Finite Group Databasebeta

← Group #13165703

Character table — Group #13165703

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222244444444668888888812121212121212121212181824242424242424242424242424242424243636363636363636363636363636727272108108108
order122236663366666644336666664412121212121212124441212121212121212121212121212121244881212121212122424242441212288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1
χ311111111111111111111111111-1-11111-1-1-1-1111-1-1111111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1111
χ51111111111111111-1-11111111111-1-1-1-11111111111111-1-111111111-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111-111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1
χ9222222222222222222222222220022220000-2-2000000022000000000000-20000-20000000-200
χ102222222222222222-2-22222222200-2-2-2-20000-2-20000000-2-2000000000000-20000-20000000200
χ112222-1-1-1-12222222200-1-1-1-1-1-1-1-12200002222222-1-1-1-12200-1-1-1-1-1-1-1-10022-10000-1-1-1-1-1000000
χ122222-1-1-1-12222222200-1-1-1-1-1-1-1-1220000222222-2-1-111-2-200-1-1-1-1111100-2-2-10000-11111000000
χ132222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-222211-1-122001111-1-1-1-100-2-2-10000-11111000000
χ142222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-222-21111-2-200111111110022-10000-1-1-1-1-1000000
χ1522-2-22-2-2222-222-2-2-22i−2i22-2-2-2-222002i2i−2i−2i00000000000002i−2i00000000002−200000022−2−20000−i2i2
χ1622-2-22-2-2222-222-2-2-22i−2i22-2-2-2-222002i2i−2i−2i00000000000002i−2i0000000000−22000000−2−2220000i2−i2
χ1722-2-22-2-2222-222-2-2-2−2i2i22-2-2-2-22200−2i−2i2i2i0000000000000−2i2i00000000002−200000022−2−20000i2−i2
χ1822-2-22-2-2222-222-2-2-2−2i2i22-2-2-2-22200−2i−2i2i2i0000000000000−2i2i0000000000−22000000−2−2220000−i2i2
χ192-2-222-22-222-2-2-22-22002222-2-2-2-20000000000-22000000000000000002i−2i0022i2i−2i−2i-20000000000
χ202-2-222-22-222-2-2-22-22002222-2-2-2-20000000000-2200000000000000000−2i2i002−2i−2i2i2i-20000000000
χ212-2-222-22-222-2-2-22-22002222-2-2-2-22i−2i00002i2i−2i−2i2-202i−2i0000002i2i−2i−2i00000000-2000020000000000
χ222-2-222-22-222-2-2-22-22002222-2-2-2-2−2i2i0000−2i−2i2i2i2-20−2i2i000000−2i−2i2i2i00000000-2000020000000000
χ232-2-22-11-1122-2-2-22-2200-1-1-1-111112i−2i00002i2i−2i−2i2-20−ii3−30000−i−iii33−3−3000010000-1−i3i3−i3i3000000
χ242-2-22-11-1122-2-2-22-2200-1-1-1-111112i−2i00002i2i−2i−2i2-20−ii−330000−i−iii−3−333000010000-1i3−i3i3−i3000000
χ252-2-22-11-1122-2-2-22-2200-1-1-1-11111−2i2i0000−2i−2i2i2i2-20i−i3−30000ii−i−i33−3−3000010000-1i3−i3i3−i3000000
χ262-2-22-11-1122-2-2-22-2200-1-1-1-11111−2i2i0000−2i−2i2i2i2-20i−i−330000ii−i−i−3−333000010000-1−i3i3−i3i3000000
χ27444444441-211-2-2-21441-21-21-21-200-2-2-2-200000020022-1-1110000-1-1-1-1000000000000002-1-1000
χ28444444441-211-2-2-21441-21-21-21-200-2-2-2-2000000-200-2-211110000111100000000000000-211000
χ29444444441-211-2-2-21-4-41-21-21-21-200222200000020022-1-1-1-10000-1-1-1-100000000000000-211000
χ30444444441-211-2-2-21-4-41-21-21-21-2002222000000-200-2-211-1-100001111000000000000002-1-1000
χ3144444444-21-2-2111-244-21-21-21-21221111-1-1-1-1000220000-2-2-1-1-1-1000022000-1-1-1-100000000000
χ3244444444-21-2-2111-244-21-21-21-21-2-211111111000-2-20000-2-211110000-2-2000111100000000000
χ3344444444-21-2-2111-2-4-4-21-21-21-2122-1-1-1-1-1-1-1-100022000022-1-1-1-10000-2-2000111100000000000
χ3444444444-21-2-2111-2-4-4-21-21-21-21-2-2-1-1-1-11111000-2-20000221111000022000-1-1-1-100000000000
χ354444-2-2-2-24444444400-2-2-2-2-2-2-2-20000000000-4-40000000000000000000002000020000000000
χ3644-4-44-4-441-2-11-222-14i−4i1-2-12-121-200−2i−2i2i2i00000000000−i3i3i−i0000−i3i3−i3i30000000000000003−3000
χ3744-4-44-4-441-2-11-222-14i−4i1-2-12-121-200−2i−2i2i2i00000000000i3−i3i−i0000i3−i3i3−i3000000000000000−33000
χ3844-4-44-4-441-2-11-222-1−4i4i1-2-12-121-2002i2i−2i−2i00000000000−i3i3−ii0000−i3i3−i3i3000000000000000−33000
