Finite Group Databasebeta

← Group #13165645

Character table — Group #13165645

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order122236663366666633666666444441212121212121212121212121212121212121212881212242424244412121212288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-11-111-1-11-1-1
χ3111111111111111111111111111-11-1-111-1-1111111-1-1-1-11111-1-111-1-1-1-1-11-1-1111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111
χ5111111111111111111111111-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-111
χ7111111111111111111111111-111-11-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-111-1-1-111
χ8111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1
χ92222222222222222222222222-2-2000000000022220000000000-2-20000000000-200
χ10222222222222222222222222-2-2-20000000000-2-2-2-20000000000-2-20000000000200
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-102222-1-1-1-122220000-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-10222-2-1-11122-2-20000-1-1-1-11111-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2211-1-1-2-22200001111-1-1-1-1-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2-21111-2-2-2-200001111111122-1-1-1-1-1-1000000000
χ152-2-222-2-2222-2-2-2-2222222-2-2-2-202-20000000000000000000000002-2000000000002i−2i
χ162-2-222-2-2222-2-2-2-2222222-2-2-2-202-20000000000000000000000002-200000000000−2i2i
χ172-2-222-2-2222-2-2-2-2222222-2-2-2-20-2200000000000000000000002-2-2222-2-2000000000
χ182-2-222-2-2222-2-2-2-2222222-2-2-2-20-220000000000000000000000-22-22-2-222000000000
χ192-2-22-111-122-2-2-2-222-1-1-1-111110-22003−33−30000000033−3−333−3−32-21-1-1-111000000000
χ202-2-22-111-122-2-2-2-222-1-1-1-111110-22003−3−330000000033−3−3−3−333-221-111-1-1000000000
χ212-2-22-111-122-2-2-2-222-1-1-1-111110-2200−333−300000000−3−33333−3−3-221-111-1-1000000000
χ222-2-22-111-122-2-2-2-222-1-1-1-111110-2200−33−3300000000−3−333−3−3332-21-1-1-111000000000
χ23444444441-21-21-21-21-21-21-21-240002002200-1-111-2-20000-1-1-1-1000000000200-1-1000
χ24444444441-21-21-21-21-21-21-21-24000-200-2-2001111-2-200001111000000000-20011000
χ25444444441-21-21-21-21-21-21-21-2-40002002200-1-1-1-1220000-1-1-1-1000000000-20011000
χ26444444441-21-21-21-21-21-21-21-2-4000-200-2-20011-1-12200001111000000000200-1-1000
χ2744444444-21-21-21-21-21-21-21-21400202200-1-100-2-211-1-1-1-100000000000020-1-100000
χ2844444444-21-21-21-21-21-21-21-21400-20-2-2001100-2-2111111000000000000-201100000
χ2944444444-21-21-21-21-21-21-21-21-400202200-1-10022-1-1-1-1-1-1000000000000-201100000
χ3044444444-21-21-21-21-21-21-21-21-400-20-2-200110022-1-1111100000000000020-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-444-4-41-2-1-212-121-2-12-1-21200000000000−i3i33i−3i000000−i3i3−i3i30000000000003−3000
χ3344-4-444-4-41-2-1-212-121-2-12-1-21200000000000−i3i3−3i3i000000−i3i3−i3i3000000000000−33000
χ3444-4-444-4-41-2-1-212-121-2-12-1-21200000000000i3−i33i−3i000000i3−i3i3−i3000000000000−33000
χ3544-4-444-4-41-2-1-212-121-2-12-1-21200000000000i3−i3−3i3i000000i3−i3i3−i30000000000003−3000
χ3644-4-444-4-444-444-4-4-444-4-4-444-4000000000000000000000000000000000000000000
χ3744-4-4-2-22244-444-4-4-4-2-2222-2-22000000000000000000000000000006−66−6000000000
χ3844-4-4-2-22244-444-4-4-4-2-2222-2-2200000000000000000000000000000−66−66000000000
χ394-44-44-44-4444-4-44-4-444-4-44-4-44000000000000000000000000000000000000000000
χ404-44-44-44-4-21-2-1212-1-212-1-2-121000000000−i3i300003i−3i−i3i3−i3i3000000000000003−300000
χ414-44-44-44-4-21-2-1212-1-212-1-2-121000000000−i3i30000−3i3i−i3i3−i3i300000000000000−3300000
χ424-44-44-44-4-21-2-1212-1-212-1-2-121000000000i3−i300003i−3ii3−i3i3−i300000000000000−3300000
χ434-44-44-44-4-21-2-1212-1-212-1-2-121000000000i3−i30000−3i3ii3−i3i3−i3000000000000003−300000
χ444-44-4-22-22444-4-44-4-4-2-222-222-2000000000000000000000000000006−6−66000000000
χ454-44-4-22-22444-4-44-4-4-2-222-222-200000000000000000000000000000−666−6000000000
χ464-4-44-222-244-4-4-4-444-2-2-2-2222204-4000000000000000000000000-220000000000000
χ478888-4-4-4-42-42-42-42-4-12-12-12-120000400-2-200-2-200000000111100000000000000000
χ488888-4-4-4-42-42-42-42-4-12-12-12-120000-40022002200000000-1-1-1-100000000000000000
χ498888-4-4-4-4-42-42-42-422-12-12-12-100040-2-200-2-20000001111000000000000000000000
χ508888-4-4-4-4-42-42-42-422-12-12-12-1000-40220022000000-1-1-1-1000000000000000000000
χ5188-8-888-8-8-4242-4-24-2-424-242-4-2000000000000000000000000000000000000000000
χ5288-8-8-4-4442-4-2-424-24-121-212-1-200000000000−2i32i300000000i3−i3i3−i300000000000000000
χ5388-8-8-4-4442-4-2-424-24-121-212-1-2000000000002i3−2i300000000−i3i3−i3i300000000000000000
χ5488-8-8-4-444-4242-4-24-22-1-21-2-121000000000000000003i−3i−3i3i000000000000000000000
χ5588-8-8-4-444-4242-4-24-22-1-21-2-12100000000000000000−3i3i3i−3i000000000000000000000
χ568-88-88-88-82-424-2-4-242-4-2424-2-4000000000000000000000000000000000000000000
χ578-88-8-44-442-424-2-4-24-121-2-1-2120000000000000000000003i−3i−3i3i00000000000000000
χ588-88-8-44-442-424-2-4-24-121-2-1-212000000000000000000000−3i3i3i−3i00000000000000000
χ598-88-8-44-44-42-4-2424-22-1-2121-2-1000000000−2i32i3000000i3−i3i3−i3000000000000000000000
χ608-88-8-44-44-42-4-2424-22-1-2121-2-10000000002i3−2i3000000−i3i3−i3i3000000000000000000000
χ618-8-888-8-882-4-24-242-42-42-4-24-24000000000000000000000000000000000000000000
χ628-8-888-8-88-424-24-2-42-42-424-24-2000000000000000000000000000000000000000000
χ638-8-88-444-42-4-24-242-4-12-121-21-2000000023−23000000000000−3−33300000000000000000
χ648-8-88-444-42-4-24-242-4-12-121-21-20000000−232300000000000033−3−300000000000000000
χ658-8-88-444-4-424-24-2-422-12-1-21-210000023−230000000000−3−333000000000000000000000
χ668-8-88-444-4-424-24-2-422-12-1-21-2100000−2323000000000033−3−3000000000000000000000

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