Finite Group Databasebeta

← Group #13165743

Character table — Group #13165743

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order122236663366666633666666444441212121212121212121212121212121212121212881212242424244412121212488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-111-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-1
χ3111111111111111111111111111-11-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-11-1-1-1111-1-1
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
χ6111111111111111111111111-1111-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-1-111-111
χ7111111111111111111111111-111-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1111-1-1-111
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
χ1522-2-22-22-22222-2-2-2-22222-2-2-2-202-200000000000000000000002-2-2222-2-2000000000
χ1622-2-22-22-22222-2-2-2-22222-2-2-2-202-20000000000000000000000-22-22-2-222000000000
χ1722-2-22-22-22222-2-2-2-22222-2-2-2-20-220000000000000000000000002-2000000000002-2
χ1822-2-22-22-22222-2-2-2-22222-2-2-2-20-220000000000000000000000002-200000000000-22
χ1922-2-2-11-112222-2-2-2-2-1-1-1-1111102-2003−33−30000000033−3−333−3−32-21-1-1-111000000000
χ2022-2-2-11-112222-2-2-2-2-1-1-1-1111102-2003−3−330000000033−3−3−3−333-221-111-1-1000000000
χ2122-2-2-11-112222-2-2-2-2-1-1-1-1111102-200−333−300000000−3−33333−3−3-221-111-1-1000000000
χ2222-2-2-11-112222-2-2-2-2-1-1-1-1111102-200−33−3300000000−3−333−3−3332-21-1-1-111000000000
χ23444444441-21-21-2-211-21-21-21-2400020022-2-20011-1-10000-1-1-1-1000000002000-1-1000
χ24444444441-21-21-2-211-21-21-21-24000-200-2-2-2-20011110000111100000000-200011000
χ25444444441-21-21-2-211-21-21-21-2-4000200222200-1-1-1-10000-1-1-1-100000000-200011000
χ26444444441-21-21-2-211-21-21-21-2-4000-200-2-22200-1-11100001111000000002000-1-1000
χ2744444444-21-21-211-2-21-21-21-2140020220011-1-1-2-200-1-1-1-100000000000002-1-100000
χ2844444444-21-21-211-2-21-21-21-21400-20-2-2001111-2-20011110000000000000-21100000
χ2944444444-21-21-211-2-21-21-21-21-400202200-1-1-1-12200-1-1-1-10000000000000-21100000
χ3044444444-21-21-211-2-21-21-21-21-400-20-2-200-1-1112200111100000000000002-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-4-22-224444-4-4-4-4-2-2-2-222220-44000000000000000000000000-220000000000000
χ334-44-44-4-441-2-12-1-2211-2-12-121-200000000000003-3−i3i30000−i3i3−i3i3000000000000−i3i3000
χ344-44-44-4-441-2-12-1-2211-2-12-121-200000000000003-3i3−i30000i3−i3i3−i3000000000000i3−i3000
χ354-44-44-4-441-2-12-1-2211-2-12-121-20000000000000-33−i3i30000−i3i3−i3i3000000000000i3−i3000
χ364-44-44-4-441-2-12-1-2211-2-12-121-20000000000000-33i3−i30000i3−i3i3−i3000000000000−i3i3000
χ374-44-44-4-4444-4-4-44-4444-4-4-4-444000000000000000000000000000000000000000000
χ384-44-4-222-244-4-4-44-44-2-22222-2-200000000000000000000000000000i6−i6i6−i6000000000
χ394-44-4-222-244-4-4-44-44-2-22222-2-200000000000000000000000000000−i6i6−i6i6000000000
χ404-4-4444-4-444-4-44-44-444-4-444-4-4000000000000000000000000000000000000000000
χ414-4-4444-4-4-212-1-2-112-212-1-212-10000000003i−3i3−300003−33−300000000000000−i3i300000
χ424-4-4444-4-4-212-1-2-112-212-1-212-10000000003i−3i−330000−33−3300000000000000i3−i300000
χ434-4-4444-4-4-212-1-2-112-212-1-212-1000000000−3i3i3−300003−33−300000000000000i3−i300000
χ444-4-4444-4-4-212-1-2-112-212-1-212-1000000000−3i3i−330000−33−3300000000000000−i3i300000
χ454-4-44-2-22244-4-44-44-4-2-222-2-22200000000000000000000000000000i6−i6−i6i6000000000
χ464-4-44-2-22244-4-44-44-4-2-222-2-22200000000000000000000000000000−i6i6i6−i6000000000
χ478888-4-4-4-42-42-42-4-42-12-12-12-120000400-2-2000000-2-20000111100000000000000000
χ488888-4-4-4-42-42-42-4-42-12-12-12-120000-40022000000220000-1-1-1-100000000000000000
χ498888-4-4-4-4-42-42-422-42-12-12-12-100040-2-20000-2-200001111000000000000000000000
χ508888-4-4-4-4-42-42-422-42-12-12-12-1000-40220000220000-1-1-1-1000000000000000000000
χ5188-8-88-88-82-42-4-244-22-42-4-24-24000000000000000000000000000000000000000000
χ5288-8-88-88-8-42-424-2-24-42-424-24-2000000000000000000000000000000000000000000
χ5388-8-8-44-442-42-4-244-2-12-121-21-2000000023−23000000000000−3−33300000000000000000
χ5488-8-8-44-442-42-4-244-2-12-121-21-20000000−232300000000000033−3−300000000000000000
χ5588-8-8-44-44-42-424-2-242-12-1-21-210000023−230000000000−3−333000000000000000000000
χ5688-8-8-44-44-42-424-2-242-12-1-21-2100000−2323000000000033−3−3000000000000000000000
χ578-88-88-8-88-424-242-2-4-424-24-2-42000000000000000000000000000000000000000000
χ588-88-8-444-42-4-24-2-442-121-21-2-12000000000000000−2i32i30000i3−i3i3−i300000000000000000
χ598-88-8-444-42-4-24-2-442-121-21-2-120000000000000002i3−2i30000−i3i3−i3i300000000000000000
χ608-88-8-444-4-424-242-2-42-1-21-212-1000000000000000003-3-33000000000000000000000
χ618-88-8-444-4-424-242-2-42-1-21-212-100000000000000000-333-3000000000000000000000
χ628-8-8888-8-82-4-2424-4-22-4-242-4-24000000000000000000000000000000000000000000
χ638-8-88-4-4442-4-2424-4-2-121-2-121-20000000000000000000003i−3i−3i3i00000000000000000
χ648-8-88-4-4442-4-2424-4-2-121-2-121-2000000000000000000000−3i3i3i−3i00000000000000000
χ658-8-88-4-444-424-2-4-2242-1-212-1-210000000000023−230000−33−33000000000000000000000
χ668-8-88-4-444-424-2-4-2242-1-212-1-2100000000000−232300003−33−3000000000000000000000

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