Finite Group Databasebeta

← Group #13166531

Character table — Group #13166531

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112224444661244888161616162424484488816161616242448991818183636363654541089918181836363636545410899181818363636365454108
order12346266128823631266661224246363126666122424622646266128824412412412121288444124124121212884
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111-1-1-1111111111-1-1-1111111111-1-1-1111111111-1-1-1111111111-1-1-1111111111-1-1-1
χ311111-1-1-1111-111111-1-1-1111-111111-1-1-1111-111111-1-1-1111-111111-1-1-1111-111111-1-1-1111-1
χ411111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-11
χ5222-22000-2000222-22000-2000222-22000-2000222-22000-2000222-22000-2000222-22000-2000
χ622-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-1000
χ722-12-1-211-100022-12-1-211-100022-12-1-211-100022-12-1-211-100022-12-1-211-100022-12-1-211-1000
χ822-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i31000
χ922-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i31000
χ102-220-200002−202-220-200002−202-220-200002−202-220-200002−202-220-200002−202-220-200002−20
χ112-220-20000−2202-220-20000−2202-220-20000−2202-220-20000−2202-220-20000−2202-220-20000−220
χ124-4-20200000004-4-20200000004-4-20200000004-4-20200000004-4-20200000004-4-2020000000
χ13111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ14111111111-1-1-1111111111-1-1-1111111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111
χ1511111-1-1-1111-111111-1-1-1111-111111-1-1-1111-111111-1-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1-1-1111-1-1-11
χ1611111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-11-1-1-1-1-1111-111-1-1-1-1-1-1111-111-1
χ17222-22000-2000222-22000-2000222-22000-2000222-22000-2000-2-2-22-20002000-2-2-22-20002000
χ1822-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-1000-2-21-21-2111000-2-21-21-2111000
χ1922-12-1-211-100022-12-1-211-100022-12-1-211-100022-12-1-211-1000-2-21-212-1-11000-2-21-212-1-11000
χ2022-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i31000-2-21210i3−i3-1000-2-21210i3−i3-1000
χ2122-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i31000-2-21210−i3i3-1000-2-21210−i3i3-1000
χ222-220-200002−202-220-200002−202-220-200002−202-220-200002−20-22-2020000−220-22-2020000−220
χ232-220-20000−2202-220-20000−2202-220-20000−2202-220-20000−220-22-20200002−20-22-20200002−20
χ244-4-20200000004-4-20200000004-4-20200000004-4-2020000000-4420-20000000-4420-20000000
χ25111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i
χ26111111111-1-1-1111111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiii
χ2711111-1-1-1111-111111-1-1-1111-111111-1-1-1111-1-1-1-1-1-1111-1-1-11iiiii−i−i−iiii−i−i−i−i−i−iiii−i−i−ii
χ2811111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-11-1-1-1-1-1111-111-1iiiii−i−i−ii−i−ii−i−i−i−i−iiii−iii−i
χ29222-22000-2000222-22000-2000222-22000-2000-2-2-22-200020002i2i2i−2i2i000−2i000−2i−2i−2i2i−2i0002i000
χ3022-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-1000-2-21-21-21110002i2i−i2i−i2i−i−i−i000−2i−2ii−2ii−2iiii000
χ3122-12-1-211-100022-12-1-211-100022-12-1-211-1000-2-21-212-1-110002i2i−i2i−i−2iii−i000−2i−2ii−2ii2i−i−ii000
χ3222-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i31000-2-21210i3−i3-10002i2i−i−2i−i03−3i000−2i−2ii2ii0−33−i000
χ3322-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i31000-2-21210−i3i3-10002i2i−i−2i−i0−33i000−2i−2ii2ii03−3−i000
χ342-220-200002−202-220-200002−202-220-200002−20-22-2020000−2202i−2i2i0−2i0000i2−i20−2i2i−2i02i0000−i2i20
