Finite Group Databasebeta

← Group #13148723

Character table — Group #13148723

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order122234466624121233666666612366666121212121212222244444412121212666121212121224444446666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-111-11-1-111-1-111-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111-1-11
χ51111111111-1-11111111111-1-11-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-1111111-1-1-1-111-1-11-1-11
χ61111111111-1-11111111111-1-11-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-11-1-111-1-1-1-1111111-111-1
χ71111111111-1-11111111111-1-11-1-11111111-1-1-1-11111-1-1111111-1-1-1-111-1-1-11-11-1-1111-1-1111111-1-111-1-1-1-1
χ81111111111-1-11111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-11111-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-111111-1-111-1-1-1-1111-11-1
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-1-111111111-1-1-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-11-1-11-111-1-1-1-1-1-11111-1-1-1-111
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1-11-11-1-1-1-111-1-1-1-1111111-1-1
χ1311111-1-1111-11-1-111111111-111-1-1111-1-1-1-111111111-1-1111111-1-1-11-1-1111-1-1-11-1-11111-1-1-1-111-1-1-1-111-1-1
χ1411111-1-1111-11-1-111111111-111-1-1111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11-1-111-111-1-111-1-11111-1-1-1-1-1-111-1-111
χ1511111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-1-1111111-1-1-1-111-1-11111-11-11
χ1611111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-111111111-1-11-11-1
χ17222222222222222-12-12-12-122-122-1-1-122-1-12200002200000000-1-1-1-1-1-1-1-1200002200000000-1-100-1-1-100-1
χ18222222222222222-12-12-12-122-122-1-1-122-1-1220000-2-200000000-1-1-1-1-1-1-1-1-20000-2-2000000001100111001
χ1922222222222222-12-12-12-1222-1-1-1-1-1-1-1-122-1-12200002222-1-1-1-12-1-12-1-1-1-1000200000-1-100-1-100-1-1000000
χ2022222222222222-12-12-12-1222-1-1-1-1-1-1-1-122-1-1-2-20000-2-2-2-211112-1-12-1-1-1-1000-2000001100110011000000
χ212222222222-2-2222-12-12-12-1-2-2-1-2-2-1-1-122-1-1-2-2000022000000001111-1-111-20000-2200000000-1-100-1-11001
χ222222222222-2-2222-12-12-12-1-2-2-1-2-2-1-1-122-1-1-2-20000-2-2000000001111-1-111200002-200000000110011-100-1
χ232222222222-2-222-12-12-12-12-2-2-111-1-1-1-1-1221122000022-2-21111-211-2-1-111000-200000-1-1001100-1-1000000
χ242222222222-2-222-12-12-12-12-2-2-111-1-1-1-1-12211-2-20000-2-222-1-1-1-1-211-2-1-1110002000001100-1-10011000000
χ2522222-2-22222-2-2-22-12-12-12-12-2-122-1-1-1-2-211-2-200002200000000-1-1-111111-200002-200000000-1-10011100-1
χ2622222-2-22222-2-2-22-12-12-12-12-2-122-1-1-1-2-211-2-20000-2-200000000-1-1-11111120000-22000000001100-1-1-1001
χ2722222-2-22222-2-2-2-12-12-12-122-2-1-1-1-1-1-111-2-211220000-2-2-2-211112-1-1-21111000200000-1-100-1-10011000000
χ2822222-2-22222-2-2-2-12-12-12-122-2-1-1-1-1-1-111-2-211-2-200002222-1-1-1-12-1-1-21111000-20000011001100-1-1000000
