Finite Group Databasebeta

← Group #13165726

Character table — Group #13165726

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order122236663366666633666666444441212121212121212121212121212121212121212881212242424244412121212488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-111-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-11-1-1
χ3111111111111111111111111111-11-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-1-11-1-1111-1-1
χ4111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111
χ5111111111111111111111111-111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1111-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-111
χ7111111111111111111111111-111-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-11-111-1-1-111
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
χ92222222222222222222222222-2-2000000220022000000000000-2-20000000000-200
χ10222222222222222222222222-2-2-2000000-2-200-2-2000000000000-2-20000000000200
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-102222-1-1-1-100220022-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-10222-2-1-111002200-2-2-1-1-1-11111-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2211-1-100-2-200221111-1-1-1-1-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2-2111100-2-200-2-21111111122-1-1-1-1-1-1000000000
χ152-22-22-2-22222-2-2-22-2222-2-2-22-202-2000000000000000000000000-22000000000002i−2i
χ162-22-22-2-22222-2-2-22-2222-2-2-22-202-2000000000000000000000000-2200000000000−2i2i
χ172-22-22-2-22222-2-2-22-2222-2-2-22-20-2200000000000000000000002i−2i2-22i2i−2i−2i000000000
χ182-22-22-2-22222-2-2-22-2222-2-2-22-20-220000000000000000000000−2i2i2-2−2i−2i2i2i000000000
χ192-22-2-111-1222-2-2-22-2-1-1-1111-110-22003−3−i3i30000000033−3−3−i3−i3i3i32i−2i-11−i−iii000000000
χ202-22-2-111-1222-2-2-22-2-1-1-1111-110-22003−3i3−i30000000033−3−3i3i3−i3−i3−2i2i-11ii−i−i000000000
χ212-22-2-111-1222-2-2-22-2-1-1-1111-110-2200−33−i3i300000000−3−333−i3−i3i3i3−2i2i-11ii−i−i000000000
χ222-22-2-111-1222-2-2-22-2-1-1-1111-110-2200−33i3−i300000000−3−333i3i3−i3−i32i−2i-11−i−iii000000000
χ23444444441-21-21-2-211-211-2-2-21400202200-2-2-1-11100-1-1-1-100000000000020-1-100000
χ24444444441-21-21-2-211-211-2-2-21400-20-2-200-2-21111001111000000000000-201100000
χ25444444441-21-21-2-211-211-2-2-21-40020220022-1-1-1-100-1-1-1-1000000000000-201100000
χ26444444441-21-21-2-211-211-2-2-21-400-20-2-2002211-1-100111100000000000020-1-100000
χ2744444444-21-21-211-2-21-2-2111-24000200221100-2-2-1-10000-1-1-1-1000000000200-1-1000
χ2844444444-21-21-211-2-21-2-2111-24000-200-2-21100-2-21100001111000000000-20011000
χ2944444444-21-21-211-2-21-2-2111-2-400020022-1-10022-1-10000-1-1-1-1000000000-20011000
χ3044444444-21-21-211-2-21-2-2111-2-4000-200-2-2-1-100221100001111000000000200-1-1000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-444-4-444-4-4-44-4444-444-4-4-4000000000000000000000000000000000000000000
χ3344-4-444-4-4-212-121-1-2-212-21-1-120000000003-300003−300003−33−30000000000003−3000
χ3444-4-444-4-4-212-121-1-2-212-21-1-120000000003-30000−330000−33−33000000000000−33000
χ3544-4-444-4-4-212-121-1-2-212-21-1-12000000000-3300003−300003−33−3000000000000−33000
χ3644-4-444-4-4-212-121-1-2-212-21-1-12000000000-330000−330000−33−330000000000003−3000
χ3744-4-4-2-22244-4-4-44-44-2-22-2-222200000000000000000000000000000i6−i6i6−i6000000000
χ3844-4-4-2-22244-4-4-44-44-2-22-2-222200000000000000000000000000000−i6i6−i6i6000000000
χ394-44-4-222-2444-4-4-44-4-2-2-2222-2204-40000000000000000000000002-20000000000000
χ404-4-444-44-41-2-1-2122-11-2-1-12-22100000000000−i3i33i−3i00−i3i3−i3i3000000000000003−300000
χ414-4-444-44-41-2-1-2122-11-2-1-12-22100000000000−i3i3−3i3i00−i3i3−i3i300000000000000−3300000
χ424-4-444-44-41-2-1-2122-11-2-1-12-22100000000000i3−i33i−3i00i3−i3i3−i300000000000000−3300000
χ434-4-444-44-41-2-1-2122-11-2-1-12-22100000000000i3−i3−3i3i00i3−i3i3−i3000000000000003−300000
χ444-4-444-44-444-444-4-4-444-4-4-44-44000000000000000000000000000000000000000000
χ454-4-44-22-2244-444-4-4-4-2-2222-22-2000000000000000000000000000006−6−66000000000
χ464-4-44-22-2244-444-4-4-4-2-2222-22-200000000000000000000000000000−666−6000000000
χ478888-4-4-4-42-42-42-4-42-12-1-1222-100040-2-20000-2-200001111000000000000000000000
χ488888-4-4-4-42-42-42-4-42-12-1-1222-1000-40220000220000-1-1-1-1000000000000000000000
χ498888-4-4-4-4-42-42-422-42-122-1-1-120000400-2-2000000-2-20000111100000000000000000
χ508888-4-4-4-4-42-42-422-42-122-1-1-120000-40022000000220000-1-1-1-100000000000000000
χ5188-8-888-8-82-4-24-2-4422-4-22-444-2000000000000000000000000000000000000000000
χ5288-8-8-4-4442-4-24-2-442-121-12-2-21000000000000000003i−3i−3i3i000000000000000000000
χ5388-8-8-4-4442-4-24-2-442-121-12-2-2100000000000000000−3i3i3i−3i000000000000000000000
χ5488-8-8-4-444-424-242-2-42-1-22-111-200000000000000023−230000−33−3300000000000000000
χ5588-8-8-4-444-424-242-2-42-1-22-111-2000000000000000−232300003−33−300000000000000000
χ568-88-88-8-882-424-24-4-22-42-244-4-2000000000000000000000000000000000000000000
χ578-88-88-8-88-42-4-24-224-42-44-2-224000000000000000000000000000000000000000000
χ588-88-8-444-42-424-24-4-2-12-11-2-2210000023−230000000000−3−333000000000000000000000
χ598-88-8-444-42-424-24-4-2-12-11-2-22100000−2323000000000033−3−3000000000000000000000
χ608-88-8-444-4-42-4-24-2242-12-211-1-20000000−2i32i3000000000000i3i3−i3−i300000000000000000
χ618-88-8-444-4-42-4-24-2242-12-211-1-200000002i3−2i3000000000000−i3−i3i3i300000000000000000
χ628-8-888-88-8-4242-4-2-24-4244-22-2-4000000000000000000000000000000000000000000
χ638-8-88-44-442-4-2-4244-2-1211-22-2-100000000000−2i32i30000i3−i3i3−i3000000000000000000000
χ648-8-88-44-442-4-2-4244-2-1211-22-2-1000000000002i3−2i30000−i3i3−i3i3000000000000000000000
χ658-8-88-44-44-4242-4-2-242-1-2-21-1120000000000000000000003i−3i−3i3i00000000000000000
χ668-8-88-44-44-4242-4-2-242-1-2-21-112000000000000000000000−3i3i3i−3i00000000000000000

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