Finite Group Databasebeta

← Group #13138037

Character table — Group #13138037

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222222444466666666881212121212121212121212121818181818182424242424242424363636363636363636363636363636363636363636727272727272
order12223446664412123366666612123666121212121212121244121212121212121212121212224666688881212242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-111-1-1
χ51111111111-1-11111111111-1-11111111-1-1-1-11111111-1-111-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-1-1-1
χ61111111111-1-11111111111-1-11111111-1-1-1-11111111-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ71111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-11111-1-1-1-11-111-1-1
χ81111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-1-1-1-1-11111-11-1-111
χ9222222222222222-122-12-1-122-1-1-1-12-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1222-1-1-1-10000-1-100000000000000
χ10222222222222222-122-12-1-122-1-1-1-12-1-1-1-1-1-12-2-2111122-1-1-1-1-1-1-2-2-2111100001100000000000000
χ1122222222222222-12-1-12-12222-1-1-1-1-1222222-1000000-1-1-1-1-1-1-1-100000000022000000-1-1-1-120-1-100
χ1222222222222222-12-1-12-12222-1-1-1-1-1222222-1000000-1-1-1-1-1-1-1-1000000000-2-20000001111-201100
χ132222222222-2-2222-122-12-1-1-2-2-1-1-1-12-1-11111222-1-1-1-1-2-2-1-11111-2-2211110000-1-100000000000000
χ142222222222-2-2222-122-12-1-1-2-2-1-1-1-12-1-111112-2-21111-2-2-1-1111122-2-1-1-1-100001100000000000000
χ152222222222-2-222-12-1-12-122-2-2-1-1-1-1-122-2-2-2-2-100000011-1-1111100000000022000000-1-1-1-1-201100
χ162222222222-2-222-12-1-12-122-2-2-1-1-1-1-122-2-2-2-2-100000011-1-11111000000000-2-2000000111120-1-100
χ1722222-2-222200-2-222222222002222-2-2-20000-222222200-2-2000000-200000000-2-200000000000000
χ1822222-2-222200-2-222222222002222-2-2-20000-2-2-2-2-2-2-200-2-20000002000000002200000000000000
χ1922222-2-222200-2-22-122-12-1-100-1-1-1-1-211−i3−i3i3i3-222-1-1-1-10011−i3−i3i3i300-2−i3−i3i3i300001100000000000000
χ2022222-2-222200-2-22-122-12-1-100-1-1-1-1-211−i3−i3i3i3-2-2-211110011−i3−i3i3i3002i3i3−i3−i30000-1-100000000000000
χ2122222-2-222200-2-22-122-12-1-100-1-1-1-1-211i3i3−i3−i3-222-1-1-1-10011i3i3−i3−i300-2i3i3−i3−i300001100000000000000
χ2222222-2-222200-2-22-122-12-1-100-1-1-1-1-211i3i3−i3−i3-2-2-211110011i3i3−i3−i3002−i3−i3i3i30000-1-100000000000000
χ2322-2-22002-2-20000222-2-2-22-20022-2-2000000002i−2i2i2i−2i−2i0000000000000002−2−i2i20022−2−2−i2−i2i2i2000000
χ2422-2-22002-2-20000222-2-2-22-20022-2-2000000002i−2i2i2i−2i−2i000000000000000−22i2−i200−2−222i2i2−i2−i2000000
χ2522-2-22002-2-20000222-2-2-22-20022-2-200000000−2i2i−2i−2i2i2i0000000000000002−2i2−i20022−2−2i2i2−i2−i2000000
χ2622-2-22002-2-20000222-2-2-22-20022-2-200000000−2i2i−2i−2i2i2i000000000000000−22−i2i200−2−222−i2−i2i2i2000000
χ272-2-2222-2-2-222i−2i2-222-222-2-2-22i−2i2-22-222-22i−2i2i−2i-20000002i−2i2-22i−2i2i−2i000000000000000000000000000
χ282-2-2222-2-2-222i−2i2-22-1-22-1-2112i−2i-11-112-11−ii−ii-2003−33−32i−2i-11−ii−ii000−i3i3−i3i300003−300000000000000
χ292-2-2222-2-2-222i−2i2-22-1-22-1-2112i−2i-11-112-11−ii−ii-200−33−332i−2i-11−ii−ii000i3−i3i3−i30000−3300000000000000
χ302-2-2222-2-2-222i−2i2-2-121-121-2-22i−2i-11-11-12-22i−2i2i−2i1000000−ii-11−ii−ii000000000000000003−33−300−i3i300
χ312-2-2222-2-2-222i−2i2-2-121-121-2-22i−2i-11-11-12-22i−2i2i−2i1000000−ii-11−ii−ii00000000000000000−33−3300i3−i300
χ322-2-2222-2-2-22−2i2i2-222-222-2-2-2−2i2i2-22-222-2−2i2i−2i2i-2000000−2i2i2-2−2i2i−2i2i000000000000000000000000000
χ332-2-2222-2-2-22−2i2i2-22-1-22-1-211−2i2i-11-112-11i−ii−i-2003−33−3−2i2i-11i−ii−i000i3−i3i3−i300003−300000000000000
χ342-2-2222-2-2-22−2i2i2-22-1-22-1-211−2i2i-11-112-11i−ii−i-200−33−33−2i2i-11i−ii−i000−i3i3−i3i30000−3300000000000000
χ352-2-2222-2-2-22−2i2i2-2-121-121-2-2−2i2i-11-11-12-2−2i2i−2i2i1000000i−i-11i−ii−i000000000000000003−33−300i3−i300
χ362-2-2222-2-2-22−2i2i2-2-121-121-2-2−2i2i-11-11-12-2−2i2i−2i2i1000000i−i-11i−ii−i00000000000000000−33−3300−i3i300
χ372-2-222-22-2-2200-2222-222-2-2-2002-22-2-2-220000200000000-2200002-202-2-2200000000000000000000
