Finite Group Databasebeta

← Group #69646

Character table — Group #69646

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order1222222234444444444446666666121212121212121212121212888888888888888822446666121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ9111-1-1-1-111iiii−i−i−i−i1-11-111-11-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−ii−i1-1
χ10111-1-1-1-111iiii−i−i−i−i1-11-111-11-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iii−ii-11
χ11111-1-1-1-111iiii−i−i−i−i1-11-111-11-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1i−i11-1-1ii−i−i−ii-11
χ12111-1-1-1-111iiii−i−i−i−i1-11-111-11-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11−ii-1-111−i−iiii−i1-1
χ13111-1-1-1-111−i−i−i−iiiii1-11-111-11-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1−ii11-1-1−i−iiii−i-11
χ14111-1-1-1-111−i−i−i−iiiii1-11-111-11-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11i−i-1-111ii−i−i−ii1-1
χ15111-1-1-1-111−i−i−i−iiiii1-11-111-11-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii−ii1-1
χ16111-1-1-1-111−i−i−i−iiiii1-11-111-11-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−ii−i-11
χ1722222222222-2-222-2-2-2-2-2-22222222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ18222222222-2-222-2-222-2-2-2-22222222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ1922222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-122-2-222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2222222222-122-2-222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2322222222-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1111111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ2422222222-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1111111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ27222-2-2-2-2222i2i−2i−2i−2i−2i2i2i-22-2222-22-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ28222-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22-2222-22-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ29222-2-2-2-22-12i2i2i2i−2i−2i−2i−2i2-22-2-1-11-1111-1-111−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii0000
χ30222-2-2-2-22-12i2i2i2i−2i−2i−2i−2i2-22-2-1-11-1111-1-111−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ31222-2-2-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11-111111-1-1−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−330000
χ32222-2-2-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11-111111-1-1−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−30000
χ33222-2-2-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11-111111-1-1ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−30000
χ34222-2-2-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11-111111-1-1ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−330000
χ35222-2-2-2-22-1−2i−2i−2i−2i2i2i2i2i2-22-2-1-11-1111-1-111iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ36222-2-2-2-22-1−2i−2i−2i−2i2i2i2i2i2-22-2-1-11-1111-1-111iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ3722-22-22-2-22002-2002-200002-2-2-22-220000002-2002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3822-22-22-2-22002-2002-200002-2-2-22-220000002-2002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3922-22-22-2-2200-2200-2200002-2-2-22-22000000-2200-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4022-22-22-2-2200-2200-2200002-2-2-22-22000000-2200-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4122-2-22-22-22002i−2i00−2i2i00002-22-2-22-20000002i−2i00−2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ4222-2-22-22-22002i−2i00−2i2i00002-22-2-22-20000002i−2i00−2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ4322-2-22-22-2200−2i2i002i−2i00002-22-2-22-2000000−2i2i002i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ4422-2-22-22-2200−2i2i002i−2i00002-22-2-22-2000000−2i2i002i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ452-222-2-22-222i−2i002i−2i000000-222-22-2-200002i−2i002i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ462-222-2-22-222i−2i002i−2i000000-222-22-2-200002i−2i002i−2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ472-222-2-22-22−2i2i00−2i2i000000-222-22-2-20000−2i2i00−2i2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ482-222-2-22-22−2i2i00−2i2i000000-222-22-2-20000−2i2i00−2i2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ492-22-222-2-222-200-22000000-22-2-2-22200002-200-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ502-22-222-2-222-200-22000000-22-2-2-22200002-200-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ512-22-222-2-22-22002-2000000-22-2-2-2220000-22002-200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ522-22-222-2-22-22002-2000000-22-2-2-2220000-22002-200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ532-2-222-2-2220000000022-2-2-2-2-2222-22-22-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ542-2-222-2-2220000000022-2-2-2-2-2222-22-22-200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ552-2-222-2-22200000000-2-222-2-2-2222-2-22-2200000000000000002-2-222-2-220000000000000000
χ562-2-222-2-22200000000-2-222-2-2-2222-2-22-220000000000000000-222-2-222-20000000000000000
χ572-2-2-2-22222000000002-2-22-2-222-2-222-2-22000000002-2-22-222-2000000000000000000000000
χ582-2-2-2-22222000000002-2-22-2-222-2-222-2-2200000000-222-22-2-22000000000000000000000000
χ592-2-2-2-2222200000000-222-2-2-222-2-22-222-200000000000000002-2-22-222-20000000000000000
χ602-2-2-2-2222200000000-222-2-2-222-2-22-222-20000000000000000-222-22-2-220000000000000000
χ6144-44-44-4-4-2004-4004-40000-2222-22-2000000-2200-2200000000000000000000000000000000
χ6244-44-44-4-4-200-4400-440000-2222-22-20000002-2002-200000000000000000000000000000000
χ6344-4-44-44-4-2004i−4i00−4i4i0000-22-222-22000000−2i2i002i−2i00000000000000000000000000000000
χ6444-4-44-44-4-200−4i4i004i−4i0000-22-222-220000002i−2i00−2i2i00000000000000000000000000000000
χ654-444-4-44-4-24i−4i004i−4i0000002-2-22-2220000−2i2i00−2i2i0000000000000000000000000000000000
χ664-444-4-44-4-2−4i4i00−4i4i0000002-2-22-22200002i−2i002i−2i0000000000000000000000000000000000
χ674-44-444-4-4-24-400-440000002-2222-2-20000-22002-20000000000000000000000000000000000
χ684-44-444-4-4-2-44004-40000002-2222-2-200002-200-220000000000000000000000000000000000
χ694-4-444-4-44-20000000044-4-4222-2-2-22-22-220000000000000000000000000000000000000000
χ704-4-444-4-44-200000000-4-444222-2-2-222-22-20000000000000000000000000000000000000000
χ714-4-4-4-4444-2000000004-4-4422-2-222-2-222-20000000000000000000000000000000000000000
χ724-4-4-4-4444-200000000-444-422-2-222-22-2-220000000000000000000000000000000000000000

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