Finite Group Databasebeta

← Group #10692670

Character table — Group #10692670

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222444444444444444488888888888888888816161616161616161616242424242424242448484848
order122234466624444412121212121212121212688888888122424242424242424882424242424242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ911111-1-1111-111-11-1111111-1-1-1-1-1ii−i−i11-1-1-11111-1-1-1-1i−iii−i−iii−i−i11-1-1ii−i−i1-1i−i
χ1011111-1-1111-111-11-1111111-1-1-1-1-1ii−i−i11-1-1-11111-1-1-1-1i−iii−i−iii−i−i-1-111−i−iii-11−ii
χ1111111-1-1111-111-11-1111111-1-1-1-1-1ii−i−i-1-111-1-1-1-1-11111−iiii−i−i−i−iii11-1-1ii−i−i-11−ii
χ1211111-1-1111-111-11-1111111-1-1-1-1-1ii−i−i-1-111-1-1-1-1-11111−iiii−i−i−i−iii-1-111−i−iii1-1i−i
χ1311111-1-1111-111-11-1111111-1-1-1-1-1−i−iii11-1-1-11111-1-1-1-1−ii−i−iii−i−iii11-1-1−i−iii1-1−ii
χ1411111-1-1111-111-11-1111111-1-1-1-1-1−i−iii11-1-1-11111-1-1-1-1−ii−i−iii−i−iii-1-111ii−i−i-11i−i
χ1511111-1-1111-111-11-1111111-1-1-1-1-1−i−iii-1-111-1-1-1-1-11111i−i−i−iiiii−i−i11-1-1−i−iii-11i−i
χ1611111-1-1111-111-11-1111111-1-1-1-1-1−i−iii-1-111-1-1-1-1-11111i−i−i−iiiii−i−i-1-111ii−i−i1-1−ii
χ17222222222222-2-2-2-222-2-2-2-222-2-222-22-20000-200000000002-22-20000000000000000
χ18222222222222-2-2-2-222-2-2-2-222-2-22-22-220000-20000000000-22-220000000000000000
χ192222222222-2-22-2-22-2-222-2-22222-200000000-200000000000000000000002-22-20000
χ202222222222-2-22-2-22-2-222-2-22222-200000000-20000000000000000000000-22-220000
χ212222222222-2-2-222-2-2-2-2-22222-2-2-20000000020000000000000000002-22-200000000
χ222222222222-2-2-222-2-2-2-2-22222-2-2-2000000002000000000000000000-22-2200000000
χ2322222-2-22222-222-2-2-2-222-2-2-2-2-2-2200000000200000000000000000000002i−2i−2i2i0000
χ2422222-2-22222-222-2-2-2-222-2-2-2-2-2-220000000020000000000000000000000−2i2i2i−2i0000
χ2522222-2-22222-2-2-222-2-2-2-222-2-222200000000-20000000000000000002-2-2200000000
χ2622222-2-22222-2-2-222-2-2-2-222-2-222200000000-2000000000000000000-222-200000000
χ2722222-2-2222-22-22-2222-2-2-2-2-2-222-22i−2i−2i2i0000200000000002i−2i−2i2i0000000000000000
χ2822222-2-2222-22-22-2222-2-2-2-2-2-222-2−2i2i2i−2i000020000000000−2i2i2i−2i0000000000000000
χ292222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ302222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-111111111-2-2-1-1-1-11111000000000000
χ312222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ322222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-111111111221111-1-1-1-1000000000000
χ332222-122-1-1-122-2-2-2-2-1-11111-1-111-12-22-20000133−3−333−3−300-11-113−33−3000000000000
χ342222-122-1-1-122-2-2-2-2-1-11111-1-111-12-22-200001−3−333−3−33300-11-11−33−33000000000000
χ352222-122-1-1-122-2-2-2-2-1-11111-1-111-1-22-220000133−3−333−3−3001-11-1−33−33000000000000
χ362222-122-1-1-122-2-2-2-2-1-11111-1-111-1-22-2200001−3−333−3−333001-11-13−33−3000000000000
