Finite Group Databasebeta

← Group #13165719

Character table — Group #13165719

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order1222366633666666336666664442466666666121212121212121212121212881212242424244412121212488
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
χ1522-2-22-2-22222-2-2-22-2222-22-2-2-202-2000000000000000000000000-22000000000002i−2i
χ1622-2-22-2-22222-2-2-22-2222-22-2-2-202-2000000000000000000000000-2200000000000−2i2i
χ1722-2-22-2-22222-2-2-22-2222-22-2-2-20-2200000000000000000000002i−2i2-22i2i−2i−2i000000000
χ1822-2-22-2-22222-2-2-22-2222-22-2-2-20-220000000000000000000000−2i2i2-2−2i−2i2i2i000000000
χ1922-2-2-111-1222-2-2-22-2-1-1-11-11110-2200−i3i300−i3−i3i3i33−300000033−3−32i−2i-11−i−iii000000000
χ2022-2-2-111-1222-2-2-22-2-1-1-11-11110-2200−i3i300−i3−i3i3i3−33000000−3−333−2i2i-11ii−i−i000000000
χ2122-2-2-111-1222-2-2-22-2-1-1-11-11110-2200i3−i300i3i3−i3−i33−300000033−3−3−2i2i-11ii−i−i000000000
χ2222-2-2-111-1222-2-2-22-2-1-1-11-11110-2200i3−i300i3i3−i3−i3−33000000−3−3332i−2i-11−i−iii000000000
χ23444444441-211-2-2-211-211-2-2-21400020000000022-2-211-1-1-1-1-1-1000000000200-1-1000
χ24444444441-211-2-2-211-211-2-2-214000-200000000-2-2-2-211111111000000000-20011000
χ25444444441-211-2-2-211-211-2-2-21-40002000000002222-1-1-1-1-1-1-1-1000000000-20011000
χ26444444441-211-2-2-211-211-2-2-21-4000-200000000-2-222-1-1111111000000000200-1-1000
χ2744444444-21-2-2111-2-21-2-2111-24002022-1-1-1-1-1-10011-2-20000000000000020-1-100000
χ2844444444-21-2-2111-2-21-2-2111-2400-20-2-21111110011-2-200000000000000-201100000
χ2944444444-21-2-2111-2-21-2-2111-2-4002022-1-1-1-1-1-100-1-12200000000000000-201100000
χ3044444444-21-2-2111-2-21-2-2111-2-400-20-2-211111100-1-1220000000000000020-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-4-222-2444-4-4-44-4-2-2-22-222204-40000000000000000000000002-20000000000000
χ334-44-444-4-444-444-4-4-444-44-44-4-4000000000000000000000000000000000000000000
χ344-44-444-4-4-212-21-1-12-212-2-11-120000000−i3i3−i3i3−i3i3003i−3i0000000000000000003−300000
χ354-44-444-4-4-212-21-1-12-212-2-11-120000000−i3i3−i3i3−i3i300−3i3i000000000000000000−3300000
χ364-44-444-4-4-212-21-1-12-212-2-11-120000000i3−i3i3−i3i3−i3003i−3i000000000000000000−3300000
χ374-44-444-4-4-212-21-1-12-212-2-11-120000000i3−i3i3−i3i3−i300−3i3i0000000000000000003−300000
χ384-44-4-2-22244-444-4-4-4-2-22-22-222000000000000000000000000000006−66−6000000000
χ394-44-4-2-22244-444-4-4-4-2-22-22-22200000000000000000000000000000−66−66000000000
χ404-4-444-44-41-2-1-12-2211-2-1-122-21000000000000000003-3−i3i3−i3i3−i3i3000000000000−i3i3000
χ414-4-444-44-41-2-1-12-2211-2-1-122-21000000000000000003-3i3−i3i3−i3i3−i3000000000000i3−i3000
χ424-4-444-44-41-2-1-12-2211-2-1-122-2100000000000000000-33−i3i3−i3i3−i3i3000000000000i3−i3000
χ434-4-444-44-41-2-1-12-2211-2-1-122-2100000000000000000-33i3−i3i3−i3i3−i3000000000000−i3i3000
χ444-4-444-44-444-4-4-44-4444-4-4-4-444000000000000000000000000000000000000000000
χ454-4-44-22-2244-4-4-44-44-2-22222-2-200000000000000000000000000000i6−i6−i6i6000000000
χ464-4-44-22-2244-4-4-44-44-2-22222-2-200000000000000000000000000000−i6i6i6−i6000000000
χ478888-4-4-4-42-422-4-4-42-12-1-1222-10000400000000-2-20000-2-2111100000000000000000
χ488888-4-4-4-42-422-4-4-42-12-1-1222-10000-40000000022000022-1-1-1-100000000000000000
χ498888-4-4-4-4-42-4-4222-42-122-1-1-1200040-2-2-2-2111100000000000000000000000000000
χ508888-4-4-4-4-42-4-4222-42-122-1-1-12000-402222-1-1-1-100000000000000000000000000000
χ5188-8-88-8-882-42-244-4-22-42-2-444-2000000000000000000000000000000000000000000
χ5288-8-88-8-88-42-44-2-224-42-442-2-24000000000000000000000000000000000000000000
χ5388-8-8-444-42-42-244-4-2-12-112-2-21000000000000023−23000000−3−33300000000000000000
χ5488-8-8-444-42-42-244-4-2-12-112-2-210000000000000−232300000033−3−300000000000000000
χ5588-8-8-444-4-42-44-2-2242-12-2-111-200000−2i32i300i3i3−i3−i300000000000000000000000000000
χ5688-8-8-444-4-42-44-2-2242-12-2-111-2000002i3−2i300−i3−i3i3i300000000000000000000000000000
χ578-88-888-8-82-4-22-444-22-4-224-44-2000000000000000000000000000000000000000000
χ588-88-8-4-4442-4-22-444-2-121-1-22-210000000000000000000003i−3i−3i3i00000000000000000
χ598-88-8-4-4442-4-22-444-2-121-1-22-21000000000000000000000−3i3i3i−3i00000000000000000
χ608-88-8-4-444-424-42-2-242-1-221-11-20000000−2i32i3i3−i3i3−i300000000000000000000000000000
χ618-88-8-4-444-424-42-2-242-1-221-11-200000002i3−2i3−i3i3−i3i300000000000000000000000000000
χ628-8-888-88-8-4244-22-2-4-4244-2-22-4000000000000000000000000000000000000000000
χ638-8-88-44-442-4-2-24-442-1211-2-22-10000000000000000000−2i32i3i3−i3i3−i300000000000000000
χ648-8-88-44-442-4-2-24-442-1211-2-22-100000000000000000002i3−2i3−i3i3−i3i300000000000000000
χ658-8-88-44-44-4244-22-2-42-1-2-211-120000000003-3-3300000000000000000000000000000
χ668-8-88-44-44-4244-22-2-42-1-2-211-12000000000-333-300000000000000000000000000000

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