Finite Group Databasebeta

← Group #13147921

Character table — Group #13147921

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666121212124412121212336666663666121212121212121212121212121212121212121212121212224422224444446666121212126661212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1
χ511111111111111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-1-11-11-111-1-111-1-111-11-1-11-1
χ611111111111111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-11-1-11-1111-1-111-1-1-1-11-111-11
χ711111111111111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-111-1-111-11-1-1111-1
χ811111111111111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-11-111-1-1-111-1-1111-111-1-1-11
χ911111-1-1111-1-1-1-11-111-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-11-1-1-11-111111-1-1-1-111-1-11-1-11
χ1011111-1-1111-1-1-1-11-111-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-11-11-11-11111-1-1-1-1-1-111-111-1
χ1111111-1-1111-1-1-1-11-111-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-111-111-1-1-1-1-11111-11-11-11-11
χ1211111-1-1111-1-1-1-11-111-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-111-1-11-1-1-1-111111-11-11-11-1
χ1311111-1-1111-1-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1-111-1-1-1-111111-1-11-1-1
χ1411111-1-1111-1-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111111-1-1-1-111-1-1-111-111
χ1511111-1-1111-1-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-111-1-11111-1-1-11111-1-1-1
χ1611111-1-1111-1-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-111-111-1-1-1-11111-1-11-1-1-1-1111
χ17222222222222222222222-1-1-1222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000220002200000000000-1-1000-1-1
χ18222222222222222222222-1-1-1222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-2-2000-2-2000000000001100011
χ1922222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000220002200000000-100-1-1-100
χ2022222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000-2-2000-2-20000000010011100
χ2122222222222222-2-2-2-2-2-22-1-1-1222-1-1-1-1-1-1-11122-2-2-2-211-1-1-1-111111111000002-20002-200000000000-11000-11
χ2222222222222222-2-2-2-2-2-22-1-1-1222-1-1-1-1-1-1-11122-2-2-2-211-1-1-1-11111111100000-22000-22000000000001-10001-1
χ2322222222222222-2-2-2-2-2-2-1222-1-1-12-1-1-1-122-2-2-1-11111-2-2-1-1-1-11111111100000002-20002-200000000-100-11100
χ2422222222222222-2-2-2-2-2-2-1222-1-1-12-1-1-1-122-2-2-1-11111-2-2-1-1-1-1111111110000000-22000-22000000001001-1-100
χ2522222-2-2222-2-2-2-22-222-2-22-1-1-1222-1-1-1-1-111-1-1-2-222-2-2111111-1-1-1-11111000002-2000-2200000000000-110001-1
χ2622222-2-2222-2-2-2-22-222-2-22-1-1-1222-1-1-1-1-111-1-1-2-222-2-2111111-1-1-1-1111100000-220002-2000000000001-1000-11
χ2722222-2-2222-2-2-2-22-222-2-2-1222-1-1-12-1-1-1-1-2-22211-1-111-2-21111-1-1-1-1111100000002-2000-2200000000-1001-1100
χ2822222-2-2222-2-2-2-22-222-2-2-1222-1-1-12-1-1-1-1-2-22211-1-111-2-21111-1-1-1-111110000000-220002-200000000100-11-100
χ2922222-2-2222-2-2-2-2-22-2-2222-1-1-1222-1-1-1-1-11111-2-2-2-222-1-111111111-1-1-1-10000022000-2-200000000000-1-100011