χ2922222-2-2222-22-2-22-12-12-12-1-22-1-2-2-1-1-1-2-2112200002200000000111-111-1-120000-2-200000000-1-10011-1001
χ3022222-2-2222-22-2-22-12-12-12-1-22-1-2-2-1-1-1-2-211220000-2-200000000111-111-1-1-2000022000000001100-1-1100-1
χ3122222-2-2222-22-2-2-12-12-12-12-22-111-1-1-111-2-2-1-1220000-2-222-1-1-1-1-211211-1-1000-200000-1-100110011000000
χ3222222-2-2222-22-2-2-12-12-12-12-22-111-1-1-111-2-2-1-1-2-2000022-2-21111-211211-1-10002000001100-1-100-1-1000000
χ3322-2-2200-2-2200002222-2-2-2-200200-22-2000000002-22i−2i002i−2i2i2i−2i−2i0000000000000002-20000002i−2i00000000
χ3422-2-2200-2-2200002222-2-2-2-200200-22-2000000002-2−2i2i00−2i2i−2i−2i2i2i0000000000000002-2000000−2i2i00000000
χ3522-2-2200-2-2200002222-2-2-2-200200-22-200000000-222i−2i00−2i2i−2i−2i2i2i000000000000000-220000002i−2i00000000
χ3622-2-2200-2-2200002222-2-2-2-200200-22-200000000-22−2i2i002i−2i2i2i−2i−2i000000000000000-22000000−2i2i00000000
χ372-22-222i−2i-22-2002i−2i22-2-222-2-2002002-2-22i−2i2i−2i002-200002i−2i00000000002i−2i000000000002-20000002i−2i000000
χ382-22-222i−2i-22-2002i−2i22-2-222-2-2002002-2-22i−2i2i−2i00-220000−2i2i00000000002i−2i00000000000-22000000−2i2i000000
χ392-22-222i−2i-22-2002i−2i-121-2-121-200-1−i3i3-111−ii2i−2i3−32-200002i−2i003−33−30−i3i30−ii3−3000000000-1100−i3i300−ii000000
χ402-22-222i−2i-22-2002i−2i-121-2-121-200-1−i3i3-111−ii2i−2i3−3-220000−2i2i00−33−330−i3i30−ii3−30000000001-100i3−i300i−i000000
χ412-22-222i−2i-22-2002i−2i-121-2-121-200-1i3−i3-111−ii2i−2i−332-200002i−2i00−33−330i3−i30−ii−33000000000-1100i3−i300−ii000000
χ422-22-222i−2i-22-2002i−2i-121-2-121-200-1i3−i3-111−ii2i−2i−33-220000−2i2i003−33−30i3−i30−ii−330000000001-100−i3i300i−i000000
χ432-22-22−2i2i-22-200−2i2i22-2-222-2-2002002-2-2−2i2i−2i2i002-20000−2i2i0000000000−2i2i000000000002-2000000−2i2i000000
χ442-22-22−2i2i-22-200−2i2i22-2-222-2-2002002-2-2−2i2i−2i2i00-2200002i−2i0000000000−2i2i00000000000-220000002i−2i000000
χ452-22-22−2i2i-22-200−2i2i-121-2-121-200-1−i3i3-111i−i−2i2i−332-20000−2i2i00−33−330−i3i30i−i−33000000000-1100−i3i300i−i000000
χ462-22-22−2i2i-22-200−2i2i-121-2-121-200-1−i3i3-111i−i−2i2i−33-2200002i−2i003−33−30−i3i30i−i−330000000001-100i3−i300−ii000000
χ472-22-22−2i2i-22-200−2i2i-121-2-121-200-1i3−i3-111i−i−2i2i3−32-20000−2i2i003−33−30i3−i30i−i3−3000000000-1100i3−i300i−i000000
χ482-22-22−2i2i-22-200−2i2i-121-2-121-200-1i3−i3-111i−i−2i2i3−3-2200002i−2i00−33−330i3−i30i−i3−30000000001-100−i3i300−ii000000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2-2-2-2-200000000000000-211-211110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-4122111-2-2-2-222000000000000002-1-1211-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-211122222200000000000000-2112-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441221112222-2-2000000000000002-1-1-2-1-1110000000000000000000000000
χ5344-4-4400-4-4400004-24-2-42-4200-2002-2200000000004i−4i0000000000000000000000000000000−2i2i00000000
χ5444-4-4400-4-4400004-24-2-42-4200-2002-220000000000−4i4i00000000000000000000000000000002i−2i00000000
