i3i31023−234ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ1103−33i−3i0000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.