χ382-2-222-22-2-2200-2222-222-2-2-2002-22-2-2-220000200000000-220000-220-222-200000000000000000000
χ392-2-222-22-2-2200-222-1-22-1-21100-11-11-21-13−3−332003−33−3001-13−3−332-20-111-10000−3300000000000000
χ402-2-222-22-2-2200-222-1-22-1-21100-11-11-21-13−3−33200−33−33001-13−3−33-2201-1-1100003−300000000000000
χ412-2-222-22-2-2200-222-1-22-1-21100-11-11-21-1−333−32003−33−3001-1−333−3-2201-1-110000−3300000000000000
χ422-2-222-22-2-2200-222-1-22-1-21100-11-11-21-1−333−3200−33−33001-1−333−32-20-111-100003−300000000000000
χ4344444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-2000000-2-2111111000000000000000000000000000
χ444444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-2-22222-20000002211-1-1-1-1000000000000000000000000000
χ4544444-4-444400-4-4-24-2-24-24400-2-2-2-22-4-40000200000000220000000000000000000000000000000
χ4644444-4-444400-4-4-2-2-2-2-2-2-2-2001111222−2i3−2i32i32i3200000000-1-1i3i3−i3−i3000000000000000000000000000
χ4744444-4-444400-4-4-2-2-2-2-2-2-2-20011112222i32i3−2i3−2i3200000000-1-1−i3−i3i3i3000000000000000000000000000
χ4844-4-44004-4-400004-24-42-4-2200-2-222000000004i−4i−2i−2i2i2i00000000000000000000000000000000000
χ4944-4-44004-4-400004-24-42-4-2200-2-22200000000−4i4i2i2i−2i−2i00000000000000000000000000000000000
χ5044-4-44004-4-40000-24-22-424-400-2-2220000000000000000000000000000000−2i22i2000000i2i2−i2−i2000000
χ5144-4-44004-4-40000-24-22-424-400-2-22200000000000000000000000000000002i2−2i2000000−i2−i2i2i2000000
χ524-44-4400-44-4000044-4-4-44-44004-4-440000000000000000000000000000000000000000000000000
χ534-44-4400-44-400004-2-4-4242-200-222-20000000000−2i32i32i3−2i300000000000000000000000000000000000
χ544-44-4400-44-400004-2-4-4242-200-222-200000000002i3−2i3−2i32i300000000000000000000000000000000000
χ554-44-4400-44-40000-2422-4-2-4400-222-2000000000000000000000000000000000000000i6−i6−i6i6000000
χ564-44-4400-44-40000-2422-4-2-4400-222-2000000000000000000000000000000000000000−i6i6i6−i6000000
χ574-4-4444-4-4-444i−4i4-4-2-22-2-22224i−4i1-11-1-2-22−2i2i−2i2i2000000−2i2i1-1i−ii−i000000000000000000000000000
χ584-4-4444-4-4-44−4i4i4-4-2-22-2-2222−4i4i1-11-1-2-222i−2i2i−2i20000002i−2i1-1−ii−ii000000000000000000000000000
χ594-4-444-44-4-4400-44-242-242-4-400-22-222-440000-2000000002-20000000000000000000000000000000
χ604-4-444-44-4-4400-44-2-22-2-2222001-11-122-223−23−2323-200000000-11−333−3000000000000000000000000000
χ614-4-444-44-4-4400-44-2-22-2-2222001-11-122-2−232323−23-200000000-113−3−33000000000000000000000000000
χ626666-366-3-3-366-3-300000000-3-3000000000000000000000000000000000220000-1-1-1-100000200-1-1
χ636666-366-3-3-366-3-300000000-3-3000000000000000000000000000000000-2-20000111100000-20011
χ646666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000000220000-1-1-1-100000-20011
χ656666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000000-2-20000111100000200-1-1
χ666-6-66-36-633-36i−6i-3300000000−3i3i0000000000000000000000000000000000000003−33−300000000−i3i3
χ676-6-66-36-633-36i−6i-3300000000−3i3i000000000000000000000000000000000000000−33−3300000000i3−i3
χ686-6-66-36-633-3−6i6i-33000000003i−3i0000000000000000000000000000000000000003−33−300000000i3−i3
χ696-6-66-36-633-3−6i6i-33000000003i−3i000000000000000000000000000000000000000−33−3300000000−i3i3
χ7088-8-88008-8-80000-4-4-4444-440022-2-20000000000000000000000000000000000000000000000000
χ718-88-8800-88-80000-4-4444-44-4002-2-220000000000000000000000000000000000000000000000000
χ7212121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000
χ731212-12-12-600-6660000000000000000000000000000000000000000000000022−220000−2−2220000000000
χ741212-12-12-600-66600000000000000000000000000000000000000000000000−2222000022−2−20000000000
χ7512-1212-12-6006-66000000000000000000000000000000000000000000000000000006−6−660000000000
χ7612-1212-12-6006-6600000000000000000000000000000000000000000000000000000−666−60000000000
χ7712-12-1212-6-121266-6006-6000000000000000000000000000000000000000000000000000000000000000

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