Finite Group Databasebeta

← Group #13167075

Character table — Group #13167075

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444444444444444888888888888888818182424242424242424242424242424242424243636363636727272727272108108108108
order12223666333346666666666661212366612121212121212121212121244441212121212121212121212121212121241212121244121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-111-1-11-111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-111-1-1-11-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1111111-111-1-11-111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1111111-111-1-1-11-1-11111-1-1
χ92222222222222222222222222222222222222222222-2-2000000000000000000-2-2-2-2-20000000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000002-2-2220000000000
χ112222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-12-1-1-1-10000000000
χ122222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-122-2-21111-2-21111-2-211112-1-1-1-10000000000
χ132222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-211110000000000
χ142222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-211110000000000
χ152222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-21111222-211-1-122-1-1-1-1-2-21111-2-1-1110000000000
χ162222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-2111122-22-1-111-2-2111122-1-1-1-1-2-1-1110000000000
χ172222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-21111-2-200−i3i3i3−i300i3i3−i3−i300−i3−i3i3i3211-1-10000000000
χ182222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-21111-2-200i3−i3−i3i300−i3−i3i3i300i3i3−i3−i3211-1-10000000000
χ1922-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-20000000000002-200000000000000000002-200000000002-2
χ2022-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-20000000000002-200000000000000000002-20000000000-22
χ2122-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-2000000000000-220000000000000000000-22000000002-200
χ2222-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-2000000000000-220000000000000000000-2200000000-2200
χ23444444441-21141-2-211111111-244-2-2-2-2111111-2-2-2-2-2-200222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ24444444441-21141-2-211111111-244-2-2-2-2111111-2-2-2-2-2-200-2-2-2-2-2-2111111111111000000000000000
χ25444444441-211-41-2-211111111-2-4-4-2-2-2-2-1-1-1-1-1-1222222002-2-2-222-1-1-1-1-1-1111111000000000000000
χ26444444441-211-41-2-211111111-2-4-4-2-2-2-2-1-1-1-1-1-122222200-2222-2-2111111-1-1-1-1-1-1000000000000000
χ2744444444-21-2-24-211-2-2-2-2-2-2-2-21441111-2-2-2-2-2-2111111000000000000000000000000022-1-1-1-10000
χ2844444444-21-2-24-211-2-2-2-2-2-2-2-21441111-2-2-2-2-2-21111110000000000000000000000000-2-211110000
χ2944444444-21-2-2-4-211-2-2-2-2-2-2-2-21-4-41111222222-1-1-1-1-1-100000000000000000000000002-2-1-1110000
χ3044444444-21-2-2-4-211-2-2-2-2-2-2-2-21-4-41111222222-1-1-1-1-1-10000000000000000000000000-2211-1-10000
χ314444-2-2-2-21-2−1−3i32−1+3i3241-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-211110022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000
χ324444-2-2-2-21-2−1−3i32−1+3i3241-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111100-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ334444-2-2-2-21-2−1−3i32−1+3i32-41-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-1002-21+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ344444-2-2-2-21-2−1−3i32−1+3i32-41-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-100-22−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000
χ354444-2-2-2-21-2−1+3i32−1−3i3241-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-211110022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000
χ364444-2-2-2-21-2−1+3i32−1−3i3241-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111100-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ374444-2-2-2-21-2−1+3i32−1−3i32-41-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2221111-1-11−3i321−3i321+3i321+3i3222-1-1-1-1002-21−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ384444-2-2-2-21-2−1+3i32−1−3i32-41-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2221111-1-11−3i321−3i321+3i321+3i3222-1-1-1-100-22−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000
χ3944-4-4-22-2244-2-2044-4-2-2-422-422-400-2-2220000000000004-40000000000000000000-22000000000000
χ4044-4-4-22-2244-2-2044-4-2-2-422-422-400-2-222000000000000-4400000000000000000002-2000000000000
χ414-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-223i−3i3i−3i3i−3i00000000000000−i3i3−i3i3−i3i33−33−33−3000000000000000
χ424-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-223i−3i3i−3i3i−3i00000000000000i3−i3i3−i3i3−i3−33−33−33000000000000000
χ434-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-22−3i3i−3i3i−3i3i00000000000000−i3i3−i3i3−i3i3−33−33−33000000000000000
