Finite Group Databasebeta

← Group #13139192

Character table — Group #13139192

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222222244444444666699121212121212121212121818181818181824242424242424242424363636363636363636363636363636367272727272727272
order122344612126881224242424336622366612121212121224466121261224242424242424244444688888812242424241212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-11111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111-1-11111111111-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-111-1-1-1-1-1-1-111-1-111
χ51111111111-1-11-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ61111111111-1-11-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111
χ71111111111-1-11-1-1-1-11111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-111-1-111-1111111-1-1-1-111
χ81111111111-1-11-1-1-1-11111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11111-1-1-11111-1-11111-1-1
χ91111-1-11-1-11i−i-1ii−i−i1111111111-1-1-1-1-1-11-1-111-1-11-1iiii−i−i−i−i1-11-11i−ii−ii−i-1ii−i−i1-11-1i−ii−i
χ101111-1-11-1-11i−i-1ii−i−i1111111111-1-1-1-1-1-11-1-111-1-11-1iiii−i−i−i−i-11-111i−i−ii−ii-1ii−i−i-11-11−ii−ii
χ111111-1-11-1-11i−i-1ii−i−i1111-1-11111-1-1-1-1-1-1-111-1-1111-1iiii−i−i−i−i1-1-11-1−iii−i−ii1−i−iii1-1-11i−i−ii
χ121111-1-11-1-11i−i-1ii−i−i1111-1-11111-1-1-1-1-1-1-111-1-1111-1iiii−i−i−i−i-111-1-1−ii−iii−i1−i−iii-111-1−iii−i
χ131111-1-11-1-11−ii-1−i−iii1111111111-1-1-1-1-1-11-1-111-1-11-1−i−i−i−iiiii1-11-11−ii−ii−ii-1−i−iii1-11-1−ii−ii
χ141111-1-11-1-11−ii-1−i−iii1111111111-1-1-1-1-1-11-1-111-1-11-1−i−i−i−iiiii-11-111−iii−ii−i-1−i−iii-11-11i−ii−i
χ151111-1-11-1-11−ii-1−i−iii1111-1-11111-1-1-1-1-1-1-111-1-1111-1−i−i−i−iiiii1-1-11-1i−i−iii−i1ii−i−i1-1-11−iii−i
χ161111-1-11-1-11−ii-1−i−iii1111-1-11111-1-1-1-1-1-1-111-1-1111-1−i−i−i−iiiii-111-1-1i−ii−i−ii1ii−i−i-111-1i−i−ii
χ17222222222222222222-12-100-12-1-12-1-1-12-10000000-1-12-1-1-12-1-1-1002200000220000000-1-100-1-1
χ18222222222222222222-12-100-12-1-12-1-1-12-10000000-1-12-1-1-12-1-1-100-2-200000-2-20000000110011
χ1922222222222222222-12-1200-1-12-1-12-1-1-120000000-1-1-12-1-1-12-1-12200000220000000-1-100-1-100
χ2022222222222222222-12-1200-1-12-1-12-1-1-120000000-1-1-12-1-1-12-1-1-2-200000-2-2000000011001100
χ212222222222-2-22-2-2-2-22-12-100-12-1-12-1-1-12-10000000-1-1-2111-2111002200000-2-20000000-1-10011
χ222222222222-2-22-2-2-2-22-12-100-12-1-12-1-1-12-10000000-1-1-2111-211100-2-2000002200000001100-1-1
χ232222222222-2-22-2-2-2-2-12-1200-1-12-1-12-1-1-120000000-1-11-2111-2112200000-2-20000000-1-1001100
χ242222222222-2-22-2-2-2-2-12-1200-1-12-1-12-1-1-120000000-1-11-2111-211-2-2000002200000001100-1-100
χ252222-2-22-2-222i−2i-22i2i−2i−2i2-12-100-12-1-1-2111-210000000-112i−i−i−i−2iiii002-2000002i−2i0000000-1100−ii
χ262222-2-22-2-222i−2i-22i2i−2i−2i2-12-100-12-1-1-2111-210000000-112i−i−i−i−2iiii00-2200000−2i2i00000001-100i−i
χ272222-2-22-2-222i−2i-22i2i−2i−2i-12-1200-1-12-11-2111-20000000-11−i2i−i−ii−2iii2-2000002i−2i0000000-1100−ii00
χ282222-2-22-2-222i−2i-22i2i−2i−2i-12-1200-1-12-11-2111-20000000-11−i2i−i−ii−2iii-2200000−2i2i00000001-100i−i00
χ292222-2-22-2-22−2i2i-2−2i−2i2i2i2-12-100-12-1-1-2111-210000000-11−2iiii2i−i−i−i002-200000−2i2i0000000-1100i−i
χ302222-2-22-2-22−2i2i-2−2i−2i2i2i2-12-100-12-1-1-2111-210000000-11−2iiii2i−i−i−i00-22000002i−2i00000001-100−ii
χ312222-2-22-2-22−2i2i-2−2i−2i2i2i-12-1200-1-12-11-2111-20000000-11i−2iii−i2i−i−i2-200000−2i2i0000000-1100i−i00
χ322222-2-22-2-22−2i2i-2−2i−2i2i2i-12-1200-1-12-11-2111-20000000-11i−2iii−i2i−i−i-22000002i−2i00000001-100−ii00
χ3322-222-2222-200-200002222222-2-222222-2-2-22-22222-2-2000000000000-2000000-2000000000000
χ3422-222-2222-200-200002222-2-22-2-222222-2-22-22-2-2-2-2-2-200000000000020000002000000000000
χ3522-22-222-2-2-200200002222222-2-22-2-2-2-222-2-2222-2-2-22000000000000-20000002000000000000
