Finite Group Databasebeta

← Group #69556

Character table — Group #69556

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order12222222344444444666666644121212121212121212121212444412121212121212122222444488888888
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
χ5111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91-1-111-1-11111-111-1-1-1-1-1111-1-11-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101-1-111-1-11111-111-1-1-1-1-1111-1-11-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ111-1-111-1-11111-111-1-1-1-1-1111-1-11-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ121-1-111-1-11111-111-1-1-1-1-1111-1-11-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ131-1-111-1-11111-1-1-111-1-1-1111-1-1-1111-1-1-1-1-1-11111i−i−iiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ141-1-111-1-11111-1-1-111-1-1-1111-1-1-1111-1-1-1-1-1-11111i−i−iiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ151-1-111-1-11111-1-1-111-1-1-1111-1-1-1111-1-1-1-1-1-11111−iii−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ161-1-111-1-11111-1-1-111-1-1-1111-1-1-1111-1-1-1-1-1-11111−iii−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222-2-2-22222-22222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-222-2-2220000000000000000000000000000
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
χ2122222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ2222222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ2322222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2422222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ272222-2-2-2-222-220000-2222-2-2-2-2002-22-2000000000000000000002-22-2000000000000
χ282222-2-2-2-222-220000-2222-2-2-2-2002-22-200000000000000000000-22-22000000000000
χ292222-2-2-2-22-22-200002222-2-2-2-200-22-220000000000000000000000002i−2i2i−2i00000000
χ302222-2-2-2-22-22-200002222-2-2-2-200-22-22000000000000000000000000−2i2i−2i2i00000000
χ3122-2-222-2-220002i−2i2i−2i02-2-22-22-20000002i−2i002i−2i00000000000000000000002−22−2−i2i2−i2i2
χ3222-2-222-2-220002i−2i2i−2i02-2-22-22-20000002i−2i002i−2i0000000000000000000000−22−22i2−i2i2−i2
χ3322-2-222-2-22000−2i2i−2i2i02-2-22-22-2000000−2i2i00−2i2i00000000000000000000002−22−2i2−i2i2−i2
χ3422-2-222-2-22000−2i2i−2i2i02-2-22-22-2000000−2i2i00−2i2i0000000000000000000000−22−22−i2i2−i2i2
χ352-22-22-22-220002i−2i−2i2i0-22-22-2-220000002i−2i00−2i2i0000000000000000000000−i2i2i2−i2−222−2
χ362-22-22-22-220002i−2i−2i2i0-22-22-2-220000002i−2i00−2i2i0000000000000000000000i2−i2−i2i22−2−22
χ372-22-22-22-22000−2i2i2i−2i0-22-22-2-22000000−2i2i002i−2i0000000000000000000000−i2i2i2−i22−2−22
χ382-22-22-22-22000−2i2i2i−2i0-22-22-2-22000000−2i2i002i−2i0000000000000000000000i2−i2−i2i2−222−2
χ392-2-222-2-222-2-2222-2-22-2-2222-2-2-22-2-22222-2-2-2-2220000000000000000000000000000
χ402-2-222-2-222-2-22-2-2222-2-2222-2-22-2-2-222-2-22222-2-20000000000000000000000000000
χ412-2-222-2-22-122-222-2-2-211-1-1-1112-2-1-111-1-1-1-111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ422-2-222-2-22-122-222-2-2-211-1-1-1112-2-1-111-1-1-1-11111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ432-2-222-2-22-122-2-2-222-211-1-1-111-22-1-1111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ442-2-222-2-22-122-2-2-222-211-1-1-111-22-1-1111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ452-2-222-2-22-1-2-2222-2-2211-1-1-111-2211-1-1-1-11111-1-100003−3−333−3−330000000000000000
χ462-2-222-2-22-1-2-2222-2-2211-1-1-111-2211-1-1-1-11111-1-10000−333−3−333−30000000000000000
χ472-2-222-2-22-1-2-22-2-222211-1-1-1112-211-1-111-1-1-1-11100003−3−33−333−30000000000000000
χ482-2-222-2-22-1-2-22-2-222211-1-1-1112-211-1-111-1-1-1-1110000−333−33−3−330000000000000000
χ492-2-22-222-222-2-200002-2-22-2-222002-2-22000000000000000000002-2-22000000000000
χ502-2-22-222-222-2-200002-2-22-2-222002-2-2200000000000000000000-222-2000000000000
χ512-2-22-222-22-2220000-2-2-22-2-22200-222-20000000000000000000000002i−2i−2i2i00000000
χ522-2-22-222-22-2220000-2-2-22-2-22200-222-2000000000000000000000000−2i2i2i−2i00000000
χ534444-4-4-4-4-24-440000-4-2-2-2222200-22-22000000000000000000000000000000000000
χ544444-4-4-4-4-2-44-400004-2-2-22222002-22-2000000000000000000000000000000000000
χ5544-4-444-4-4-20004i−4i4i−4i0-222-22-22000000−2i2i00−2i2i000000000000000000000000000000
χ5644-4-444-4-4-2000−4i4i−4i4i0-222-22-220000002i−2i002i−2i000000000000000000000000000000
χ5744-4-4-4-4444000000004-4-4-44-44000000000000000000000000000000000000000000
χ5844-4-4-4-444-200000000-2222-22-20000000023−230023−230000000000000000000000000000
χ5944-4-4-4-444-200000000-2222-22-200000000−232300−23230000000000000000000000000000
χ604-44-44-44-4-20004i−4i−4i4i02-22-222-2000000−2i2i002i−2i000000000000000000000000000000
χ614-44-44-44-4-2000−4i4i4i−4i02-22-222-20000002i−2i00−2i2i000000000000000000000000000000
χ624-44-4-44-44400000000-44-4-444-4000000000000000000000000000000000000000000
χ634-44-4-44-44-2000000002-222-2-220000000023−2300−23230000000000000000000000000000
χ644-44-4-44-44-2000000002-222-2-2200000000−23230023−230000000000000000000000000000
χ654-4-44-444-4-24-4-40000422-222-2-200-222-2000000000000000000000000000000000000
χ664-4-44-444-4-2-4440000-422-222-2-2002-2-22000000000000000000000000000000000000

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