Finite Group Databasebeta

← Group #67624

Character table — Group #67624

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order1222222222223444466666664466661212121212121212444412121212121212124444444488888888
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
χ511111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111-1-11-1-111-1-11-1-11111-1-11-1-11-111-1-111-1-111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ10111-1-11-1-111-1-11-1-11111-1-11-1-11-111-1-111-1-111-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ11111-1-11-1-111-1-11-1-11111-1-11-1-11-111-1-111-1-111-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ12111-1-11-1-111-1-11-1-11111-1-11-1-11-111-1-111-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ13111-1-11-1-1-1-111111-1-111-1-11-1-11-1-1-11111-1-1-1-111i−i−iiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ14111-1-11-1-1-1-111111-1-111-1-11-1-11-1-1-11111-1-1-1-111i−i−iiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ15111-1-11-1-1-1-111111-1-111-1-11-1-11-1-1-11111-1-1-1-111−iii−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ16111-1-11-1-1-1-111111-1-111-1-11-1-11-1-1-11111-1-1-1-111−iii−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ20222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ21222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-211111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2422222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-211111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1221111-1-1-1-1111122-2-2-1-1-1-111110000000000000000
χ2622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1221111-1-1-1-11111-2-2221111-1-1-1-10000000000000000
χ27222-2-22-2-222-2-2222-2-222-2-22-2-2-2222-2-2-2-222-2-2220000000000000000000000000000
χ28222-2-22-2-222-2-2-122-2-2-1-111-111-22-1-11111-1-111-1-100003−3−333−3−330000000000000000
χ29222-2-22-2-222-2-2-122-2-2-1-111-111-22-1-11111-1-111-1-10000−333−3−333−30000000000000000
χ30222-2-22-2-222-2-2-1-2-222-1-111-1112-2-1-111-1-111-1-1112i−2i2i−2i−i−iii−i−iii0000000000000000
χ31222-2-22-2-222-2-2-1-2-222-1-111-1112-2-1-111-1-111-1-111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ32222-2-22-2-2-2-2222-2-22222-2-22-2-2-22-2-222-2-22222-2-20000000000000000000000000000
χ33222-2-22-2-2-2-222-122-2-2-1-111-1112-211-1-1-1-11111-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ34222-2-22-2-2-2-222-122-2-2-1-111-1112-211-1-1-1-11111-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ35222-2-22-2-2-2-222-1-2-222-1-111-111-2211-1-111-1-1-1-11100003−3−33−333−30000000000000000
χ36222-2-22-2-2-2-222-1-2-222-1-111-111-2211-1-111-1-1-1-1110000−333−33−3−330000000000000000
χ3722-222-2-2-22-22-2200002-222-2-2-2002-22-200000000000000000000000000002−22−22−22−2
χ3822-222-2-2-22-22-2200002-222-2-2-2002-22-20000000000000000000000000000−22−22−22−22
χ3922-222-2-2-2-22-22200002-222-2-2-200-22-220000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ4022-222-2-2-2-22-22200002-222-2-2-200-22-220000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ4122-2-2-2-2222-2-22200002-2-2-2-222002-2-2200000000000000000000000000002−2−222−2−22
χ4222-2-2-2-2222-2-22200002-2-2-2-222002-2-220000000000000000000000000000−222−2−222−2
χ4322-2-2-2-222-222-2200002-2-2-2-22200-222-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ4422-2-2-2-222-222-2200002-2-2-2-22200-222-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ452-222-2-22-2000022i−2i2i−2i-222-2-22-200000000002i−2i2i−2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ462-222-2-22-2000022i−2i2i−2i-222-2-22-200000000002i−2i2i−2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ472-222-2-22-200002−2i2i−2i2i-222-2-22-20000000000−2i2i−2i2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ482-222-2-22-200002−2i2i−2i2i-222-2-22-20000000000−2i2i−2i2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ492-22-22-2-22000022i−2i−2i2i-22-22-2-220000000000−2i2i2i−2i0000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ502-22-22-2-22000022i−2i−2i2i-22-22-2-220000000000−2i2i2i−2i000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ512-22-22-2-2200002−2i2i2i−2i-22-22-2-2200000000002i−2i−2i2i0000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ522-22-22-2-2200002−2i2i2i−2i-22-22-2-2200000000002i−2i−2i2i000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ5344-444-4-4-44-44-4-20000-22-2-222200-22-22000000000000000000000000000000000000
χ5444-444-4-4-4-44-44-20000-22-2-2222002-22-2000000000000000000000000000000000000
χ5544-4-4-4-4444-4-44-20000-22222-2-200-222-2000000000000000000000000000000000000
χ5644-4-4-4-444-444-4-20000-22222-2-2002-2-22000000000000000000000000000000000000
χ574-444-4-44-40000-24i−4i4i−4i2-2-222-220000000000−2i2i−2i2i0000000000000000000000000000
χ584-444-4-44-40000-2−4i4i−4i4i2-2-222-2200000000002i−2i2i−2i0000000000000000000000000000
χ594-44-44-4-440000-24i−4i−4i4i2-22-222-200000000002i−2i−2i2i0000000000000000000000000000
χ604-44-44-4-440000-2−4i4i4i−4i2-22-222-20000000000−2i2i2i−2i0000000000000000000000000000
χ614-4-44-44-44000040000-4-44-44-44000000000000000000000000000000000000000000
χ624-4-44-44-440000-2000022-22-22-2000000−2i32i3−2i32i300000000000000000000000000000000
χ634-4-44-44-440000-2000022-22-22-20000002i3−2i32i3−2i300000000000000000000000000000000
χ644-4-4-4444-4000040000-4-4-4444-4000000000000000000000000000000000000000000
χ654-4-4-4444-40000-20000222-2-2-22000000−2i32i32i3−2i300000000000000000000000000000000
χ664-4-4-4444-40000-20000222-2-2-220000002i3−2i3−2i32i300000000000000000000000000000000

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