χ5544-4-4400-4-440000-24-242-42-400-2002-22000000000000004i−4i−2i−2i2i2i000000000000000000000000000000000
χ5644-4-4400-4-440000-24-242-42-400-2002-2200000000000000−4i4i2i2i−2i−2i000000000000000000000000000000000
χ574-44-444i−4i-44-4004i−4i4-2-424-2-4200-200-2224i−4i−2i2i00000000000000000000−2i2i000000000000000000000000000
χ584-44-444i−4i-44-4004i−4i-2-222-2-222001−2i32i31-1-1−2i2i−2i2i23−23000000000000000i3−i30i−i−330000000000000000000000000
χ594-44-444i−4i-44-4004i−4i-2-222-2-2220012i3−2i31-1-1−2i2i−2i2i−2323000000000000000−i3i30i−i3−30000000000000000000000000
χ604-44-44−4i4i-44-400−4i4i4-2-424-2-4200-200-222−4i4i2i−2i000000000000000000002i−2i000000000000000000000000000
χ614-44-44−4i4i-44-400−4i4i-2-222-2-222001−2i32i31-1-12i−2i2i−2i−2323000000000000000i3−i30−ii3−30000000000000000000000000
χ624-44-44−4i4i-44-400−4i4i-2-222-2-2220012i3−2i31-1-12i−2i2i−2i23−23000000000000000−i3i30−ii−330000000000000000000000000
χ634-4-444004-4-4000044-4-4-4-44400400-4-4400000000000000000000000000000000000000000000000000000
χ644-4-444004-4-400004-2-42-424-200-20022-200000000000000000000000000000000000000000000000−2i32i30000
χ654-4-444004-4-400004-2-42-424-200-20022-2000000000000000000000000000000000000000000000002i3−2i30000
χ664-4-444004-4-40000-242-42-4-2400-20022-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ674-4-444004-4-40000-242-42-4-2400-20022-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-300000000000000220000000000000000000220200-1-100-1-1000000000-1-10
χ696666-366-3-3-366-3-300000000-3-300000000000000-2-20000000000000000000-2-20-200110011000000000110
χ706666-366-3-3-3-6-6-3-30000000033000000000000002200000000000000000002-20-200-1-100-1-1000000000110
χ716666-366-3-3-3-6-6-3-3000000003300000000000000-2-20000000000000000000-220200110011000000000-1-10
χ726666-3-6-6-3-3-36-63300000000-3300000000000000220000000000000000000-220-200-1-100110000000001-10
χ736666-3-6-6-3-3-36-63300000000-3300000000000000-2-200000000000000000002-202001100-1-1000000000-110
χ746666-3-6-6-3-3-3-6633000000003-300000000000000220000000000000000000-2-20200-1-10011000000000-110
χ756666-3-6-6-3-3-3-6633000000003-300000000000000-2-20000000000000000000220-2001100-1-10000000001-10
χ7688-8-8800-8-880000-4-4-4-4444400200-22-200000000000000000000000000000000000000000000000000000
χ778-8-888008-8-80000-4-44444-4-400200-2-2200000000000000000000000000000000000000000000000000000
χ781212-12-12-60066-600000000000000000000000000004-40000000000000000000000000-220000000000000000
χ791212-12-12-60066-60000000000000000000000000000-4400000000000000000000000002-20000000000000000
χ8012-1212-12-612i−12i6-6600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6−12i12i6-66006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-600-6660000000000000000000000000000000000000000000000000000000000023−23000000000000
χ8312-12-1212-600-66600000000000000000000000000000000000000000000000000000000000−2323000000000000

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