Finite Group Databasebeta

← Group #10694753

Character table — Group #10694753

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order122222344444444666446612121212121212128888121224242424242424248888888824668812122424242488882488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1
χ91111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1111-1-1-1-11-111i−i-1-1ii−i−iii−i−i1-1i−i
χ101111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1111-1-1-1-1-11-1-1−ii11−i−iiiii−i−i-11−ii
χ111111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-1-1-1-111111-111i−i-1-1ii−i−i−i−iii-11−ii
χ121111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-1-1-1-11111-11-1-1−ii11−i−iii−i−iii1-1i−i
χ131111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1111-1-1-1-11-111−ii-1-1−i−iii−i−iii1-1−ii
χ141111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1111-1-1-1-1-11-1-1i−i11ii−i−i−i−iii-11i−i
χ151111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-1-1-1-111111-111−ii-1-1−i−iiiii−i−i-11i−i
χ161111111-1-1-1-111-1-1111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-1-1-1-11111-11-1-1i−i11ii−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
χ192222222-2-222-2-2-2-22222-22222-2-2-2-2-2-22i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ202222222-2-222-2-2-2-22222-22222-2-2-2-2-2-2−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-122-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-211-2-211111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-1-1-2-2-1-1111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2112211-1-1-1-100000000
χ25222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-12-22-211-1-111-1-1110000000000−i3i300−i3i3−i3i3−i3i300000000
χ26222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-12-22-211-1-111-1-1110000000000i3−i300i3−i3i3−i3i3−i300000000
χ27222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-1-22-221111-1-111-1-10000000000−i3i300−i3i3i3−i3i3−i300000000
χ28222222-122-2-2-2-222-1-1-1-2-2-1-11111-1-1-1-1-22-221111-1-111-1-10000000000i3−i300i3−i3−i3i3−i3i300000000
χ29222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-11111112i−2i−2i2i-11−i−iiiii−i−i0000000000−i3i300i3−i33−3−3300000000
χ30222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-11111112i−2i−2i2i-11−i−iiiii−i−i0000000000i3−i300−i3i3−333−300000000
χ31222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-1111111−2i2i2i−2i-11ii−i−i−i−iii0000000000−i3i300i3−i3−333−300000000
χ32222222-1-2-222-2-2-2-2-1-1-12-2-1-1-1-1111111−2i2i2i−2i-11ii−i−i−i−iii0000000000i3−i300−i3i33−3−3300000000
χ33222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii000000002-2-1-12i−2i11−i−iii00000000
χ34222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii00000000-2211−2i2i-1-1ii−i−i00000000
χ35222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i000000002-2-1-1−2i2i11ii−i−i00000000
χ36222222-1-2-2-2-222-2-2-1-1-1-22-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i00000000-22112i−2i-1-1−i−iii00000000
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
χ412222-2-22-2-222-2-222222-22-2-222-2-2-2-2220000-2200000000000000000000000000002-2-220000
χ422222-2-22-2-222-2-222222-22-2-222-2-2-2-2220000-220000000000000000000000000000-222-20000
χ432222-2-22-2-2-2-222222222-2-2-2-2-222-2-22200002-20000000022-2-2-2-22200000000000000000000
χ442222-2-22-2-2-2-222222222-2-2-2-2-222-2-22200002-200000000-2-22222-2-200000000000000000000
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
χ4944-4-4004004i−4i00004-4-400004i−4i000000000000000000000022−2200−2i22i200000000000000000000
χ5044-4-4004004i−4i00004-4-400004i−4i0000000000000000000000−2222002i2−2i200000000000000000000
χ5144-4-400400−4i4i00004-4-40000−4i4i000000000000000000000022−22002i2−2i200000000000000000000
χ5244-4-400400−4i4i00004-4-40000−4i4i0000000000000000000000−222200−2i22i200000000000000000000
χ534-44-44-444i−4i00004i−4i-44-4004-400004i−4i4i−4i000000000000000000000000000000000000000000
χ544-44-44-44−4i4i0000−4i4i-44-4004-40000−4i4i−4i4i000000000000000000000000000000000000000000
χ554-44-44-4-24i−4i00004i−4i2-2200-220000−2i2i−2i2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000
χ564-44-44-4-24i−4i00004i−4i2-2200-220000−2i2i−2i2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000
χ574-44-44-4-2−4i4i0000−4i4i2-2200-2200002i−2i2i−2i0000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000
χ584-44-44-4-2−4i4i0000−4i4i2-2200-2200002i−2i2i−2i000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000
χ594-44-4-4444i−4i0000−4i4i-44-400-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ604-44-4-444−4i4i00004i−4i-44-400-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ614-44-4-44-24i−4i0000−4i4i2-22002-20000−2i2i2i−2i000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ624-44-4-44-24i−4i0000−4i4i2-22002-20000−2i2i2i−2i00000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ634-44-4-44-2−4i4i00004i−4i2-22002-200002i−2i−2i2i00000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ644-44-4-44-2−4i4i00004i−4i2-22002-200002i−2i−2i2i000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ654-4-4400400004-400-4-440000004-400000000000000000000004-40000000000000000000000
χ664-4-4400400004-400-4-440000004-40000000000000000000000-440000000000000000000000
χ674-4-440040000-4400-4-44000000-440000000000000000004-400000000000000000000000000
χ684-4-440040000-4400-4-44000000-44000000000000000000-4400000000000000000000000000
χ6988-8-800-4008i−8i0000-4440000−4i4i000000000000000000000000000000000000000000000000
χ7088-8-800-400−8i8i0000-44400004i−4i000000000000000000000000000000000000000000000000
χ718-8-8800-400008-80044-4000000-440000000000000000000000000000000000000000000000
χ728-8-8800-40000-880044-40000004-40000000000000000000000000000000000000000000000

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