χ3944-4-44-4-441-2-11-222-1−4i4i1-2-12-121-2002i2i−2i−2i00000000000i3−i3−ii0000i3−i3i3−i30000000000000003−3000
χ4044-4-44-4-44-212-21-1-124i−4i-212-12-1-2100ii−i−i−i3i3−i3i3000000000−2i2i−i3i3−i3i30000000003−33−300000000000
χ4144-4-44-4-44-212-21-1-124i−4i-212-12-1-2100ii−i−ii3−i3i3−i3000000000−2i2ii3−i3i3−i3000000000−33−3300000000000
χ4244-4-44-4-44-212-21-1-12−4i4i-212-12-1-2100−i−iii−i3i3−i3i30000000002i−2i−i3i3−i3i3000000000−33−3300000000000
χ4344-4-44-4-44-212-21-1-12−4i4i-212-12-1-2100−i−iiii3−i3i3−i30000000002i−2ii3−i3i3−i30000000003−33−300000000000
χ4444-4-4-222-244-444-4-4-400-2-22222-2-2000000000000000000000000000000022−22000000−2−222000000
χ4544-4-4-222-244-444-4-4-400-2-22222-2-20000000000000000000000000000000−222200000022−2−2000000
χ464-44-444-4-4444-4-4-44-40044-4-444-4-40000000000000000000000000000000000000000000000000
χ474-44-444-4-4-21-22-1-11200-212-1-212-1003i−3i3i−3i3−3−33000000000003−3−33000000000−i3i3i3−i300000000000
χ484-44-444-4-4-21-22-1-11200-212-1-212-1003i−3i3i−3i−333−300000000000−333−3000000000i3−i3−i3i300000000000
χ494-44-444-4-4-21-22-1-11200-212-1-212-100−3i3i−3i3i3−3−33000000000003−3−33000000000i3−i3−i3i300000000000
χ504-44-444-4-4-21-22-1-11200-212-1-212-100−3i3i−3i3i−333−300000000000−333−3000000000−i3i3i3−i300000000000
χ514-44-4-2-222444-4-4-44-400-2-222-2-222000000000000000000000000000000000000000i6−i6−i6i6000000
χ524-44-4-2-222444-4-4-44-400-2-222-2-222000000000000000000000000000000000000000−i6i6i6−i6000000
χ534-4-444-44-4-2122-11-1-200-21-212-12-12i−2i3-3-33−i−iii0002i−2i000000−i−iii0000−2i2i000ii−i−i00000000000
χ544-4-444-44-4-2122-11-1-200-21-212-12-12i−2i-333-3−i−iii0002i−2i000000−i−iii00002i−2i000−i−iii00000000000
χ554-4-444-44-4-2122-11-1-200-21-212-12-1−2i2i3-3-33ii−i−i000−2i2i000000ii−i−i00002i−2i000−i−iii00000000000
χ564-4-444-44-4-2122-11-1-200-21-212-12-1−2i2i-333-3ii−i−i000−2i2i000000ii−i−i0000−2i2i000ii−i−i00000000000
χ574-4-44-22-2244-4-4-44-4400-2-2-2-222220000000000-44000000000000000000000-2000020000000000
χ588888-4-4-4-42-422-4-4-4200-12-12-12-12000000000000400-2-2-2-2000000111100000000000000000000
χ598888-4-4-4-42-422-4-4-4200-12-12-12-12000000000000-4002222000000-1-1-1-100000000000000000000
χ608888-4-4-4-4-42-4-4222-4002-12-12-12-1440000-2-2-2-2000-2-20000001111000000000000000000000000
χ618888-4-4-4-4-42-4-4222-4002-12-12-12-1-4-40000222200022000000-1-1-1-1000000000000000000000000
χ6288-8-8-444-42-4-22-444-200-121-21-2-1200000000000000000−2i32i3000000i3−i3i3−i300000000000000000000
χ6388-8-8-444-42-4-22-444-200-121-21-2-12000000000000000002i3−2i3000000−i3i3−i3i300000000000000000000
χ6488-8-8-444-4-424-42-2-24002-1-21-212-1000000−2i32i3−2i32i300000000000i3−i3i3−i3000000000000000000000000
χ6588-8-8-444-4-424-42-2-24002-1-21-212-10000002i3−2i32i3−2i300000000000−i3i3−i3i3000000000000000000000000
χ668-88-888-8-82-42-244-4-2002-4-242-4-240000000000000000000000000000000000000000000000000
χ678-88-8-4-4442-42-244-4-200-121-2-121-200000000000000000000000003i−3i−3i3i00000000000000000000
χ688-88-8-4-4442-42-244-4-200-121-2-121-20000000000000000000000000−3i3i3i−3i00000000000000000000
χ698-88-8-4-444-42-44-2-224002-1-212-1-2100000023−23−232300000000000−333−3000000000000000000000000
χ708-88-8-4-444-42-44-2-224002-1-212-1-21000000−232323−23000000000003−3−33000000000000000000000000
χ718-8-888-88-82-4-2-24-442002-42-4-24-240000000000000000000000000000000000000000000000000
χ728-8-88-44-442-4-2-24-44200-12-121-21-200000000000000023−2300000000−3−33300000000000000000000
χ738-8-88-44-442-4-2-24-44200-12-121-21-2000000000000000−23230000000033−3−300000000000000000000
χ748-8-88-44-44-4244-22-2-4002-12-1-21-214i−4i0000−2i−2i2i2i000−2i2i000000ii−i−i000000000000000000000000
χ758-8-88-44-44-4244-22-2-4002-12-1-21-21−4i4i00002i2i−2i−2i0002i−2i000000−i−iii000000000000000000000000

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