Finite Group Databasebeta

← Group #10768904

Character table — Group #10768904

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order12222234444666444466121212121212121244444444121212121212121212128812121212242424242224444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-1111111-1-1-111-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-11111-1-1111-1-111111-1-1-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-11-11-1-111111-1-1-1-11-11-11-111-1-11-111-11-1-111-1-111-1-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-11-11-1-111111-1-1-1-11-11-11-111-1-1-11-1-11-111-1-111-1-111
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-11-11-111111-1-1-1-1-11-11-11-1-1111-1-1-111-1111-1-1-1-111
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-11-11-111111-1-1-1-1-11-11-11-1-111-1111-1-11-1-1-11111-1-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1111-11-1-1-1-1-1-111111-111-11-1-1-1111-111-11-1-1-1-111-1-111
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1111-11-1-1-1-1-1-111111-111-11-1-1-111-11-1-11-11111-1-111-1-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-11-11-1-1-1-1-1111111-1-11-1111-1-11-1-1-111-11-1-11111-1-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-11-11-1-1-1-1-1111111-1-11-1111-1-1-1111-1-11-111-1-1-1-111
χ17222222222-2-22222-2-2-22222-2-2-2-2-2-20000000020000-2000000000000002-2000-22000000000
χ18222222222-2-22222-2-2-22222-2-2-2-2-2-20000000020000-200000000000000-220002-2000000000
χ192222222-2-222222-22-2-222-2-22222-2-200000000-20000-20000000000000022000-2-2000000000
χ202222222-2-222222-22-2-222-2-22222-2-200000000-20000-200000000000000-2-200022000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2111111110000000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-11111-11111-2-2-1-1-1-111110000000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-11111221111-1-1-1-10000000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-22-22-21-1-1-1-1-111112-2-11-11-1-1110000000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-2-22-221-1-1-1-1-11111-221-11-111-1-10000000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-2222-22-211111-1-1-1-1-1-22-11-1111-1-10000000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-222-22-2211111-1-1-1-1-12-21-11-1-1-1110000000000000000
χ292222-2-222222222-2-2-22-2-22222-2-2-2-200000000-20000200000000000000002-2-200200000000
χ302222-2-222222222-2-2-22-2-22222-2-2-2-200000000-2000020000000000000000-22200-200000000
χ312222-2-2222-2-2222-222-2-2-222-2-2222200002-2-22-20000-2000000-222-200000000000000000000
χ322222-2-2222-2-2222-222-2-2-222-2-222220000-222-2-20000-20000002-2-2200000000000000000000
χ332222-2-22-2-2222222-22-2-2-2-2-222-2-222000022-2-220000-2000000-2-22200000000000000000000
χ342222-2-22-2-2222222-22-2-2-2-2-222-2-2220000-2-22220000-200000022-2-200000000000000000000
χ352222-2-22-2-2-2-222222-22-2-2-2-2-2-222-2-20000000020000200000000000000002-2200-200000000
χ362222-2-22-2-2-2-222222-22-2-2-2-2-2-222-2-2000000002000020000000000000000-22-200200000000
χ372222-2-2-122-2-2-1-1-1-222-211-1-111-1-1-1-100002-2-221−i3−i3i3i31−i3−i3i3i3001-1-11−i3i3−i3i30000000000000000
χ382222-2-2-122-2-2-1-1-1-222-211-1-111-1-1-1-100002-2-221i3i3−i3−i31i3i3−i3−i3001-1-11i3−i3i3−i30000000000000000
χ392222-2-2-122-2-2-1-1-1-222-211-1-111-1-1-1-10000-222-21−i3−i3i3i31−i3−i3i3i300-111-1i3−i3i3−i30000000000000000