χ352-220-20000−2202-220-20000−2202-220-20000−220-22-20200002−202i−2i2i0−2i0000−i2i20−2i2i−2i02i0000i2−i20
χ364-4-20200000004-4-20200000004-4-2020000000-4420-200000004i−4i−2i02i0000000−4i4i2i0−2i0000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii
χ38111111111-1-1-1111111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i
χ3911111-1-1-1111-111111-1-1-1111-111111-1-1-1111-1-1-1-1-1-1111-1-1-11−i−i−i−i−iiii−i−i−iiiiiii−i−i−iiii−i
χ4011111-1-1-11-1-1111111-1-1-11-1-1111111-1-1-11-1-11-1-1-1-1-1111-111-1−i−i−i−i−iiii−iii−iiiiii−i−i−ii−i−ii
χ41222-22000-2000222-22000-2000222-22000-2000-2-2-22-20002000−2i−2i−2i2i−2i0002i0002i2i2i−2i2i000−2i000
χ4222-12-12-1-1-100022-12-12-1-1-100022-12-12-1-1-1000-2-21-21-2111000−2i−2ii−2ii−2iiii0002i2i−i2i−i2i−i−i−i000
χ4322-12-1-211-100022-12-1-211-100022-12-1-211-1000-2-21-212-1-11000−2i−2ii−2ii2i−i−ii0002i2i−i2i−i−2iii−i000
χ4422-1-2-10−i3i3100022-1-2-10−i3i3100022-1-2-10−i3i31000-2-21210i3−i3-1000−2i−2ii2ii0−33−i0002i2i−i−2i−i03−3i000
χ4522-1-2-10i3−i3100022-1-2-10i3−i3100022-1-2-10i3−i31000-2-21210−i3i3-1000−2i−2ii2ii03−3−i0002i2i−i−2i−i0−33i000
χ462-220-200002−202-220-200002−202-220-200002−20-22-2020000−220−2i2i−2i02i0000−i2i202i−2i2i0−2i0000i2−i20
χ472-220-20000−2202-220-20000−2202-220-20000−220-22-20200002−20−2i2i−2i02i0000i2−i202i−2i2i0−2i0000−i2i20
χ484-4-20200000004-4-20200000004-4-2020000000-4420-20000000−4i4i2i0−2i00000004i−4i−2i02i0000000
χ49444444444444111111111111-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ50444444444-4-4-4111111111-1-1-1-2-2-2-2-2-2-2-2-2222000000000000000000000000000000000000
χ5144444-4-4-4444-411111-1-1-1111-1-2-2-2-2-2222-2-2-22000000000000000000000000000000000000
χ5244444-4-4-44-4-4411111-1-1-11-1-11-2-2-2-2-2222-222-2000000000000000000000000000000000000
χ53888-88000-8000222-22000-2000-4-4-44-40004000000000000000000000000000000000000000
χ5488-48-48-4-4-400022-12-12-1-1-1000-4-42-42-4222000000000000000000000000000000000000000
χ5588-48-4-844-400022-12-1-211-1000-4-42-424-2-22000000000000000000000000000000000000000
χ5688-4-8-40−4i34i3400022-1-2-10−i3i31000-4-424202i3−2i3-2000000000000000000000000000000000000000
χ5788-4-8-404i3−4i3400022-1-2-10i3−i31000-4-42420−2i32i3-2000000000000000000000000000000000000000
χ588-880-8000042−4202-220-200002−20-44-4040000−22220000000000000000000000000000000000000
χ598-880-80000−424202-220-20000−220-44-404000022−220000000000000000000000000000000000000
χ6016-16-80800000004-4-2020000000-8840-40000000000000000000000000000000000000000000
χ61444444444444-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ62444444444-4-4-4-2-2-2-2-2-2-2-2-2222111111111-1-1-1000000000000000000000000000000000000
χ6344444-4-4-4444-4-2-2-2-2-2222-2-2-2211111-1-1-1111-1000000000000000000000000000000000000
χ6444444-4-4-44-4-44-2-2-2-2-2222-222-211111-1-1-11-1-11000000000000000000000000000000000000
χ65888-88000-8000-4-4-44-40004000222-22000-2000000000000000000000000000000000000000
χ6688-48-48-4-4-4000-4-42-42-422200022-12-12-1-1-1000000000000000000000000000000000000000
χ6788-48-4-844-4000-4-42-424-2-2200022-12-1-211-1000000000000000000000000000000000000000
χ6888-4-8-40−4i34i34000-4-424202i3−2i3-200022-1-2-10−i3i31000000000000000000000000000000000000000
χ6988-4-8-404i3−4i34000-4-42420−2i32i3-200022-1-2-10i3−i31000000000000000000000000000000000000000
χ708-880-8000042−420-44-4040000−222202-220-200002−20000000000000000000000000000000000000
χ718-880-80000−42420-44-404000022−2202-220-20000−220000000000000000000000000000000000000
χ7216-16-8080000000-8840-400000004-4-2020000000000000000000000000000000000000000000

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