Finite Group Databasebeta

← Group #10692162

Character table — Group #10692162

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222444444444444444488888888888888888816161616161616161616242424242424242448484848
order122234466624444466121212121212121288888888121224242424242424242466121224242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ911111-1-11111-11-1-1111-1-111-1-1-1-1ii−i−iii−i−i-11iiii−i−i−i−i1-111-1-1ii−i−i1-11-1ii−i−ii−i1-1
χ1011111-1-11111-11-1-1111-1-111-1-1-1-1ii−i−iii−i−i-11iiii−i−i−i−i1-111-1-1ii−i−i-11-11−i−iii−ii-11
χ1111111-1-11111-11-1-1111-1-111-1-1-1-1ii−i−i−i−iii-11−i−i−i−iiiii-11-1-111ii−i−i1-11-1ii−i−i−ii-11
χ1211111-1-11111-11-1-1111-1-111-1-1-1-1ii−i−i−i−iii-11−i−i−i−iiiii-11-1-111ii−i−i-11-11−i−iiii−i1-1
χ1311111-1-11111-11-1-1111-1-111-1-1-1-1−i−iiiii−i−i-11iiii−i−i−i−i-11-1-111−i−iii1-11-1−i−iiii−i-11
χ1411111-1-11111-11-1-1111-1-111-1-1-1-1−i−iiiii−i−i-11iiii−i−i−i−i-11-1-111−i−iii-11-11ii−i−i−ii1-1
χ1511111-1-11111-11-1-1111-1-111-1-1-1-1−i−iii−i−iii-11−i−i−i−iiiii1-111-1-1−i−iii1-11-1−i−iii−ii1-1
χ1611111-1-11111-11-1-1111-1-111-1-1-1-1−i−iii−i−iii-11−i−i−i−iiiii1-111-1-1−i−iii-11-11ii−i−ii−i-11
χ1722222222222-2-22-2-222-2-2-2-222222-22-20000-2-2000000000000002-22-2000000000000
χ1822222222222-2-22-2-222-2-2-2-22222-22-220000-2-200000000000000-22-22000000000000
χ192222222222-22-2-2-22-2-222-2-222-2-200000000-220000000000000000002-2-2200000000
χ202222222222-22-2-2-22-2-222-2-222-2-200000000-22000000000000000000-222-200000000
χ212222222222-2-22-22-2-2-2-2-22222-2-2000000002-200000000000000000000002-22-20000
χ222222222222-2-22-22-2-2-2-2-22222-2-2000000002-20000000000000000000000-22-220000
χ2322222-2-222222-2-22-22222-2-2-2-2-2-22i−2i−2i2i00002-2000000000000002i−2i−2i2i000000000000
χ2422222-2-222222-2-22-22222-2-2-2-2-2-2−2i2i2i−2i00002-200000000000000−2i2i2i−2i000000000000
χ2522222-2-2222-2222-2-2-2-22222-2-22200000000-2-200000000000000000000002i−2i−2i2i0000
χ2622222-2-2222-2222-2-2-2-22222-2-22200000000-2-20000000000000000000000−2i2i2i−2i0000
χ2722222-2-2222-2-2-2222-2-2-2-2-2-2-2-222000000002200000000000000000022-2-200000000
χ2822222-2-2222-2-2-2222-2-2-2-2-2-2-2-2220000000022000000000000000000-2-22200000000
χ292222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ302222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-2-21111-1-1-1-1000000000000
χ312222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ322222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111122-1-1-1-11111000000000000
χ332222-122-1-1-12-2-22-2-2-1-11111-1-1-1-12-22-2000011−i3−i3i3i3−i3−i3i3i300−i3i3−i3i3-11-11000000000000
χ342222-122-1-1-12-2-22-2-2-1-11111-1-1-1-12-22-2000011i3i3−i3−i3i3i3−i3−i300i3−i3i3−i3-11-11000000000000
χ352222-122-1-1-12-2-22-2-2-1-11111-1-1-1-1-22-22000011−i3−i3i3i3−i3−i3i3i300i3−i3i3−i31-11-1000000000000
χ362222-122-1-1-12-2-22-2-2-1-11111-1-1-1-1-22-22000011i3i3−i3−i3i3i3−i3−i300−i3i3−i3i31-11-1000000000000
