Finite Group Databasebeta

← Group #13167085

Character table — Group #13167085

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
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1111111-111-1-11-111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1111111-111-1-1-11-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111111-1-1-1-1-1-1-111-1-11-111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111111-1-1-1-1-1-1-111-1-1-11-1-11111-1-1
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
χ112222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-12-1-1-1-10000000000
χ122222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-21111-2-21111-2-211112-1-1-1-10000000000
χ132222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-211110000000000
χ142222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-211110000000000
χ152222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111222-2-1-111-2-2111122-1-1-1-1-2-1-1110000000000
χ162222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-21111111122-2211-1-122-1-1-1-1-2-21111-2-1-1110000000000
χ172222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111-2-200−i3i3i3−i300i3i3−i3−i300−i3−i3i3i3211-1-10000000000
χ182222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111-2-200i3−i3−i3i300−i3−i3i3i300i3i3−i3−i3211-1-10000000000
χ192-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-20000000000002-200000000000000000002-200000000002-2
χ202-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-20000000000002-200000000000000000002-20000000000-22
χ212-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-220000000000000000000-22000000002-200
χ222-22-22-22-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-220000000000000000000-2200000000-2200
χ23444444441-21141-211-2111111-244-2-2-2-2-2-2111111-2-2-2-200222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ24444444441-21141-211-2111111-244-2-2-2-2-2-2111111-2-2-2-200-2-2-2-2-2-2111111111111000000000000000
χ25444444441-211-41-211-2111111-2-4-4-2-2-2-222-1-1-1-1-1-12222002-222-2-2111111-1-1-1-1-1-1000000000000000
χ26444444441-211-41-211-2111111-2-4-4-2-2-2-222-1-1-1-1-1-1222200-22-2-222-1-1-1-1-1-1111111000000000000000
χ2744444444-21-2-24-21-2-21-2-2-2-2-2-2144111111-2-2-2-2-2-21111000000000000000000000000022-1-1-1-10000
χ2844444444-21-2-24-21-2-21-2-2-2-2-2-2144111111-2-2-2-2-2-211110000000000000000000000000-2-211110000
χ2944444444-21-2-2-4-21-2-21-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-100000000000000000000000002-2-1-1110000
χ3044444444-21-2-2-4-21-2-21-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-10000000000000000000000000-2211-1-10000
χ314444-2-2-2-21-2−1−3i32−1+3i3241-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-211−1−3i32−1−3i32−1+3i32−1+3i3211110022−1−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+3i3241-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-211−1−3i32−1−3i32−1+3i32−1+3i32111100-2-21+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+3i32-41-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-1-11+3i321+3i321−3i321−3i32-1-1-1-1002-2−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000
χ344444-2-2-2-21-2−1−3i32−1+3i32-41-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-1-11+3i321+3i321−3i321−3i32-1-1-1-100-221+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ354444-2-2-2-21-2−1+3i32−1−3i3241-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-211−1+3i32−1+3i32−1−3i32−1−3i3211110022−1+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+3i32−1−3i3241-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-211−1+3i32−1+3i32−1−3i32−1−3i32111100-2-21−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+3i32−1−3i32-41-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-1-11−3i321−3i321+3i321+3i32-1-1-1-1002-2−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000
χ384444-2-2-2-21-2−1+3i32−1−3i32-41-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-1-11−3i321−3i321+3i321+3i32-1-1-1-100-221−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ3944-4-444-4-444440-4-4-4-44-4-4-4444-4004-4-4400000000000000000000000000000000000000000000000
χ4044-4-444-4-4-21-2-202-1221222-2-2-2-1001-1-113-300000033-3-30000000000000000000000000003−33−30000
χ4144-4-444-4-4-21-2-202-1221222-2-2-2-1001-1-113-300000033-3-3000000000000000000000000000−33−330000
χ4244-4-444-4-4-21-2-202-1221222-2-2-2-1001-1-11-33000000-3-3330000000000000000000000000003−3−330000
χ4344-4-444-4-4-21-2-202-1221222-2-2-2-1001-1-11-33000000-3-333000000000000000000000000000−333−30000
χ4444-4-4-2-22244-2-20-4-4224-4224-2-2-400-222-20000000000000000000000000000000000023−230000000000
χ4544-4-4-2-22244-2-20-4-4224-4224-2-2-400-222-200000000000000000000000000000000000−23230000000000
