Finite Group Databasebeta

← Group #13146558

Character table — Group #13146558

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222222449912121212121212121818181818181824242424363636363636363636363636363636363636363636367272727272727272
order1223446661212443366121212122241212121266121222446688888888242424242424242466121224242424
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ51111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-11-11-111ii−i−iii−i−iiiii−i−i−i−i1-11-1ii−i−i
χ61111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-11-11-111−i−iii−i−iii−i−i−i−iiiii1-11-1−i−iii
χ71111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-11-1111ii−i−i−i−iii−i−i−i−iiiii-11-11ii−i−i
χ81111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-11-1111−i−iiiii−i−iiiii−i−i−i−i-11-11−i−iii
χ911-111-1-1-111-111111111-1-11-1-111-1-1-1-11-11-1-111-1i−ii−ii−ii−iii−i−iii−i−i1-1-11i−ii−i
χ1011-111-1-1-111-111111111-1-11-1-111-1-1-1-11-11-1-111-1−ii−ii−ii−ii−i−iii−i−iii1-1-11−ii−ii
χ1111-111-1-1-111-111111111-1-11-1-111-1-1-1-11-1-111-11-1i−ii−i−ii−ii−i−iii−i−iii-111-1i−ii−i
χ1211-111-1-1-111-111111111-1-11-1-111-1-1-1-11-1-111-11-1−ii−iii−ii−iii−i−iii−i−i-111-1−ii−ii
χ1311-11-11-1-11-11-1-11111-1-1111-11-1-111-1-1-1111-1-11-11-1-111-1-1111-1-1-1-11111-1-11-1-11
χ1411-11-11-1-11-11-1-11111-1-1111-11-1-111-1-1-1111-1-11-1-111-1-111-1-1-11111-1-111-1-1-111-1
χ1511-11-11-1-11-11-1-11111-1-1111-11-1-111-1-1-11-1-1111-11-1-11-111-1-1-11111-1-1-1-1111-1-11
χ1611-11-11-1-11-11-1-11111-1-1111-11-1-111-1-1-11-1-1111-1-111-11-1-1111-1-1-1-111-1-111-111-1
χ1722222222222-2-222222222-2-2-2-2-2-2-222220000-2-2000000000000000000000000
χ182222-2-2222-2-2222222-2-2-2-2-2-22222222-2-20000-2-2000000000000000000000000
χ1922-222-2-2-222-2-2-2222222-2-2-222-2-222-2-22-20000-22000000000000000000000000
χ2022-22-22-2-22-22222222-2-222-22-222-2-2-2-2-220000-22000000000000000000000000
χ2144444444444001-21-2-2-21100000001-21-200000022220000000000000000-1-1-1-1
χ2244444444444001-21-2-2-21100000001-21-2000000-2-2-2-200000000000000001111
χ234444444444400-21-2111-2-20000000-21-212222000000000000000000-1-1-1-10000
χ244444444444400-21-2111-2-20000000-21-21-2-2-2-200000000000000000011110000
χ254444-4-4444-4-4001-21-222-1-100000001-2-120000002i2i−2i−2i0000000000000000−i−iii
χ264444-4-4444-4-4001-21-222-1-100000001-2-12000000−2i−2i2i2i0000000000000000ii−i−i
χ274444-4-4444-4-400-21-21-1-1220000000-212-12-22-2000000000000000000-11-110000
χ284444-4-4444-4-400-21-21-1-1220000000-212-1-22-220000000000000000001-11-10000
χ2944-444-4-4-444-4001-21-2-2-2-1-10000000-12120000002i−2i2i−2i0000000000000000−ii−ii
χ3044-444-4-4-444-4001-21-2-2-2-1-10000000-1212000000−2i2i−2i2i0000000000000000i−ii−i
χ3144-444-4-4-444-400-21-21112200000002-1-2-12-2-22000000000000000000-111-10000
χ3244-444-4-4-444-400-21-21112200000002-1-2-1-222-20000000000000000001-1-110000
χ3344-44-44-4-44-44001-21-222110000000-12-1-20000002-2-220000000000000000-111-1
χ3444-44-44-4-44-44001-21-222110000000-12-1-2000000-222-200000000000000001-1-11
χ3544-44-44-4-44-4400-21-21-1-1-2-200000002-12122-2-2000000000000000000-1-1110000
χ3644-44-44-4-44-4400-21-21-1-1-2-200000002-121-2-22200000000000000000011-1-10000
χ374-4040000-4004i−4i44-4-400000004i−4i000000000000000000000000000000000000
χ384-4040000-400−4i4i44-4-40000000−4i4i000000000000000000000000000000000000
χ39666-366-3-3-3-3-32200000000222-1-1-1-100000000-1-1000000003−33−33−33−300000000
χ40666-366-3-3-3-3-32200000000222-1-1-1-100000000-1-100000000−33−33−33−3300000000
χ41666-366-3-3-3-3-3-2-200000000-2-2-21111000000001100002222-1-1-1-1-1-1-1-100000000
χ42666-366-3-3-3-3-3-2-200000000-2-2-2111100000000110000-2-2-2-21111111100000000
χ43666-3-6-6-3-3-3332200000000-2-22-1-1-1-1000000001100002i2i−2i−2i−i−i−i−iiiii00000000
χ44666-3-6-6-3-3-3332200000000-2-22-1-1-1-100000000110000−2i−2i2i2iiiii−i−i−i−i00000000
χ45666-3-6-6-3-3-333-2-20000000022-2111100000000-1-100000000−i3i3−i3i3i3−i3i3−i300000000
χ46666-3-6-6-3-3-333-2-20000000022-2111100000000-1-100000000i3−i3i3−i3−i3i3−i3i300000000
χ4766-6-36-633-3-3322000000002-2-2-1-11100000000-1100000000−i3i3i3−i3−i3i3i3−i300000000
χ4866-6-36-633-3-3322000000002-2-2-1-11100000000-1100000000i3−i3−i3i3i3−i3−i3i300000000
χ4966-6-36-633-3-33-2-200000000-22211-1-1000000001-100002i−2i2i−2i−i−iii−i−iii00000000
χ5066-6-36-633-3-33-2-200000000-22211-1-1000000001-10000−2i2i−2i2iii−i−iii−i−i00000000
χ5166-6-3-6633-33-32200000000-22-2-1-111000000001-100002-2-22-1-11111-1-100000000
χ5266-6-3-6633-33-32200000000-22-2-1-111000000001-10000-222-211-1-1-1-11100000000
χ5366-6-3-6633-33-3-2-2000000002-2211-1-100000000-11000000003−3−33−333−300000000
χ5466-6-3-6633-33-3-2-2000000002-2211-1-100000000-1100000000−333−33−3−3300000000
χ558-8080000-800002-4-24006i−6i00000000000000000000000000000000000000000
χ568-8080000-800002-4-2400−6i6i00000000000000000000000000000000000000000
χ578-8080000-80000-424-26i−6i0000000000000000000000000000000000000000000
χ588-8080000-80000-424-2−6i6i0000000000000000000000000000000000000000000
χ5912-120-600−6i36i36004i−4i00000000000−2i2i23−230000000000000000000000000000000000
χ6012-120-600−6i36i3600−4i4i000000000002i−2i−23230000000000000000000000000000000000
χ6112-120-6006i3−6i36004i−4i00000000000−2i2i−23230000000000000000000000000000000000
χ6212-120-6006i3−6i3600−4i4i000000000002i−2i23−230000000000000000000000000000000000

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