χ372222-1-2-2-1-1-122-2-22-2-1-1-1-11111112i−2i−2i2i0000-1133−3−3−3−33300−i3i3i3−i3−iii−i000000000000
χ382222-1-2-2-1-1-122-2-22-2-1-1-1-11111112i−2i−2i2i0000-11−3−33333−3−300i3−i3−i3i3−iii−i000000000000
χ392222-1-2-2-1-1-122-2-22-2-1-1-1-1111111−2i2i2i−2i0000-1133−3−3−3−33300i3−i3−i3i3i−i−ii000000000000
χ402222-1-2-2-1-1-122-2-22-2-1-1-1-1111111−2i2i2i−2i0000-11−3−33333−3−300−i3i3i3−i3i−i−ii000000000000
χ412222-1-2-2-1-1-12-22-2-22-1-111-1-111112i2i−2i−2i2i2i−2i−2i1-1−i−i−i−iiiii2-2-1-111−i−iii000000000000
χ422222-1-2-2-1-1-12-22-2-22-1-111-1-111112i2i−2i−2i−2i−2i2i2i1-1iiii−i−i−i−i-2211-1-1−i−iii000000000000
χ432222-1-2-2-1-1-12-22-2-22-1-111-1-11111−2i−2i2i2i2i2i−2i−2i1-1−i−i−i−iiiii-2211-1-1ii−i−i000000000000
χ442222-1-2-2-1-1-12-22-2-22-1-111-1-11111−2i−2i2i2i−2i−2i2i2i1-1iiii−i−i−i−i2-2-1-111ii−i−i000000000000
χ454444-244-2-2-2-44-4-4-4422-2-222-2-222000000002-2000000000000000000000000000000
χ464444-244-2-2-2-4-44-44-42222-2-2-2-22200000000-22000000000000000000000000000000
χ474444-2-4-4-2-2-2-4444-4-422-2-2-2-222-2-20000000022000000000000000000000000000000
χ484444-2-4-4-2-2-2-4-4-444422222222-2-200000000-2-2000000000000000000000000000000
χ494-44-444i−4i4-4-40000000000004i−4i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ504-44-444i−4i4-4-40000000000004i−4i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ514-44-44−4i4i4-4-4000000000000−4i4i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ524-44-44−4i4i4-4-4000000000000−4i4i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ534-44-4-24i−4i-222000000−2i32i30000−2i2i23−2300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ50000000000000000000000
χ544-44-4-24i−4i-222000000−2i32i30000−2i2i23−230000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ50000000000000000000000
χ554-44-4-24i−4i-2220000002i3−2i30000−2i2i−232300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ130000000000000000000000
χ564-44-4-24i−4i-2220000002i3−2i30000−2i2i−23230000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ130000000000000000000000
χ574-44-4-2−4i4i-222000000−2i32i300002i−2i−23230000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000
χ584-44-4-2−4i4i-222000000−2i32i300002i−2i−232300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000
χ594-44-4-2−4i4i-2220000002i3−2i300002i−2i23−230000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000
χ604-44-4-2−4i4i-2220000002i3−2i300002i−2i23−2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000
χ6188-8-8800-88-800000000000000000000000000000000000000000000000000000000
χ6288-8-8-4004-440000000043−430000000000000000000000000000000000000000000000
χ6388-8-8-4004-4400000000−43430000000000000000000000000000000000000000000000
χ648-8-88800-8-8800000000000000000000000000000000000000000000000000000000
χ658-8-88-40044-40000000000−4i34i300000000000000000000000000000000000000000000
χ668-8-88-40044-400000000004i3−4i300000000000000000000000000000000000000000000

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