Finite Group Databasebeta

← Group #69636

Character table — Group #69636

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
χ511111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-11-1-11-111-1ii−i−i1-111-11-1-1-1i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011-11-1-11-111-1ii−i−i1-111-11-1-1-1i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ1111-11-1-11-111-1ii−i−i1-111-11-1-1-1i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ1211-11-1-11-111-1ii−i−i1-111-11-1-1-1i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ1311-11-1-11-111-1−i−iii1-111-11-1-1-1−ii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ1411-11-1-11-111-1−i−iii1-111-11-1-1-1−ii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ1511-11-1-11-111-1−i−iii1-111-11-1-1-1−ii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ1611-11-1-11-111-1−i−iii1-111-11-1-1-1−ii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222-2-22222-2-22222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
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
χ2122222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ2222222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ2322222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2422222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000i3−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
χ2722-22-2-22-22-222i2i−2i−2i-2222-22-2-2-2−2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ2822-22-2-22-22-22−2i−2i2i2i-2222-22-2-2-22i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ2922-22-2-22-2-12-22i2i−2i−2i2-2-1-11-11112i−2i-1-111−i−i−i−iiiii2-22i−2i-1-111−i−iii0000000000000000
χ3022-22-2-22-2-12-22i2i−2i−2i2-2-1-11-11112i−2i-1-111−i−i−i−iiiii-22−2i2i11-1-1ii−i−i0000000000000000
χ3122-22-2-22-2-12-2−2i−2i2i2i2-2-1-11-1111−2i2i-1-111iiii−i−i−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ3222-22-2-22-2-12-2−2i−2i2i2i2-2-1-11-1111−2i2i-1-111iiii−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
χ3322-22-2-22-2-1-222i2i−2i−2i-22-1-11-1111−2i2i11-1-1−i−iiiii−i−i0000−i3i3i3−i33−3−330000000000000000
χ3422-22-2-22-2-1-222i2i−2i−2i-22-1-11-1111−2i2i11-1-1−i−iiiii−i−i0000i3−i3−i3i3−333−30000000000000000
χ3522-22-2-22-2-1-22−2i−2i2i2i-22-1-11-11112i−2i11-1-1ii−i−i−i−iii0000−i3i3i3−i3−333−30000000000000000
χ3622-22-2-22-2-1-22−2i−2i2i2i-22-1-11-11112i−2i11-1-1ii−i−i−i−iii0000i3−i3−i3i33−3−330000000000000000
χ372-222-2-2-222220000-2-2-2-222-2-22002-22-2000000000000000000002i−2i2i−2i000000000000
χ382-222-2-2-222220000-2-2-2-222-2-22002-22-200000000000000000000−2i2i−2i2i000000000000
χ392-222-2-2-222-2-2000022-2-222-2-2200-22-220000000000000000000000002-22-200000000
χ402-222-2-2-222-2-2000022-2-222-2-2200-22-22000000000000000000000000-22-2200000000
χ412-22-22-22-22002i−2i2i−2i002-22-22-2-20000002i−2i002i−2i00000000000000000000002−22−2−i2i2−i2i2
χ422-22-22-22-22002i−2i2i−2i002-22-22-2-20000002i−2i002i−2i0000000000000000000000−22−22i2−i2i2−i2
χ432-22-22-22-2200−2i2i−2i2i002-22-22-2-2000000−2i2i00−2i2i00000000000000000000002−22−2i2−i2i2−i2
χ442-22-22-22-2200−2i2i−2i2i002-22-22-2-2000000−2i2i00−2i2i0000000000000000000000−22−22−i2i2−i2i2
χ452-2-2222-2-222-20000-22-2-2-2222-2002-2-22000000000000000000002i−2i−2i2i000000000000
χ462-2-2222-2-222-20000-22-2-2-2222-2002-2-2200000000000000000000−2i2i2i−2i000000000000
χ472-2-2222-2-22-2200002-2-2-2-2222-200-222-20000000000000000000000002i−2i−2i2i00000000
χ482-2-2222-2-22-2200002-2-2-2-2222-200-222-2000000000000000000000000−2i2i2i−2i00000000
χ492-2-2-2-22222002-2-22002-2-2-2-2220000002-200-2200000000000000000000002−2−22−222−2
χ502-2-2-2-22222002-2-22002-2-2-2-2220000002-200-220000000000000000000000−222−22−2−22
χ512-2-2-2-2222200-222-2002-2-2-2-222000000-22002-200000000000000000000002−2−222−2−22
χ522-2-2-2-2222200-222-2002-2-2-2-222000000-22002-20000000000000000000000−222−2−222−2
χ53444-4-44-4-4400000000-444-4-44-4000000000000000000000000000000000000000000
χ54444-4-44-4-4-2000000002-2-222-220000000023−230023−230000000000000000000000000000
χ55444-4-44-4-4-2000000002-2-222-2200000000−232300−23230000000000000000000000000000
χ5644-4-44-4-44400000000-44-4-44-44000000000000000000000000000000000000000000
χ5744-4-44-4-44-2000000002-222-22-200000000−2i32i3002i3−2i30000000000000000000000000000
χ5844-4-44-4-44-2000000002-222-22-2000000002i3−2i300−2i32i30000000000000000000000000000
χ594-444-4-4-44-2440000-4-422-2-222-200-22-22000000000000000000000000000000000000
χ604-444-4-4-44-2-4-400004422-2-222-2002-22-2000000000000000000000000000000000000
χ614-44-44-44-4-2004i−4i4i−4i00-22-22-222000000−2i2i00−2i2i000000000000000000000000000000
χ624-44-44-44-4-200−4i4i−4i4i00-22-22-2220000002i−2i002i−2i000000000000000000000000000000
χ634-4-4444-4-4-24-40000-44222-2-2-2200-222-2000000000000000000000000000000000000
χ644-4-4444-4-4-2-4400004-4222-2-2-22002-2-22000000000000000000000000000000000000
χ654-4-4-4-4444-2004-4-4400-22222-2-2000000-22002-2000000000000000000000000000000
χ664-4-4-4-4444-200-444-400-22222-2-20000002-200-22000000000000000000000000000000

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