Finite Group Databasebeta

← Group #13165628

Character table — Group #13165628

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order1222366633666666336666664442466666666121212121212121212121212881212242424244412121212288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-11-1-1
χ3111111111111111111111111111-11-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-11-1-1111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111
χ5111111111111111111111111-111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-111
χ7111111111111111111111111-111-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11-111-1-1-111
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
χ92222222222222222222222222-2-2000000000000222200000000-2-20000000000-200
χ10222222222222222222222222-2-2-2000000000000-2-2-2-200000000-2-20000000000200
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-102222-1-122-1-1-1-1-1-1000022-1-1-1-122-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-10222-2-1-122-1-1-1-1110000-2-21111-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2211-2-21111-1-1000022-1-1-1-1-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2-211-2-21111110000-2-2111122-1-1-1-1-1-1000000000
χ152-22-22-2-2222-2-222-2-222-2-22-2-2202-20000000000000000000000002-2000000000002i−2i
χ162-22-22-2-2222-2-222-2-222-2-22-2-2202-20000000000000000000000002-200000000000−2i2i
χ172-22-22-2-2222-2-222-2-222-2-22-2-220-2200000000000000000000002-2-2222-2-2000000000
χ182-22-22-2-2222-2-222-2-222-2-22-2-220-220000000000000000000000-22-22-2-222000000000
χ192-22-2-111-122-2-222-2-2-1-111-111-10-2200−i3i300−i3−i3i3i3−i3i3000000−i3−i3i3i32-21-1-1-111000000000
χ202-22-2-111-122-2-222-2-2-1-111-111-10-2200−i3i300−i3−i3i3i3i3−i3000000i3i3−i3−i3-221-111-1-1000000000
χ212-22-2-111-122-2-222-2-2-1-111-111-10-2200i3−i300i3i3−i3−i3−i3i3000000−i3−i3i3i3-221-111-1-1000000000
χ222-22-2-111-122-2-222-2-2-1-111-111-10-2200i3−i300i3i3−i3−i3i3−i3000000i3i3−i3−i32-21-1-1-111000000000
χ23444444441-21-2-211-21-211-2-2-21400020000000022-2-211-1-1-1-1-1-1000000000200-1-1000
χ24444444441-21-2-211-21-211-2-2-214000-200000000-2-2-2-211111111000000000-20011000
χ25444444441-21-2-211-21-211-2-2-21-40002000000002222-1-1-1-1-1-1-1-1000000000-20011000
χ26444444441-21-2-211-21-211-2-2-21-4000-200000000-2-222-1-1111111000000000200-1-1000
χ2744444444-21-211-2-21-21-2-2111-24002022-1-1-1-1-1-10011-2-20000000000000020-1-100000
χ2844444444-21-211-2-21-21-2-2111-2400-20-2-21111110011-2-200000000000000-201100000
χ2944444444-21-211-2-21-21-2-2111-2-4002022-1-1-1-1-1-100-1-12200000000000000-201100000
χ3044444444-21-211-2-21-21-2-2111-2-400-20-2-211111100-1-1220000000000000020-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-444-4-44444-4-4-4-4444-4-44-4-4000000000000000000000000000000000000000000
χ3344-4-444-4-4-21-21-122-1-21-22-11-120000000−i3i3−i3i3−i3i3003i−3i0000000000000000003−300000
χ3444-4-444-4-4-21-21-122-1-21-22-11-120000000−i3i3−i3i3−i3i300−3i3i000000000000000000−3300000
χ3544-4-444-4-4-21-21-122-1-21-22-11-120000000i3−i3i3−i3i3−i3003i−3i000000000000000000−3300000
χ3644-4-444-4-4-21-21-122-1-21-22-11-120000000i3−i3i3−i3i3−i300−3i3i0000000000000000003−300000
χ3744-4-4-2-2224444-4-4-4-4-2-2-222-222000000000000000000000000000006−66−6000000000
χ3844-4-4-2-2224444-4-4-4-4-2-2-222-22200000000000000000000000000000−66−66000000000
χ394-44-4-222-244-4-444-4-4-2-222-222-204-4000000000000000000000000-220000000000000
χ404-4-444-44-41-2-122-11-21-2-1122-2-1000000000000000003i−3i3−33−33−3000000000000−i3i3000
χ414-4-444-44-41-2-122-11-21-2-1122-2-1000000000000000003i−3i−33−33−33000000000000i3−i3000
χ424-4-444-44-41-2-122-11-21-2-1122-2-100000000000000000−3i3i3−33−33−3000000000000i3−i3000
χ434-4-444-44-41-2-122-11-21-2-1122-2-100000000000000000−3i3i−33−33−33000000000000−i3i3000
χ444-4-444-44-444-4-4-4-44444-44-4-44-4000000000000000000000000000000000000000000
χ454-4-44-22-2244-4-4-4-444-2-22-222-22000000000000000000000000000006−6−66000000000
χ464-4-44-22-2244-4-4-4-444-2-22-222-2200000000000000000000000000000−666−6000000000
χ478888-4-4-4-42-42-4-422-4-12-1-1222-10000400000000-2-20000-2-2111100000000000000000
χ488888-4-4-4-42-42-4-422-4-12-1-1222-10000-40000000022000022-1-1-1-100000000000000000
χ498888-4-4-4-4-42-422-4-422-122-1-1-1200040-2-2-2-2111100000000000000000000000000000
χ508888-4-4-4-4-42-422-4-422-122-1-1-12000-402222-1-1-1-100000000000000000000000000000
χ5188-8-888-8-82-42-44-2-242-42-24-44-2000000000000000000000000000000000000000000
χ5288-8-8-4-4442-42-44-2-24-12-11-22-210000000000000000000003i−3i−3i3i00000000000000000
χ5388-8-8-4-4442-42-44-2-24-12-11-22-21000000000000000000000−3i3i3i−3i00000000000000000
χ5488-8-8-4-444-42-42-244-22-12-21-11-20000000−2i32i3i3−i3i3−i300000000000000000000000000000
χ5588-8-8-4-444-42-42-244-22-12-21-11-200000002i3−2i3−i3i3−i3i300000000000000000000000000000
χ568-88-88-8-882-4-24-42-242-4-2-2-4442000000000000000000000000000000000000000000
χ578-88-88-8-88-424-22-44-2-42442-2-2-4000000000000000000000000000000000000000000
χ588-88-8-444-42-4-24-42-24-12112-2-2-10000000000000−2i32i3000000i3i3−i3−i300000000000000000
χ598-88-8-444-42-4-24-42-24-12112-2-2-100000000000002i3−2i3000000−i3−i3i3i300000000000000000
χ608-88-8-444-4-424-22-44-22-1-2-2-111200000−2i32i300i3i3−i3−i300000000000000000000000000000
χ618-88-8-444-4-424-22-44-22-1-2-2-1112000002i3−2i300−i3−i3i3i300000000000000000000000000000
χ628-8-888-88-8-424-2-24-42-424-4-2-224000000000000000000000000000000000000000000
χ638-8-88-44-442-4-244-22-4-121-1-2-221000000000000000000023−23−33−3300000000000000000
χ648-8-88-44-442-4-244-22-4-121-1-2-2210000000000000000000−23233−33−300000000000000000
χ658-8-88-44-44-424-2-24-422-1-2211-1-20000000003-3-3300000000000000000000000000000
χ668-8-88-44-44-424-2-24-422-1-2211-1-2000000000-333-300000000000000000000000000000

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