χ3622-22-222-2-2-200200002222-2-22-2-22-2-2-2-22222-2-2-222-220000000000002000000-2000000000000
χ3744444444444444444-2-2-2-2001-2-21-2-211-2-2000000011-2-211-2-211000000000000000000000000
χ384444444444-4-44-4-4-4-4-2-2-2-2001-2-21-2-211-2-200000001122-1-122-1-1000000000000000000000000
χ394444-4-44-4-444i−4i-44i4i−4i−4i-2-2-2-2001-2-2122-1-12200000001-1−2i−2iii2i2i−i−i000000000000000000000000
χ404444-4-44-4-44−4i4i-4−4i−4i4i4i-2-2-2-2001-2-2122-1-12200000001-12i2i−i−i−2i−2iii000000000000000000000000
χ4144-444-4444-400-400004-24-200-2-42-24-2-2-2-4200000002200000000000000000000000000000000
χ4244-444-4444-400-40000-24-2400-22-4-2-24-2-22-400000002200000000000000000000000000000000
χ4344-444-4444-400-40000-2-2-2-2001221-2-211220000000-1-1003-3003-3000000000000000000000000
χ4444-444-4444-400-40000-2-2-2-2001221-2-211220000000-1-100-3300-33000000000000000000000000
χ4544-44-444-4-4-400400004-24-200-2-42-2-42224-200000002-200000000000000000000000000000000
χ4644-44-444-4-4-40040000-24-2400-22-4-22-422-2400000002-200000000000000000000000000000000
χ4744-44-444-4-4-40040000-2-2-2-200122122-1-1-2-20000000-11003i−3i00−3i3i000000000000000000000000
χ4844-44-444-4-4-40040000-2-2-2-200122122-1-1-2-20000000-1100−3i3i003i−3i000000000000000000000000
χ494-40400-4000000000044-4-44-4400-40000000004-4000000000000000000000000000000000000
χ504-40400-4000000000044-4-4-44400-4000000000-44000000000000000000000000000000000000
χ51666-366-3-3-3-366-3-3-3-3-30000220000000000222-1-1-1-100000000000000-1220000-1-1-1-1-100000000
χ52666-366-3-3-3-366-3-3-3-3-30000-2-20000000000-2-2-21111000000000000001-2-200001111100000000
χ53666-366-3-3-3-3-6-6-333330000220000000000222-1-1-1-100000000000000-1-2-20000-1111100000000
χ54666-366-3-3-3-3-6-6-333330000-2-20000000000-2-2-211110000000000000012200001-1-1-1-100000000
χ55666-3-6-6-333-36i−6i3−3i−3i3i3i00002200000000002-2-2-1-11100000000000000-12i−2i00001−i−iii00000000
χ56666-3-6-6-333-36i−6i3−3i−3i3i3i0000-2-20000000000-22211-1-1000000000000001−2i2i0000-1ii−i−i00000000
χ57666-3-6-6-333-3−6i6i33i3i−3i−3i00002200000000002-2-2-1-11100000000000000-1−2i2i00001ii−i−i00000000
χ58666-3-6-6-333-3−6i6i33i3i−3i−3i0000-2-20000000000-22211-1-10000000000000012i−2i0000-1−i−iii00000000
χ5966-6-36-6-3-3-33003−3i33i3−3i33i30000220000000000-22-2-1-1-1-10000000000000010000001−i3i3−i3i300000000
χ6066-6-36-6-3-3-33003−3i33i3−3i33i30000-2-200000000002-22111100000000000000-1000000-1i3−i3i3−i300000000
χ6166-6-36-6-3-3-330033i3−3i33i3−3i30000220000000000-22-2-1-1-1-10000000000000010000001i3−i3i3−i300000000
χ6266-6-36-6-3-3-330033i3−3i33i3−3i30000-2-200000000002-22111100000000000000-1000000-1−i3i3−i3i300000000
χ6366-6-3-66-333300-333−33−33330000220000000000-2-22-1-111000000000000001000000-13−3−3300000000
χ6466-6-3-66-333300-333−33−33330000-2-2000000000022-211-1-100000000000000-10000001−333−300000000
χ6566-6-3-66-333300-3−333333−330000220000000000-2-22-1-111000000000000001000000-1−333−300000000
χ6666-6-3-66-333300-3−333333−330000-2-2000000000022-211-1-100000000000000-100000013−3−3300000000
χ678-80800-800000000008-4-8400-400400000000000000000000000000000000000000000000000
χ688-80800-80000000000-484-800-400400000000000000000000000000000000000000000000000
χ698-80800-80000000000-4-44400200-2006i−6i0000000000000000000000000000000000000000000
χ708-80800-80000000000-4-44400200-200−6i6i0000000000000000000000000000000000000000000
χ7112-120-600663−630000000000004-40000000000000-2223−230000000000000000000000000000000000
χ7212-120-600663−63000000000000-4400000000000002-2−23230000000000000000000000000000000000
χ7312-120-6006−63630000000000004-40000000000000-22−23230000000000000000000000000000000000
χ7412-120-6006−6363000000000000-4400000000000002-223−230000000000000000000000000000000000

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