χ3022222-2-2222-2-2-2-2-22-2-2222-1-1-1222-1-1-1-1-11111-2-2-2-222-1-111111111-1-1-1-100000-2-2000220000000000011000-1-1
χ3122222-2-2222-2-2-2-2-22-2-222-1222-1-1-12-1-1-1-1-2-2-2-21111-1-12211111111-1-1-1-1000000022000-2-200000000-10011-100
χ3222222-2-2222-2-2-2-2-22-2-222-1222-1-1-12-1-1-1-1-2-2-2-21111-1-12211111111-1-1-1-10000000-2-20002200000000100-1-1100
χ3322-2-222i−2i2-2-22i2i−2i−2i000000222-22-2-2-222-2-22i−2i002i−2i0000002i2i−2i−2i000000002-22i−2i00000000002-2002i−2i0000000000
χ3422-2-222i−2i2-2-22i2i−2i−2i000000222-22-2-2-222-2-22i−2i002i−2i0000002i2i−2i−2i00000000-22−2i2i0000000000-2200−2i2i0000000000
χ3522-2-22−2i2i2-2-2−2i−2i2i2i000000222-22-2-2-222-2-2−2i2i00−2i2i000000−2i−2i2i2i000000002-2−2i2i00000000002-200−2i2i0000000000
χ3622-2-22−2i2i2-2-2−2i−2i2i2i000000222-22-2-2-222-2-2−2i2i00−2i2i000000−2i−2i2i2i00000000-222i−2i0000000000-22002i−2i0000000000
χ3744444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ3844444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-222-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ3944444-4-4444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2111122-2-222-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4044444-4-4444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-2111122222222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4144-4-444i−4i4-4-44i4i−4i−4i0000004-2-224-4-42-2-222−2i2i004i−4i000000−2i−2i2i2i00000000000000000000000000000000000000
χ4244-4-444i−4i4-4-44i4i−4i−4i000000-244-4-222-4-2-2224i−4i00−2i2i000000−2i−2i2i2i00000000000000000000000000000000000000
χ4344-4-444i−4i4-4-44i4i−4i−4i000000-2-2-22-222211-1-1−2i2i00−2i2i000000ii−i−i33-3-33i3i−3i−3i000000000000000000000000000000
χ4444-4-444i−4i4-4-44i4i−4i−4i000000-2-2-22-222211-1-1−2i2i00−2i2i000000ii−i−i-3-333−3i−3i3i3i000000000000000000000000000000
χ4544-4-44−4i4i4-4-4−4i−4i4i4i0000004-2-224-4-42-2-2222i−2i00−4i4i0000002i2i−2i−2i00000000000000000000000000000000000000
χ4644-4-44−4i4i4-4-4−4i−4i4i4i000000-244-4-222-4-2-222−4i4i002i−2i0000002i2i−2i−2i00000000000000000000000000000000000000
χ4744-4-44−4i4i4-4-4−4i−4i4i4i000000-2-2-22-222211-1-12i−2i002i−2i000000−i−iii33-3-3−3i−3i3i3i000000000000000000000000000000
χ4844-4-44−4i4i4-4-4−4i−4i4i4i000000-2-2-22-222211-1-12i−2i002i−2i000000−i−iii-3-3333i3i−3i−3i000000000000000000000000000000
χ494-44-4400-4-44000000000044-44-44-4-44-44-4000000000000000000000000000000000000000000000000000000
χ504-44-4400-4-4400000000004-22-2-44-42-22-220023−2300000000000023−2323−230000000000000000000000000000000000
χ514-44-4400-4-4400000000004-22-2-44-42-22-2200−2323000000000000−2323−23230000000000000000000000000000000000
χ524-44-4400-4-440000000000-24-442-22-4-22-220000000023−23000000000023−2323−23000000000000000000000000000000
χ534-44-4400-4-440000000000-24-442-22-4-22-2200000000−23230000000000−2323−2323000000000000000000000000000000
χ544-44-4400-4-440000000000-2-22-22-2221-11-10023−23000023−23003-33-3−33−33−33−33000000000000000000000000000000
χ554-44-4400-4-440000000000-2-22-22-2221-11-10023−230000−232300-33-33−33−333−33−3000000000000000000000000000000
χ564-44-4400-4-440000000000-2-22-22-2221-11-100−2323000023−2300-33-333−33−3−33−33000000000000000000000000000000
