Finite Group Databasebeta

← Group #10692671

Character table — Group #10692671

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222444444444444444488888888888888888816161616161616161616242424242424242448484848
order122234466624444412121212121212121212444468888122424242424242424441212121212121212888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
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
χ711111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1
χ911111-1-1111-111-11-11111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-11-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ1011111-1-1111-111-11-11111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-11-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ1111111-1-1111-111-11-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1111-1-1-1-111ii−i−iii−i−i−ii−ii
χ1211111-1-1111-111-11-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1111-1-1-1-111−i−iii−i−iiii−ii−i
χ1311111-1-1111-111-11-11111-1-1-1-111-1-111-111-1-1-11111-1-1-1-1-11-1-1-1-11111ii−i−i−i−iiii−i−ii
χ1411111-1-1111-111-11-11111-1-1-1-111-1-111-111-1-1-11111-1-1-1-1-11-1-1-1-11111−i−iiiii−i−i−iii−i
χ1511111-1-1111-111-11-11111-1-1-1-111-1-111-1-1-111-1-1-1-1-111111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ1611111-1-1111-111-11-11111-1-1-1-111-1-111-1-1-111-1-1-1-1-111111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222-2-2-2-222-2-222-2-2-2-2000020000-200000000000000000000002-22-20000
χ18222222222222-2-2-2-222-2-222-2-2-2-2000020000-20000000000000000000000-22-220000
χ192222222222-2-22-2-22-2-22222-2-2-2-20000-2000020000000000000000002-22-200000000
χ202222222222-2-22-2-22-2-22222-2-2-2-20000-200002000000000000000000-22-2200000000
χ212222222222-2-2-222-2-2-2-2-22222222-22-2-20000-200000000002-2002-200000000000000
χ222222222222-2-2-222-2-2-2-2-2222222-22-22-20000-20000000000-2200-2200000000000000
χ2322222-2-22222-222-2-2-2-222-2-222-2-2000020000-20000000000000000002i−2i−2i2i00000000
χ2422222-2-22222-222-2-2-2-222-2-222-2-2000020000-2000000000000000000−2i2i2i−2i00000000
χ2522222-2-22222-2-2-222-2-2-2-2-2-2-2-2222-2-2220000200000000002-200-2200000000000000
χ2622222-2-22222-2-2-222-2-2-2-2-2-2-2-222-222-22000020000000000-22002-200000000000000
χ2722222-2-2222-22-22-2222-2-2-2-222-2-20000-20000200000000000000000000002i−2i−2i2i0000
χ2822222-2-2222-22-22-2222-2-2-2-222-2-20000-2000020000000000000000000000−2i2i2i−2i0000
χ292222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ302222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-111111111-2-2-1-111-1-111000000000000
χ312222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ322222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-1111111112211-1-111-1-1000000000000
χ332222-122-1-1-1-2-2-222-21111-1-1-1-1-1-12-22-2100001−i3−i3i3i3−i3−i3i3i300-11−i3i3-11−i3i3000000000000
χ342222-122-1-1-1-2-2-222-21111-1-1-1-1-1-12-22-2100001i3i3−i3−i3i3i3−i3−i300-11i3−i3-11i3−i3000000000000
χ352222-122-1-1-1-2-2-222-21111-1-1-1-1-1-1-22-22100001−i3−i3i3i3−i3−i3i3i3001-1i3−i31-1i3−i3000000000000
χ362222-122-1-1-1-2-2-222-21111-1-1-1-1-1-1-22-22100001i3i3−i3−i3i3i3−i3−i3001-1−i3i31-1−i3i3000000000000
χ372222-1-2-2-1-1-12-2-2-22211111111-1-12-2-22-10000-1−i3−i3i3i3i3i3−i3−i300-11−i3i31-1i3−i3000000000000
χ382222-1-2-2-1-1-12-2-2-22211111111-1-12-2-22-10000-1i3i3−i3−i3−i3−i3i3i300-11i3−i31-1−i3i3000000000000
χ392222-1-2-2-1-1-12-2-2-22211111111-1-1-222-2-10000-1−i3−i3i3i3i3i3−i3−i3001-1i3−i3-11−i3i3000000000000
χ402222-1-2-2-1-1-12-2-2-22211111111-1-1-222-2-10000-1i3i3−i3−i3−i3−i3i3i3001-1−i3i3-11i3−i3000000000000
χ412222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-122-2-2122-2-21-1-1-1-111112-2-1-1-1-11111000000000000
χ422222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-122-2-21-2-22211111-1-1-1-1-22-1-11111-1-1000000000000
χ432222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-1-2-222122-2-21-1-1-1-11111-221111-1-1-1-1000000000000
χ442222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-1-2-2221-2-22211111-1-1-1-12-211-1-1-1-111000000000000
χ454444-244-2-2-244-4-4-4-4-2-222-2-222220000-200002000000000000000000000000000000
χ464444-244-2-2-2-4-44-4-4422-2-2-2-22222000020000-2000000000000000000000000000000
χ474444-2-4-4-2-2-24-444-4-422-2-222-2-2220000-200002000000000000000000000000000000
χ484444-2-4-4-2-2-2-44-44-44-2-22222-2-222000020000-2000000000000000000000000000000
χ494-4-4444i−4i-4-4400000000004i−4i0000000002-22i−2i02-22-22i−2i2i−2i0000000000000000000000
χ504-4-4444i−4i-4-4400000000004i−4i000000000-22−2i2i0-22-22−2i2i−2i2i0000000000000000000000
χ514-4-444−4i4i-4-440000000000−4i4i0000000002-2−2i2i02-22-2−2i2i−2i2i0000000000000000000000
χ524-4-444−4i4i-4-440000000000−4i4i000000000-222i−2i0-22-222i−2i2i−2i0000000000000000000000
χ534-4-44-24i−4i22-20000000000−2i2i23−23−2i32i3000002-22i−2i0−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ544-4-44-24i−4i22-20000000000−2i2i23−23−2i32i300000-22−2i2i01+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ554-4-44-24i−4i22-20000000000−2i2i−23232i3−2i3000002-22i−2i0−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ564-4-44-24i−4i22-20000000000−2i2i−23232i3−2i300000-22−2i2i01−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ574-4-44-2−4i4i22-200000000002i−2i23−232i3−2i3000002-2−2i2i0−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ584-4-44-2−4i4i22-200000000002i−2i23−232i3−2i300000-222i−2i01−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ594-4-44-2−4i4i22-200000000002i−2i−2323−2i32i3000002-2−2i2i0−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ604-4-44-2−4i4i22-200000000002i−2i−2323−2i32i300000-222i−2i01+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ6188-8-88008-8-800000000000000000000000000000000000000000000000000000000
χ6288-8-8-400-444000000−4i34i3000000000000000000000000000000000000000000000000
χ6388-8-8-400-4440000004i3−4i3000000000000000000000000000000000000000000000000
χ648-88-8800-88-800000000000000000000000000000000000000000000000000000000
χ658-88-8-4004-4400000000−4i34i30000000000000000000000000000000000000000000000
χ668-88-8-4004-44000000004i3−4i30000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.