Finite Group Databasebeta

← Group #69690

Character table — Group #69690

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order12222222344444444666666644121212121212121212121212444412121212121212124444444488888888
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
χ9111-1-1-1-111ii−i−i1-11-111-1-1-1-11i−iiiii−i−i−i−i11-1-1i−i1-1ii−i−i11-1-1ii−i−i11-1-111-1-1ii−i−i
χ10111-1-1-1-111ii−i−i1-11-111-1-1-1-11i−iiiii−i−i−i−i11-1-1i−i1-1ii−i−i11-1-1−i−iii-1-111-1-111−i−iii
χ11111-1-1-1-111ii−i−i1-11-111-1-1-1-11i−iiiii−i−i−i−i11-1-1−ii-11−i−iii-1-111ii−i−i11-1-1-1-111−i−iii
χ12111-1-1-1-111ii−i−i1-11-111-1-1-1-11i−iiiii−i−i−i−i11-1-1−ii-11−i−iii-1-111−i−iii-1-11111-1-1ii−i−i
χ13111-1-1-1-111−i−iii1-11-111-1-1-1-11−ii−i−i−i−iiiii11-1-1i−i-11ii−i−i-1-111ii−i−i-1-11111-1-1−i−iii
χ14111-1-1-1-111−i−iii1-11-111-1-1-1-11−ii−i−i−i−iiiii11-1-1i−i-11ii−i−i-1-111−i−iii11-1-1-1-111ii−i−i
χ15111-1-1-1-111−i−iii1-11-111-1-1-1-11−ii−i−i−i−iiiii11-1-1−ii1-1−i−iii11-1-1ii−i−i-1-111-1-111ii−i−i
χ16111-1-1-1-111−i−iii1-11-111-1-1-1-11−ii−i−i−i−iiiii11-1-1−ii1-1−i−iii11-1-1−i−iii11-1-111-1-1−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
χ27222-2-2-2-2222i2i−2i−2i-22-2222-2-2-2-22−2i2i2i2i−2i−2i−2i−2i2i2i-2-2220000000000000000000000000000
χ28222-2-2-2-222−2i−2i2i2i-22-2222-2-2-2-222i−2i−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000000000000000
χ29222-2-2-2-22-12i2i−2i−2i2-22-2-1-11111-12i−2i−i−i−i−iiiii-1-1112i−2i2-2−i−iii-1-1110000000000000000
χ30222-2-2-2-22-12i2i−2i−2i2-22-2-1-11111-12i−2i−i−i−i−iiiii-1-111−2i2i-22ii−i−i11-1-10000000000000000
χ31222-2-2-2-22-12i2i−2i−2i-22-22-1-11111-1−2i2i−i−iiiii−i−i11-1-100003−3−33−i3i3i3−i30000000000000000
χ32222-2-2-2-22-12i2i−2i−2i-22-22-1-11111-1−2i2i−i−iiiii−i−i11-1-10000−333−3i3−i3−i3i30000000000000000
χ33222-2-2-2-22-1−2i−2i2i2i2-22-2-1-11111-1−2i2iiiii−i−i−i−i-1-1112i−2i-22−i−iii11-1-10000000000000000
χ34222-2-2-2-22-1−2i−2i2i2i2-22-2-1-11111-1−2i2iiiii−i−i−i−i-1-111−2i2i2-2ii−i−i-1-1110000000000000000
χ35222-2-2-2-22-1−2i−2i2i2i-22-22-1-11111-12i−2iii−i−i−i−iii11-1-100003−3−33i3−i3−i3i30000000000000000
χ36222-2-2-2-22-1−2i−2i2i2i-22-22-1-11111-12i−2iii−i−i−i−iii11-1-10000−333−3−i3i3i3−i30000000000000000
χ3722-222-2-2-222-22-200002-222-2-2-2002-2002-2000000000000000000000000002−22−22−22−2
χ3822-222-2-2-222-22-200002-222-2-2-2002-2002-200000000000000000000000000−22−22−22−22
χ3922-222-2-2-22-22-2200002-222-2-2-200-2200-22000000000000000000000000002−22−2−22−22
χ4022-222-2-2-22-22-2200002-222-2-2-200-2200-2200000000000000000000000000−22−222−22−2
χ4122-2-2-222-222i−2i−2i2i00002-2-2-222-2002i−2i00−2i2i000000000000000000000000002−2−22i2−i2−i2i2
χ4222-2-2-222-222i−2i−2i2i00002-2-2-222-2002i−2i00−2i2i00000000000000000000000000−222−2−i2i2i2−i2
χ4322-2-2-222-22−2i2i2i−2i00002-2-2-222-200−2i2i002i−2i000000000000000000000000002−2−22−i2i2i2−i2
χ4422-2-2-222-22−2i2i2i−2i00002-2-2-222-200−2i2i002i−2i00000000000000000000000000−222−2i2−i2−i2i2
χ452-2-22-22-222000022-2-2-2-22-2-22200000000002-22-20000000000002i−2i2i−2i000000000000
χ462-2-22-22-222000022-2-2-2-22-2-22200000000002-22-2000000000000−2i2i−2i2i000000000000
χ472-2-22-22-2220000-2-222-2-22-2-2220000000000-22-2200000000000000002-22-200000000
χ482-2-22-22-2220000-2-222-2-22-2-2220000000000-22-220000000000000000-22-2200000000
χ492-2-2-22-222200002-2-22-2-2-222-2200000000002-2-220000000000002-2-22000000000000
χ502-2-2-22-222200002-2-22-2-2-222-2200000000002-2-22000000000000-222-2000000000000
χ512-2-2-22-22220000-222-2-2-2-222-220000000000-222-200000000000000002-2-2200000000
χ522-2-2-22-22220000-222-2-2-2-222-220000000000-222-20000000000000000-222-200000000
χ5344-444-4-4-4-24-44-40000-22-2-222200-2200-220000000000000000000000000000000000
χ5444-444-4-4-4-2-44-440000-22-2-2222002-2002-20000000000000000000000000000000000
χ5544-4-4-444-4-24i−4i−4i4i0000-2222-2-2200−2i2i002i−2i0000000000000000000000000000000000
χ5644-4-4-444-4-2−4i4i4i−4i0000-2222-2-22002i−2i00−2i2i0000000000000000000000000000000000
χ574-444-4-44-4400000000-444-44-4-4000000000000000000000000000000000000000000
χ584-444-4-44-4-2000000002-2-22-2220000−2i32i300−2i32i300000000000000000000000000000000
χ594-444-4-44-4-2000000002-2-22-22200002i3−2i3002i3−2i300000000000000000000000000000000
χ604-44-444-4-4400000000-44-44-44-4000000000000000000000000000000000000000000
χ614-44-444-4-4-2000000002-22-22-22000023−2300−232300000000000000000000000000000000
χ624-44-444-4-4-2000000002-22-22-220000−23230023−2300000000000000000000000000000000
χ634-4-44-44-44-2000044-4-422-222-2-20000000000-22-220000000000000000000000000000
χ644-4-44-44-44-20000-4-44422-222-2-200000000002-22-20000000000000000000000000000
χ654-4-4-44-444-200004-4-44222-2-22-20000000000-222-20000000000000000000000000000
χ664-4-4-44-444-20000-444-4222-2-22-200000000002-2-220000000000000000000000000000

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