Finite Group Databasebeta

← Group #10692792

Character table — Group #10692792

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121212121212161616161616161616162424242448484848
order12223444444666244466121212121212121244448888121224242424242424248888888844121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ911111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1ii−i−iii−i−i1-111-1-111-1-1i−ii−ii−ii−i
χ1011111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1−i−iii−i−iii1-111-1-111-1-1−ii−ii−ii−ii
χ1111111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i-1111-1-1-1-111i−ii−i−ii−ii
χ1211111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iii-1111-1-1-1-111−ii−iii−ii−i
χ1311111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1ii−i−i−i−iii-11-1-111-1-111i−i−iii−i−ii
χ1411111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1−i−iiiii−i−i-11-1-111-1-111−iii−i−iii−i
χ1511111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111ii−i−i−i−iii1-1-1-11111-1-1i−i−ii−iii−i
χ1611111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111−i−iiiii−i−i1-1-1-11111-1-1−iii−ii−i−ii
χ17222222222-2-2222-2-2-22-2-22222-2-2222-22-20000-2-20000000000000000002-22-2000000000000
χ18222222222-2-2222-2-2-22-2-22222-2-222-22-220000-2-2000000000000000000-22-22000000000000
χ19222222-22-222222-22-2-2-2-222-2-222-2-2000000002-20000000000002222000000000000-2-20000
χ20222222-22-222222-22-2-2-2-222-2-222-2-2000000002-2000000000000-2-2-2-2000000000000220000
χ21222222-22-2-2-22222-22-22222-2-2-2-2-2-200000000-22000000002i2i−2i−2i00000000000000−2i2i000000
χ22222222-22-2-2-22222-22-22222-2-2-2-2-2-200000000-2200000000−2i−2i2i2i000000000000002i−2i000000
χ2322222-22-2222222-2-22-2-2-2-2-22222-2-200000000-2200000000222200000000000000-2-2000000
χ2422222-22-2222222-2-22-2-2-2-2-22222-2-200000000-2200000000-2-2-2-20000000000000022000000
χ2522222-22-22-2-222222-2-222-2-222-2-2-2-2000000002-20000000000002i2i−2i−2i000000000000−2i2i0000
χ2622222-22-22-2-222222-2-222-2-222-2-2-2-2000000002-2000000000000−2i−2i2i2i0000000000002i−2i0000
χ2722222-2-2-2-2222222-2-2222-2-2-2-222222-2-220000-2-20000000000000000002-2-22000000000000
χ2822222-2-2-2-2222222-2-2222-2-2-2-22222-222-20000-2-2000000000000000000-222-2000000000000
χ292222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-100000000
χ302222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-1-1-1-1111100000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-21111111100000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000221111-1-1-1-100000000
χ332222-12222-2-2-1-1-1-2-2-2211-1-1-1-111-1-12-22-2000011−i3−i3i3i3−i3−i3i3i30000000000-11-11−i3i3−i3i300000000
χ342222-12222-2-2-1-1-1-2-2-2211-1-1-1-111-1-12-22-2000011i3i3−i3−i3i3i3−i3−i30000000000-11-11i3−i3i3−i300000000
χ352222-12222-2-2-1-1-1-2-2-2211-1-1-1-111-1-1-22-22000011−i3−i3i3i3−i3−i3i3i300000000001-11-1i3−i3i3−i300000000
χ362222-12222-2-2-1-1-1-2-2-2211-1-1-1-111-1-1-22-22000011i3i3−i3−i3i3i3−i3−i300000000001-11-1−i3i3−i3i300000000
χ372222-1-2-2-2-222-1-1-12-2-22-1-11111-1-1-1-12-2-22000011−i3−i3i3i3i3i3−i3−i30000000000-111-1−i3i3i3−i300000000
χ382222-1-2-2-2-222-1-1-12-2-22-1-11111-1-1-1-12-2-22000011i3i3−i3−i3−i3−i3i3i30000000000-111-1i3−i3−i3i300000000
χ392222-1-2-2-2-222-1-1-12-2-22-1-11111-1-1-1-1-222-2000011−i3−i3i3i3i3i3−i3−i300000000001-1-11i3−i3−i3i300000000
χ402222-1-2-2-2-222-1-1-12-2-22-1-11111-1-1-1-1-222-2000011i3i3−i3−i3−i3−i3i3i300000000001-1-11−i3i3i3−i300000000
χ412222-1-2-2-2-2-2-2-1-1-1-222211111111-1-122-2-222-2-2-1-1-1-1-1-11111000000002-2-1-111-1-11100000000
χ422222-1-2-2-2-2-2-2-1-1-1-222211111111-1-122-2-2-2-222-1-11111-1-1-1-100000000-22-1-11111-1-100000000
χ432222-1-2-2-2-2-2-2-1-1-1-222211111111-1-1-2-22222-2-2-1-1-1-1-1-1111100000000-2211-1-111-1-100000000
χ442222-1-2-2-2-2-2-2-1-1-1-222211111111-1-1-2-222-2-222-1-11111-1-1-1-1000000002-211-1-1-1-11100000000
χ454444-24-44-444-2-2-2-44-4-422-2-222-2-22200000000-220000000000000000000000000000000000
χ464444-24-44-4-4-4-2-2-24-44-4-2-2-2-2222222000000002-20000000000000000000000000000000000
χ474444-2-44-4444-2-2-2-4-44-42222-2-2-2-222000000002-20000000000000000000000000000000000
χ484444-2-44-44-4-4-2-2-244-4-4-2-222-2-2222200000000-220000000000000000000000000000000000
χ4944-4-44040-4004-4-4000000004-4000000000000000000000022−2222−220000000000000000000000
χ5044-4-44040-4004-4-4000000004-40000000000000000000000−2222−22220000000000000000000000
χ5144-4-440-404004-4-400000000-440000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5244-4-440-404004-4-400000000-4400000000000000000000002i2−2i2−2i22i20000000000000000000000
χ534-44-4440-4000-44-40000004-4000000000000000000000000000022−2222−22000000000000000000
χ544-44-4440-4000-44-40000004-40000000000000000000000000000−2222−2222000000000000000000
χ554-44-44-404000-44-4000000-440000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ564-44-44-404000-44-4000000-4400000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ574-4-44400004-4-4-4400000000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ584-4-44400004-4-4-4400000000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ594-4-4440000-44-4-440000000000-440000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ604-4-4440000-44-4-440000000000-44000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ614-4-44-200004-422-20000−2i32i30000-22−2i32i300002i−2i2i−2i002ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ624-4-44-200004-422-20000−2i32i30000-22−2i32i30000−2i2i−2i2i00−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ634-4-44-200004-422-200002i3−2i30000-222i3−2i300002i−2i2i−2i002ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ644-4-44-200004-422-200002i3−2i30000-222i3−2i30000−2i2i−2i2i00−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ654-4-44-20000-4422-20000−2i32i300002-22i3−2i300002i−2i−2i2i002ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ664-4-44-20000-4422-20000−2i32i300002-22i3−2i30000−2i2i2i−2i00−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ674-4-44-20000-4422-200002i3−2i300002-2−2i32i300002i−2i−2i2i002ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ684-4-44-20000-4422-200002i3−2i300002-2−2i32i30000−2i2i2i−2i00−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ6988-8-8-4080-800-44400000000-44000000000000000000000000000000000000000000000000
χ7088-8-8-40-80800-444000000004-4000000000000000000000000000000000000000000000000
χ718-88-8-480-80004-44000000-4400000000000000000000000000000000000000000000000000
χ728-88-8-4-8080004-440000004-400000000000000000000000000000000000000000000000000

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