χ574-44-4400-4-440000000000-2-22-22-2221-11-100−23230000−2323003-33-33−33−33−33−3000000000000000000000000000000
χ584-4-44400-44-4000000000044-4-4-4-4444-4-44000000000000000000000000000000000000000000000000000000
χ594-4-44400-44-400000000004-222-4-44-2-222-20000000000−2i32i300000000−2i32i32i3−2i3000000000000000000000000000000
χ604-4-44400-44-400000000004-222-4-44-2-222-200000000002i3−2i3000000002i3−2i3−2i32i3000000000000000000000000000000
χ614-4-44400-44-40000000000-24-4-422-24-222-200000023−230000000023−23−23230000000000000000000000000000000000
χ624-4-44400-44-40000000000-24-4-422-24-222-2000000−232300000000−232323−230000000000000000000000000000000000
χ634-4-44400-44-40000000000-2-22222-2-21-1-1100000023−2300−2i32i3−3i3i3i−3i−333−3i3−i3−i3i3000000000000000000000000000000
χ644-4-44400-44-40000000000-2-22222-2-21-1-1100000023−23002i3−2i33i−3i−3i3i−333−3−i3i3i3−i3000000000000000000000000000000
χ654-4-44400-44-40000000000-2-22222-2-21-1-11000000−232300−2i32i33i−3i−3i3i3−3−33i3−i3−i3i3000000000000000000000000000000
χ664-4-44400-44-40000000000-2-22222-2-21-1-11000000−2323002i3−2i3−3i3i3i−3i3−3−33−i3i3i3−i3000000000000000000000000000000
χ676666-366-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022222000020000-1-1-1-1-1-1-1-100000000
χ686666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-2-20000-200001111111100000000
χ696666-366-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000002222-20000-20000-1-111-1-11100000000
χ706666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-2200002000011-1-111-1-100000000
χ716666-3-6-6-3-3-333336-6-3-33300000000000000000000000000000000000022-2-220000-20000-1-1-1-1111100000000
χ726666-3-6-6-3-3-333336-6-3-333000000000000000000000000000000000000-2-222-20000200001111-1-1-1-100000000
χ736666-3-6-6-3-3-33333-6633-3-300000000000000000000000000000000000022-2-2-2000020000-1-11111-1-100000000
χ746666-3-6-6-3-3-33333-6633-3-3000000000000000000000000000000000000-2-22220000-2000011-1-1-1-11100000000
χ7566-6-6-36i−6i-333−3i−3i3i3i00−3i33i333−330000000000000000000000000000000000002-22i−2i0000000000-11−i3i3−ii3−300000000
χ7666-6-6-36i−6i-333−3i−3i3i3i00−3i33i333−33000000000000000000000000000000000000-22−2i2i00000000001-1i3−i3i−i−3300000000
χ7766-6-6-36i−6i-333−3i−3i3i3i003i3−3i3−33330000000000000000000000000000000000002-22i−2i0000000000-11i3−i3−ii−3300000000
χ7866-6-6-36i−6i-333−3i−3i3i3i003i3−3i3−3333000000000000000000000000000000000000-22−2i2i00000000001-1−i3i3i−i3−300000000
χ7966-6-6-3−6i6i-3333i3i−3i−3i00−3i33i3−33330000000000000000000000000000000000002-2−2i2i0000000000-11−i3i3i−i−3300000000
χ8066-6-6-3−6i6i-3333i3i−3i−3i00−3i33i3−3333000000000000000000000000000000000000-222i−2i00000000001-1i3−i3−ii3−300000000
χ8166-6-6-3−6i6i-3333i3i−3i−3i003i3−3i333−330000000000000000000000000000000000002-2−2i2i0000000000-11i3−i3i−i3−300000000
χ8266-6-6-3−6i6i-3333i3i−3i−3i003i3−3i333−33000000000000000000000000000000000000-222i−2i00000000001-1−i3i3−ii−3300000000
χ8312-1212-12-60066-6−6i36i3−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-60066-66i3−6i36i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000000000

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