Finite Group Databasebeta

← Group #10694758

Character table — Group #10694758

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888884488121212122424242488884488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ91111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−i1-1i−i
χ101111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iiiii−i−i-11−ii
χ111111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-1-1-1-111111-1i−i11-1-1ii−i−i−i−iii-11−ii
χ121111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-1-1-1-11111-11−ii-1-111−i−iii−i−iii1-1i−i
χ131111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii1-1−ii
χ141111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−i−i−iii-11i−i
χ151111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-1-1-1-111111-1−ii11-1-1−i−iiiii−i−i-11i−i
χ161111111-1-111-1-1-1-11111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-1-1-1-11111-11i−i-1-111ii−i−iii−i−i1-1−ii
χ17222222222-2-2-2-222222-2-222-2-2-2-222222-22-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222-2-2-2-222222-2-222-2-2-2-22222-22-22-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-222-2-2222-2222-2-222-2-2-2-22i−2i−2i2i-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ202222222-2-2-2-222-2-2222-2222-2-222-2-2-2-2−2i2i2i−2i-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ25222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-12-22-211-1-111-1-111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ26222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-12-22-211-1-111-1-111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ27222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-1-22-221111-1-111-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ28222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-1-22-221111-1-111-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ29222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii000000002-22i−2i-1-111−i−iii00000000
χ30222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii00000000-22−2i2i11-1-1ii−i−i00000000
χ31222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i000000002-2−2i2i-1-111ii−i−i00000000
χ32222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i00000000-222i−2i11-1-1−i−iii00000000
χ33222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-111112i−2i−2i2i1-1−i−iiiii−i−i000000000000−i3i3i3−i33−3−3300000000
χ34222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-111112i−2i−2i2i1-1−i−iiiii−i−i000000000000i3−i3−i3i3−333−300000000
χ35222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-11111−2i2i2i−2i1-1ii−i−i−i−iii000000000000−i3i3i3−i3−333−300000000
χ36222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-11111−2i2i2i−2i1-1ii−i−i−i−iii000000000000i3−i3−i3i33−3−3300000000
χ372222-2-22222222-2-2222-2-2-2-2222222-2-20000-2-20000000022-2-222-2-200000000000000000000
χ382222-2-22222222-2-2222-2-2-2-2222222-2-20000-2-200000000-2-222-2-22200000000000000000000
χ392222-2-2222-2-2-2-2-2-222222-2-2-2-2-2-222-2-200002200000000000000000000000000002i−2i2i−2i0000
χ402222-2-2222-2-2-2-2-2-222222-2-2-2-2-2-222-2-20000220000000000000000000000000000−2i2i−2i2i0000
χ412222-2-22-2-222-2-222222-22-2-222-2-2-2-2220000-220000000022-2-2-2-22200000000000000000000
χ422222-2-22-2-222-2-222222-22-2-222-2-2-2-2220000-2200000000-2-22222-2-200000000000000000000
χ432222-2-22-2-2-2-222222222-2-2-2-2-222-2-22200002-200000000000000000000000000002-2-220000
χ442222-2-22-2-2-2-222222222-2-2-2-2-222-2-22200002-20000000000000000000000000000-222-20000
χ454444-4-4-2444444-4-4-2-2-2-4-422-2-2-2-2-2-222000022000000000000000000000000000000000000
χ464444-4-4-244-4-4-4-4-4-4-2-2-244222222-2-2220000-2-2000000000000000000000000000000000000
χ474444-4-4-2-4-444-4-444-2-2-2-4422-2-22222-2-200002-2000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-44444-2-2-24-42222-2-222-2-20000-22000000000000000000000000000000000000
χ4944-4-4004004-400004-4-400004-400000000000000000000004-4000000000000000000000000
χ5044-4-4004004-400004-4-400004-40000000000000000000000-44000000000000000000000000
χ5144-4-400400-4400004-4-40000-44000000000000000000000000004-400000000000000000000
χ5244-4-400400-4400004-4-40000-4400000000000000000000000000-4400000000000000000000
χ534-44-400400004i−4i00-44-40000004i−4i00000000000000000022−2200−2i22i20000000000000000000000
χ544-44-400400004i−4i00-44-40000004i−4i000000000000000000−2222002i2−2i20000000000000000000000
χ554-44-40040000−4i4i00-44-4000000−4i4i00000000000000000022−22002i2−2i20000000000000000000000
χ564-44-40040000−4i4i00-44-4000000−4i4i000000000000000000−222200−2i22i20000000000000000000000
χ574-4-444-444i−4i00004i−4i-4-44004-400004i−4i4i−4i000000000000000000000000000000000000000000
χ584-4-444-44−4i4i0000−4i4i-4-44004-40000−4i4i−4i4i000000000000000000000000000000000000000000
χ594-4-444-4-24i−4i00004i−4i22-200-220000−2i2i−2i2i000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ604-4-444-4-24i−4i00004i−4i22-200-220000−2i2i−2i2i00000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ614-4-444-4-2−4i4i0000−4i4i22-200-2200002i−2i2i−2i00000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ624-4-444-4-2−4i4i0000−4i4i22-200-2200002i−2i2i−2i000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ634-4-44-4444i−4i0000−4i4i-4-4400-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ644-4-44-444−4i4i00004i−4i-4-4400-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-44-44-24i−4i0000−4i4i22-2002-20000−2i2i2i−2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000
χ664-4-44-44-24i−4i0000−4i4i22-2002-20000−2i2i2i−2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000
χ674-4-44-44-2−4i4i00004i−4i22-2002-200002i−2i−2i2i0000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000
χ684-4-44-44-2−4i4i00004i−4i22-2002-200002i−2i−2i2i000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000
χ6988-8-800-4008-80000-4440000-44000000000000000000000000000000000000000000000000
χ7088-8-800-400-880000-44400004-4000000000000000000000000000000000000000000000000
χ718-88-800-400008i−8i004-44000000−4i4i0000000000000000000000000000000000000000000000
χ728-88-800-40000−8i8i004-440000004i−4i0000000000000000000000000000000000000000000000

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