Finite Group Databasebeta

← Group #71721

Character table — Group #71721

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order1222222234444444466666664412121212121212121212121222446666121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131-1-1111-1-11-1-11111-1-1-1-1-1-1111-11-1-1-1-1111111-1-11-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141-1-1111-1-11-1-11111-1-1-1-1-1-1111-11-1-1-1-1111111-1-11-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151-1-1111-1-11-1-11111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161-1-1111-1-11-1-11111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-22222222-2-222-2-222-2-2-2-2-2-20000000000000000000000000000
χ18222222222-2-2-2-2-2-2-2-2222222222-2-222-2-222-2-2-2-20000000000000000000000000000
χ1922222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2122222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-111-1-11111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2222222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-111-1-11111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2322222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-211111111-1-1-1-122-2-2-1-1-1-111110000000000000000
χ2422222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-211111111-1-1-1-1-2-2221111-1-1-1-10000000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211-1-111-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211-1-111-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2722-22-2-22-222i−2i2i−2i000022-2-22-2-2002i−2i002i−2i000000000000000000000000002−22−2−i2i2−i2i2
χ2822-22-2-22-222i−2i2i−2i000022-2-22-2-2002i−2i002i−2i00000000000000000000000000−22−22i2−i2i2−i2
χ2922-22-2-22-22−2i2i−2i2i000022-2-22-2-200−2i2i00−2i2i000000000000000000000000002−22−2i2−i2i2−i2
χ3022-22-2-22-22−2i2i−2i2i000022-2-22-2-200−2i2i00−2i2i00000000000000000000000000−22−22−i2i2−i2i2
χ3122-2-2-22-22200002-22-22-22-2-2-2200000000002-22-20000000000002i−2i2i−2i000000000000
χ3222-2-2-22-22200002-22-22-22-2-2-2200000000002-22-2000000000000−2i2i−2i2i000000000000
χ3322-2-2-22-2220000-22-222-22-2-2-220000000000-22-2200000000000000002-22-200000000
χ3422-2-2-22-2220000-22-222-22-2-2-220000000000-22-220000000000000000-22-2200000000
χ352-222-2-2-2222i−2i−2i2i0000-2-2222-2-2002i−2i00−2i2i00000000000000000000000000−i2i2i2−i2−222−2
χ362-222-2-2-2222i−2i−2i2i0000-2-2222-2-2002i−2i00−2i2i00000000000000000000000000i2−i2−i2i22−2−22
χ372-222-2-2-222−2i2i2i−2i0000-2-2222-2-200−2i2i002i−2i00000000000000000000000000−i2i2i2−i22−2−22
χ382-222-2-2-222−2i2i2i−2i0000-2-2222-2-200−2i2i002i−2i00000000000000000000000000i2−i2−i2i2−222−2
χ392-22-2-222-2200002-2-22-22-22-2-2200000000002-2-220000000000002-2-22000000000000
χ402-22-2-222-2200002-2-22-22-22-2-2200000000002-2-22000000000000-222-2000000000000
χ412-22-2-222-220000-222-2-22-22-2-220000000000-222-200000000000000002i−2i−2i2i00000000
χ422-22-2-222-220000-222-2-22-22-2-220000000000-222-20000000000000000−2i2i2i−2i00000000
χ432-2-2222-2-2222-2-2-2-222-2-2-2-2222-2222-2-2-2-222-2-2220000000000000000000000000000
χ442-2-2222-2-22-2-222-2-222-2-2-2-22222-2-2-22222-2-2-2-2220000000000000000000000000000
χ452-2-2222-2-2-122-2-222-2-21111-1-1-12-2-1-1-1-11111-1-1112-22-2-1-111-1-1110000000000000000
χ462-2-2222-2-2-122-2-222-2-21111-1-1-12-2-1-1-1-11111-1-111-22-2211-1-111-1-10000000000000000
χ472-2-2222-2-2-122-2-2-2-2221111-1-1-1-22-1-11111-1-111-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ482-2-2222-2-2-122-2-2-2-2221111-1-1-1-22-1-11111-1-111-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ492-2-2222-2-2-1-2-22222-2-21111-1-1-1-221111-1-1-1-1-1-1112-2-22-1-11111-1-10000000000000000
χ502-2-2222-2-2-1-2-22222-2-21111-1-1-1-221111-1-1-1-1-1-111-222-211-1-1-1-1110000000000000000
χ512-2-2222-2-2-1-2-222-2-2221111-1-1-12-211-1-1-1-11111-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ522-2-2222-2-2-1-2-222-2-2221111-1-1-12-211-1-1-1-11111-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ53444-44-4-4-44000000004-4-44-44-4000000000000000000000000000000000000000000
χ54444-44-4-4-4-200000000-222-22-22000023−230023−2300000000000000000000000000000000
χ55444-44-4-4-4-200000000-222-22-220000−232300−232300000000000000000000000000000000
χ5644-44-4-44-4-24i−4i4i−4i0000-2-222-22200−2i2i00−2i2i0000000000000000000000000000000000
χ5744-44-4-44-4-2−4i4i−4i4i0000-2-222-222002i−2i002i−2i0000000000000000000000000000000000
χ5844-4-4-44-44-200004-44-4-22-2222-20000000000-22-220000000000000000000000000000
χ5944-4-4-44-44-20000-44-44-22-2222-200000000002-22-20000000000000000000000000000
χ604-444-4-4-44-24i−4i−4i4i000022-2-2-22200−2i2i002i−2i0000000000000000000000000000000000
χ614-444-4-4-44-2−4i4i4i−4i000022-2-2-222002i−2i00−2i2i0000000000000000000000000000000000
χ624-44-4-444-4-200004-4-442-22-222-20000000000-222-20000000000000000000000000000
χ634-44-4-444-4-20000-444-42-22-222-200000000002-2-220000000000000000000000000000
χ644-4-4-44-444400000000-444-4-44-4000000000000000000000000000000000000000000
χ654-4-4-44-444-2000000002-2-222-22000023−2300−232300000000000000000000000000000000
χ664-4-4-44-444-2000000002-2-222-220000−23230023−2300000000000000000000000000000000

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