χ444-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-22−3i3i−3i3i−3i3i00000000000000i3−i3i3−i3i3−i33−33−33−3000000000000000
χ454-44-44-4-4444440-4-44-4-4444-4-4-4-4004-44-400000000000000000000000000000000000000000000000
χ464-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32223−231-11-13i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ110033−3−300000000−i3i3−3+i323−i323+i32−3−i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000
χ474-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32223−231-11-13i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ110033−3−300000000i3−i33−i32−3+i32−3−i323+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000
χ484-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322−23231-11-1−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ1100−3−33300000000−i3i3−3+i323−i323+i32−3−i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000
χ494-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322−23231-11-1−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ1100−3−33300000000i3−i33−i32−3+i32−3−i323+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000
χ504-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32223−231-11-1−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ110033−3−300000000−i3i33+i32−3−i32−3+i323−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000
χ514-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32223−231-11-1−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ110033−3−300000000i3−i3−3−i323+i323−i32−3+i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000
χ524-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322−23231-11-13i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ1100−3−33300000000−i3i33+i32−3−i32−3+i323−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000
χ534-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322−23231-11-13i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ1100−3−33300000000i3−i3−3−i323+i323−i32−3+i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000
χ544-44-4-222-244-2-20-4-44224-2-2-422-423−23-22-220023−23−232300−23−23232300000000000000000000000000000000000
χ554-44-4-222-244-2-20-4-44224-2-2-422-4−2323-22-2200−232323−23002323−23−2300000000000000000000000000000000000
χ564-4-4444-4-444440-4-4-4-4-4-4-4-44444004-4-4400000000000000000000000000000000000000000000000
χ574-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-110000003-33-33-3000000000000000000000000000−i3i3−i3i30000
χ584-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-110000003-33-33-3000000000000000000000000000i3−i3i3−i30000
χ594-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-11000000-33-33-33000000000000000000000000000−i3i3i3−i30000
χ604-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-11000000-33-33-33000000000000000000000000000i3−i3−i3i30000
χ614-4-44-2-22244-2-20-4-4-422-4224-2-2400-222-20000000000000000000000000000000000023−230000000000
χ624-4-44-2-22244-2-20-4-4-422-4224-2-2400-222-200000000000000000000000000000000000−23230000000000
χ638888-4-4-4-4-42228-42222-422-4222-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000
χ648888-4-4-4-4-4222-8-42222-422-422244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000
χ6588-8-88-88-82-42202-4422-2-2-2-2-2-2400-4-44400000000000000000000000000000000000000000000000
χ6688-8-88-88-8-42-4-40-42-2-4-4444444-20022-2-200000000000000000000000000000000000000000000000
χ6788-8-8-44-442-4−1−3i3−1+3i302-44−1−3i3−1+3i3-21+3i31−3i3-21+3i31−3i340022-2-200000000000000000000000000000000000000000000000
χ6888-8-8-44-442-4−1+3i3−1−3i302-44−1+3i3−1−3i3-21−3i31+3i3-21−3i31+3i340022-2-200000000000000000000000000000000000000000000000
χ6988-8-8-44-44-42220-42-2224-2-24-2-2-200-1-1110000000033−33−333300000000000000000000000000000000000
χ7088-8-8-44-44-42220-42-2224-2-24-2-2-200-1-11100000000−333333−3300000000000000000000000000000000000
χ718-88-88-8-88-42-4-404-2244-4-4-4444-2002-22-200000000000000000000000000000000000000000000000
χ728-88-8-444-4-422204-22-2-2-4224-2-2-243−43-11-1100−232323−2300−3−33300000000000000000000000000000000000
χ738-88-8-444-4-422204-22-2-2-4224-2-2-2−4343-11-110023−23−23230033−3−300000000000000000000000000000000000
χ748-8-8888-8-82-4220-244-2-2-2-2-2222-400-444-400000000000000000000000000000000000000000000000
χ758-8-88-4-4442-4−1−3i3−1+3i30-2441+3i31−3i3-21+3i31−3i32−1−3i3−1+3i3-4002-2-2200000000000000000000000000000000000000000000000
χ768-8-88-4-4442-4−1+3i3−1−3i30-2441−3i31+3i3-21−3i31+3i32−1+3i3−1−3i3-4002-2-2200000000000000000000000000000000000000000000000
χ778-8-88-4-444-422204-2-2-2-24-2-2-422200-111-10000006-6-33-3300000000000000000000000000000000000
χ788-8-88-4-444-422204-2-2-2-24-2-2-422200-111-1000000-663-33-300000000000000000000000000000000000

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