Finite Group Databasebeta

← Group #10694911

Character table — Group #10694911

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222222344444466624666612121212121268888122424242424242424888888884488121212122424242444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ81111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ9111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−i1-1i−i
χ10111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iiiii−i−i-11−ii
χ11111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−i-1-1-1-111111-1i−i11-1-1ii−i−i−i−iii-11−ii
χ12111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−i-1-1-1-11111-11−ii-1-111−i−iii−i−iii1-1i−i
χ13111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii1-1−ii
χ14111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−i−i−iii-11i−i
χ15111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiii-1-1-1-111111-1−ii11-1-1−i−iiiii−i−i-11i−i
χ16111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiii-1-1-1-11111-11i−i-1-111ii−i−iii−i−i1-1−ii
χ17222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-222i−2i2i−2i-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ18222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-22−2i2i−2i2i-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ1922222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ2022222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ2122222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1111111110000000022-2-2-1-1-1-1111100000000
χ2222222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111111100000000-2-2221111-1-1-1-100000000
χ2322222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111-12i−2i2i−2i1−i−iii−i−iii000000000000−i3i3−i3i33−33−300000000
χ2422222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111-12i−2i2i−2i1−i−iii−i−iii000000000000i3−i3i3−i3−33−3300000000
χ2522222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111-1−2i2i−2i2i1ii−i−iii−i−i000000000000−i3i3−i3i3−33−3300000000
χ2622222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111-1−2i2i−2i2i1ii−i−iii−i−i000000000000i3−i3i3−i33−33−300000000
χ27222222-2-22-22222-2222-2-222-2-2-2-22222-22-2-22-222-2-2-2-2220000000000000000000000000000
χ28222222-2-22-22222-2222-2-222-2-2-2-22222-2-222-2-2-2-22222-2-20000000000000000000000000000
χ29222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-1111112i2i−2i−2i-1−i−i−i−iiiii000000002-22i−2i-1-111−i−iii00000000
χ30222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-1111112i2i−2i−2i-1−i−i−i−iiiii00000000-22−2i2i11-1-1ii−i−i00000000
χ31222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-111111−2i−2i2i2i-1iiii−i−i−i−i000000002-2−2i2i-1-111ii−i−i00000000
χ32222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-111111−2i−2i2i2i-1iiii−i−i−i−i00000000-222i−2i11-1-1−i−iii00000000
χ33222222-2-2-1-22222-2-1-1-1-2-2-1-11111-1-1-1-112-2-221-1-11111-1-1000000000000−i3i3i3−i3−i3i3i3−i300000000
χ34222222-2-2-1-22222-2-1-1-1-2-2-1-11111-1-1-1-112-2-221-1-11111-1-1000000000000i3−i3−i3i3i3−i3−i3i300000000
χ35222222-2-2-1-22222-2-1-1-1-2-2-1-11111-1-1-1-11-222-2111-1-1-1-111000000000000−i3i3i3−i3i3−i3−i3i300000000
χ36222222-2-2-1-22222-2-1-1-1-2-2-1-11111-1-1-1-11-222-2111-1-1-1-111000000000000i3−i3−i3i3−i3i3i3−i300000000
χ372222-2-2222222-2-22222-2-2-2-2222222-2-2-20000-20000000022-2-222-2-200000000000000000000
χ382222-2-2222222-2-22222-2-2-2-2222222-2-2-20000-200000000-2-222-2-22200000000000000000000
χ392222-2-2222-2-2-222-2222-22-2-222-2-2-2-222-20000200000000000000000000000000002-22-20000
χ402222-2-2222-2-2-222-2222-22-2-222-2-2-2-222-2000020000000000000000000000000000-22-220000
χ412222-2-2-2-222-2-22222222-2-2-2-2-222-2-22220000-20000000022-2-2-2-22200000000000000000000
χ422222-2-2-2-222-2-22222222-2-2-2-2-222-2-22220000-200000000-2-22222-2-200000000000000000000
χ432222-2-2-2-22-222-2-2-222222-2-2-2-2-2-222-2-220000200000000000000000000000000002i−2i−2i2i0000
χ442222-2-2-2-22-222-2-2-222222-2-2-2-2-2-222-2-22000020000000000000000000000000000−2i2i2i−2i0000
χ454444-4-444-2444-4-44-2-2-2-4-422-2-2-2-2-2-222200002000000000000000000000000000000000000
χ464444-4-444-2-4-4-444-4-2-2-2-4422-2-22222-2-220000-2000000000000000000000000000000000000
χ474444-4-4-4-4-24-4-4444-2-2-24-42222-2-222-2-2-200002000000000000000000000000000000000000
χ484444-4-4-4-4-2-444-4-4-4-2-2-244222222-2-222-20000-2000000000000000000000000000000000000
χ4944-4-4004-440000004-4-400004-4000000000000000000000022−220022−2200000000000000000000
χ5044-4-4004-440000004-4-400004-40000000000000000000000−222200−222200000000000000000000
χ5144-4-400-4440000004-4-40000-44000000000000000000000022−2200−222200000000000000000000
χ5244-4-400-4440000004-4-40000-440000000000000000000000−22220022−2200000000000000000000
χ534-44-44-400404i−4i4i−4i0-44-4004-400004i−4i4i−4i000000000000000000000000000000000000000000
χ544-44-44-40040−4i4i−4i4i0-44-4004-40000−4i4i−4i4i000000000000000000000000000000000000000000
χ554-44-44-400-204i−4i4i−4i02-2200-220000−2i2i−2i2i000000−2ζ7+2ζ232ζ7−2ζ2300002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ564-44-44-400-204i−4i4i−4i02-2200-220000−2i2i−2i2i0000002ζ7−2ζ23−2ζ7+2ζ230000−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ574-44-44-400-20−4i4i−4i4i02-2200-2200002i−2i2i−2i0000002ζ5−2ζ13−2ζ5+2ζ130000−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ584-44-44-400-20−4i4i−4i4i02-2200-2200002i−2i2i−2i000000−2ζ5+2ζ132ζ5−2ζ1300002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ594-44-4-4400404i−4i−4i4i0-44-400-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ604-44-4-440040−4i4i4i−4i0-44-400-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ614-44-4-4400-204i−4i−4i4i02-22002-20000−2i2i2i−2i000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000
χ624-44-4-4400-204i−4i−4i4i02-22002-20000−2i2i2i−2i00000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000
χ634-44-4-4400-20−4i4i4i−4i02-22002-200002i−2i−2i2i00000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000
χ644-44-4-4400-20−4i4i4i−4i02-22002-200002i−2i−2i2i000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000
χ654-4-440000440000-4-4-440000004-400000000000000000000004i−4i0000000000000000000000
χ664-4-440000440000-4-4-440000004-40000000000000000000000−4i4i0000000000000000000000
χ674-4-4400004-400004-4-44000000-440000000000000000004-400000000000000000000000000
χ684-4-4400004-400004-4-44000000-44000000000000000000-4400000000000000000000000000
χ6988-8-8008-8-4000000-4440000-44000000000000000000000000000000000000000000000000
χ7088-8-800-88-4000000-44400004-4000000000000000000000000000000000000000000000000
χ718-8-880000-480000-844-4000000-440000000000000000000000000000000000000000000000
χ728-8-880000-4-80000844-40000004-40000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.