χ402222-2-2-122-2-2-1-1-1-222-211-1-111-1-1-1-10000-222-21i3i3−i3−i31i3i3−i3−i300-111-1−i3i3−i3i30000000000000000
χ412222-2-2-1-2-222-1-1-12-22-21111-1-111-1-1000022-2-2-1−i3−i3i3i31i3i3−i3−i30011-1-1−i3i3i3−i30000000000000000
χ422222-2-2-1-2-222-1-1-12-22-21111-1-111-1-1000022-2-2-1i3i3−i3−i31−i3−i3i3i30011-1-1i3−i3−i3i30000000000000000
χ432222-2-2-1-2-222-1-1-12-22-21111-1-111-1-10000-2-222-1−i3−i3i3i31i3i3−i3−i300-1-111i3−i3−i3i30000000000000000
χ442222-2-2-1-2-222-1-1-12-22-21111-1-111-1-10000-2-222-1i3i3−i3−i31−i3−i3i3i300-1-111−i3i3i3−i30000000000000000
χ45444444-244-4-4-2-2-24-4-4-4-2-2-2-222222200000000-200002000000000000000000000000000000
χ46444444-2-4-444-2-2-2-44-4-4-2-222-2-2-2-22200000000200002000000000000000000000000000000
χ474444-4-4-24444-2-2-2-4-4-4422-2-2-2-222220000000020000-2000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-244-44222222-2-22200000000-20000-2000000000000000000000000000000
χ4944-4-44-4400004-4-400004-400000000000000000000000000000000000000000000000022−2200
χ5044-4-44-4400004-4-400004-4000000000000000000000000000000000000000000000000−222200
χ5144-4-4-44400004-4-40000-4400000000000000000000000000000000000000000000000000−2i22i2
χ5244-4-4-44400004-4-40000-44000000000000000000000000000000000000000000000000002i2−2i2
χ534-44-40044i−4i00-4-440000004i−4i0000002i−2i2-2000002i−2i2i−2i02-22-200000000000000000000000000
χ544-44-40044i−4i00-4-440000004i−4i000000−2i2i-2200000−2i2i−2i2i0-22-2200000000000000000000000000
χ554-44-4004−4i4i00-4-44000000−4i4i0000002i−2i-22000002i−2i2i−2i0-22-2200000000000000000000000000
χ564-44-4004−4i4i00-4-44000000−4i4i000000−2i2i2-200000−2i2i−2i2i02-22-200000000000000000000000000
χ574-44-400-24i−4i0022-2000000−2i2i0023−23−2i32i32i−2i2-2000002ζ14−2ζ142ζ22−2ζ220−1+i31−i3−1−i31+i300000000000000000000000000
χ584-44-400-24i−4i0022-2000000−2i2i0023−23−2i32i3−2i2i-2200000−2ζ142ζ14−2ζ222ζ2201−i3−1+i31+i3−1−i300000000000000000000000000
χ594-44-400-24i−4i0022-2000000−2i2i00−23232i3−2i32i−2i2-2000002ζ22−2ζ222ζ14−2ζ140−1−i31+i3−1+i31−i300000000000000000000000000
χ604-44-400-24i−4i0022-2000000−2i2i00−23232i3−2i3−2i2i-2200000−2ζ222ζ22−2ζ142ζ1401+i3−1−i31−i3−1+i300000000000000000000000000
χ614-44-400-2−4i4i0022-20000002i−2i0023−232i3−2i32i−2i-22000002ζ22−2ζ222ζ14−2ζ1401+i3−1−i31−i3−1+i300000000000000000000000000
χ624-44-400-2−4i4i0022-20000002i−2i0023−232i3−2i3−2i2i2-200000−2ζ222ζ22−2ζ142ζ140−1−i31+i3−1+i31−i300000000000000000000000000
χ634-44-400-2−4i4i0022-20000002i−2i00−2323−2i32i32i−2i-22000002ζ14−2ζ142ζ22−2ζ2201−i3−1+i31+i3−1−i300000000000000000000000000
χ644-44-400-2−4i4i0022-20000002i−2i00−2323−2i32i3−2i2i2-200000−2ζ142ζ14−2ζ222ζ220−1+i31−i3−1−i31+i300000000000000000000000000
χ654-4-44004004-4-44-4000000004-400000000000000000000000000000000000000002i−2i2i−2i0000
χ664-4-44004004-4-44-4000000004-40000000000000000000000000000000000000000−2i2i−2i2i0000
χ674-4-4400400-44-44-400000000-4400000000000000000000000000000000000000002i−2i−2i2i0000
χ684-4-4400400-44-44-400000000-440000000000000000000000000000000000000000−2i2i2i−2i0000
χ6988-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000000000
χ718-8-8800-4008-84-4400000000-44000000000000000000000000000000000000000000000000
χ728-8-8800-400-884-44000000004-4000000000000000000000000000000000000000000000000

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