χ464-44-4-22-2244-2-2044-2-2-4-422-422-400-2-2220000000000004-40000000000000000000-22000000000000
χ474-44-4-22-2244-2-2044-2-2-4-422-422-400-2-222000000000000-4400000000000000000002-2000000000000
χ484-4-444-4-441-2110-12-1-12111-1-1-1-200-22-22003i−3i3i−3i3i−3i000000000000−i3i3−i3i3−i3i33−33−33−3000000000000000
χ494-4-444-4-441-2110-12-1-12111-1-1-1-200-22-22003i−3i3i−3i3i−3i000000000000i3−i3i3−i3i3−i3−33−33−33000000000000000
χ504-4-444-4-441-2110-12-1-12111-1-1-1-200-22-2200−3i3i−3i3i−3i3i000000000000−i3i3−i3i3−i3i3−33−33−33000000000000000
χ514-4-444-4-441-2110-12-1-12111-1-1-1-200-22-2200−3i3i−3i3i−3i3i000000000000i3−i3i3−i3i3−i33−33−33−3000000000000000
χ524-4-444-4-4444440-4-4-4-4-4444-4-4-44004-44-400000000000000000000000000000000000000000000000
χ534-4-44-222-21-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-223−231-11-1003i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ113−33−300000000−i3i3−3+i323−i323+i32−3−i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000
χ544-4-44-222-21-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-223−231-11-1003i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ113−33−300000000i3−i33−i32−3+i32−3−i323+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000
χ554-4-44-222-21-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-2−23231-11-100−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ11−33−3300000000−i3i3−3+i323−i323+i32−3−i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000
χ564-4-44-222-21-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-2−23231-11-100−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ11−33−3300000000i3−i33−i32−3+i32−3−i323+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000
χ574-4-44-222-21-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-223−231-11-100−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ113−33−300000000−i3i33+i32−3−i32−3+i323−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000
χ584-4-44-222-21-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-223−231-11-100−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ113−33−300000000i3−i3−3−i323+i323−i32−3+i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000
χ594-4-44-222-21-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-2−23231-11-1003i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−33−3300000000−i3i33+i32−3−i32−3+i323−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000
χ604-4-44-222-21-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-2−23231-11-1003i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−33−3300000000i3−i3−3−i323+i323−i32−3+i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000
χ614-4-44-222-244-2-20-4-422-44-2-2-422423−23-22-22000023−23−2323−2323−232300000000000000000000000000000000000
χ624-4-44-222-244-2-20-4-422-44-2-2-4224−2323-22-220000−232323−2323−2323−2300000000000000000000000000000000000
χ638888-4-4-4-4-42228-42222-422-4222-4-4-1-1-1-122-4-42222-1-1-1-100000000000000000000000000000000000
χ648888-4-4-4-4-4222-8-42222-422-422244-1-1-1-1-2-244-2-2-2-2111100000000000000000000000000000000000
χ6588-8-888-8-82-4220-24-2-2-4-2-2-2222400-444-400000000000000000000000000000000000000000000000
χ6688-8-8-4-4442-4−1−3i3−1+3i30-241+3i31−3i3-4-21+3i31−3i32−1−3i3−1+3i34002-2-2200000000000000000000000000000000000000000000000
χ6788-8-8-4-4442-4−1+3i3−1−3i30-241−3i31+3i3-4-21−3i31+3i32−1+3i3−1−3i34002-2-2200000000000000000000000000000000000000000000000
χ6888-8-8-4-444-422204-2-2-224-2-2-422-200-111-16-6000000-3-33300000000000000000000000000000000000
χ6988-8-8-4-444-422204-2-2-224-2-2-422-200-111-1-6600000033-3-300000000000000000000000000000000000
χ708-88-88-88-82-42202-4224-2-2-2-2-2-2400-4-44400000000000000000000000000000000000000000000000
χ718-88-88-88-8-42-4-40-42-4-4-2444444-20022-2-200000000000000000000000000000000000000000000000
χ728-88-8-44-442-4−1−3i3−1+3i302-4−1−3i3−1+3i34-21+3i31−3i3-21+3i31−3i340022-2-200000000000000000000000000000000000000000000000
χ738-88-8-44-442-4−1+3i3−1−3i302-4−1+3i3−1−3i34-21−3i31+3i3-21−3i31+3i340022-2-200000000000000000000000000000000000000000000000
χ748-88-8-44-44-42220-4222-24-2-24-2-2-200-1-1110000000033−33−333300000000000000000000000000000000000
χ758-88-8-44-44-42220-4222-24-2-24-2-2-200-1-11100000000−333333−3300000000000000000000000000000000000
χ768-8-888-8-88-42-4-404-244-2-4-4-44442002-22-200000000000000000000000000000000000000000000000
χ778-8-88-444-4-422204-2-2-2-2-4224-2-2243−43-11-110000−232323−23−33−3300000000000000000000000000000000000
χ788-8-88-444-4-422204-2-2-2-2-4224-2-22−4343-11-11000023−23−23233−33−300000000000000000000000000000000000

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