χ372222-1-2-2-1-1-1-222-22-2-1-1-1-1-1-1111112i2i−2i−2i22-2-21-1-1-1-111112i−2i−i−iii−i−iii000000000000
χ382222-1-2-2-1-1-1-222-22-2-1-1-1-1-1-1111112i2i−2i−2i-2-22211111-1-1-1-1−2i2i−i−iiiii−i−i000000000000
χ392222-1-2-2-1-1-1-222-22-2-1-1-1-1-1-111111−2i−2i2i2i22-2-21-1-1-1-11111−2i2iii−i−iii−i−i000000000000
χ402222-1-2-2-1-1-1-222-22-2-1-1-1-1-1-111111−2i−2i2i2i-2-22211111-1-1-1-12i−2iii−i−i−i−iii000000000000
χ412222-1-2-2-1-1-1-22-22-22-1-1111111-1-112i−2i−2i2i0000-133−3−3−3−33300−iii−ii3−i3−i3i3000000000000
χ422222-1-2-2-1-1-1-22-22-22-1-1111111-1-112i−2i−2i2i0000-1−3−33333−3−300−iii−i−i3i3i3−i3000000000000
χ432222-1-2-2-1-1-1-22-22-22-1-1111111-1-11−2i2i2i−2i0000-133−3−3−3−33300i−i−ii−i3i3i3−i3000000000000
χ442222-1-2-2-1-1-1-22-22-22-1-1111111-1-11−2i2i2i−2i0000-1−3−33333−3−300i−i−iii3−i3−i3i3000000000000
χ454444-244-2-2-2-4-44-4-4422-2-222-2-2-2-22000000002000000000000000000000000000000
χ464444-244-2-2-2-4-4-444-42222-2-2-2-222200000000-2000000000000000000000000000000
χ474444-2-4-4-2-2-24-444-4-422-2-2222222-200000000-2000000000000000000000000000000
χ484444-2-4-4-2-2-24-4-4-4442222-2-222-2-2-2000000002000000000000000000000000000000
χ494-4-4444i−4i4-4-40000000000004i−4i00000002-22i−2i02-22-22i−2i2i−2i0000000000000000000000
χ504-4-4444i−4i4-4-40000000000004i−4i0000000-22−2i2i0-22-22−2i2i−2i2i0000000000000000000000
χ514-4-444−4i4i4-4-4000000000000−4i4i00000002-2−2i2i02-22-2−2i2i−2i2i0000000000000000000000
χ524-4-444−4i4i4-4-4000000000000−4i4i0000000-222i−2i0-22-222i−2i2i−2i0000000000000000000000
χ534-4-44-24i−4i-2220000000023−2300−2i2i−2i32i3000002-22i−2i0−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ544-4-44-24i−4i-2220000000023−2300−2i2i−2i32i300000-22−2i2i01−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ554-4-44-24i−4i-22200000000−232300−2i2i2i3−2i3000002-22i−2i0−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ564-4-44-24i−4i-22200000000−232300−2i2i2i3−2i300000-22−2i2i01+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ574-4-44-2−4i4i-2220000000023−23002i−2i2i3−2i3000002-2−2i2i0−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ584-4-44-2−4i4i-2220000000023−23002i−2i2i3−2i300000-222i−2i01−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ594-4-44-2−4i4i-22200000000−2323002i−2i−2i32i3000002-2−2i2i0−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ604-4-44-2−4i4i-22200000000−2323002i−2i−2i32i300000-222i−2i01+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ6188-8-8800-88-800000000000000000000000000000000000000000000000000000000
χ6288-8-8-4004-44000000000043−4300000000000000000000000000000000000000000000
χ6388-8-8-4004-440000000000−434300000000000000000000000000000000000000000000
χ648-88-8800-8-8800000000000000000000000000000000000000000000000000000000
χ658-88-8-40044-400000043−43000000000000000000000000000000000000000000000000
χ668-88-8-40044-4000000−4343000000000000000000000000000000000000000000000000

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