Finite Group Databasebeta

← Group #10692202

Character table — Group #10692202

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222444444444444444488888888888888888816161616161616161616242424242424242448484848
order122234466624444412121212121212121212688888888122424242424242424882424242424242424244488882288
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
χ5111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ6111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ911111-1-111111-11-1-111-1-111-1-1-1-11i−ii−iii−i−i-1iiii−i−i−i−i1-1ii−i−i11-1-111-1-1ii−i−i1-1i−i
χ1011111-1-111111-11-1-111-1-111-1-1-1-11i−ii−iii−i−i-1iiii−i−i−i−i1-1ii−i−i11-1-1-1-111−i−iii-11−ii
χ1111111-1-111111-11-1-111-1-111-1-1-1-11i−ii−i−i−iii-1−i−i−i−iiiii-11ii−i−i-1-11111-1-1ii−i−i-11−ii
χ1211111-1-111111-11-1-111-1-111-1-1-1-11i−ii−i−i−iii-1−i−i−i−iiiii-11ii−i−i-1-111-1-111−i−iii1-1i−i
χ1311111-1-111111-11-1-111-1-111-1-1-1-11−ii−iiii−i−i-1iiii−i−i−i−i-11−i−iii-1-11111-1-1−i−iii-11i−i
χ1411111-1-111111-11-1-111-1-111-1-1-1-11−ii−iiii−i−i-1iiii−i−i−i−i-11−i−iii-1-111-1-111ii−i−i1-1−ii
χ1511111-1-111111-11-1-111-1-111-1-1-1-11−ii−ii−i−iii-1−i−i−i−iiiii1-1−i−iii11-1-111-1-1−i−iii1-1−ii
χ1611111-1-111111-11-1-111-1-111-1-1-1-11−ii−ii−i−iii-1−i−i−i−iiiii1-1−i−iii11-1-1-1-111ii−i−i-11i−i
χ1722222222222-2-2-22-2-2-2-2-2-2-22222200000000-200000000000000000000002-22-20000
χ1822222222222-2-2-22-2-2-2-2-2-2-22222200000000-20000000000000000000000-22-220000
χ192222222222-22-2-2-2222-2-2-2-222-2-2-222-2-20000200000000002-22-20000000000000000
χ202222222222-22-2-2-2222-2-2-2-222-2-2-2-2-222000020000000000-22-220000000000000000
χ212222222222-2-222-2-2-2-2222222-2-2-200000000-20000000000000000002-22-200000000
χ222222222222-2-222-2-2-2-2222222-2-2-200000000-2000000000000000000-22-2200000000
χ2322222-2-22222-22-2-22-2-222-2-2-2-2-2-2200000000200000000000000000000002i−2i−2i2i0000
χ2422222-2-22222-22-2-22-2-222-2-2-2-2-2-220000000020000000000000000000000−2i2i2i−2i0000
χ2522222-2-2222-222-22-22222-2-2-2-222-22i−2i−2i2i0000-200000000002i−2i−2i2i0000000000000000
χ2622222-2-2222-222-22-22222-2-2-2-222-2−2i2i2i−2i0000-20000000000−2i2i2i−2i0000000000000000
χ2722222-2-2222-2-2-2222-2-2-2-222-2-222-20000000020000000000000000002-2-2200000000
χ2822222-2-2222-2-2-2222-2-2-2-222-2-222-2000000002000000000000000000-222-200000000
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
χ332222-122-1-1-1-22-2-2-22-1-11111-1-111122-2-20000-133−3−333−3−300-11-113−33−3000000000000
χ342222-122-1-1-1-22-2-2-22-1-11111-1-111122-2-20000-1−3−333−3−33300-11-11−33−33000000000000
χ352222-122-1-1-1-22-2-2-22-1-11111-1-1111-2-2220000-133−3−333−3−3001-11-1−33−33000000000000
χ362222-122-1-1-1-22-2-2-22-1-11111-1-1111-2-2220000-1−3−333−3−333001-11-13−33−3000000000000
χ372222-1-2-2-1-1-122-22-2-2-1-111-1-11111-12i−2i2i−2i2i2i−2i−2i1−i−i−i−iiiii2-2−i−iii-1-111000000000000
χ382222-1-2-2-1-1-122-22-2-2-1-111-1-11111-12i−2i2i−2i−2i−2i2i2i1iiii−i−i−i−i-22−i−iii11-1-1000000000000
χ392222-1-2-2-1-1-122-22-2-2-1-111-1-11111-1−2i2i−2i2i2i2i−2i−2i1−i−i−i−iiiii-22ii−i−i11-1-1000000000000
χ402222-1-2-2-1-1-122-22-2-2-1-111-1-11111-1−2i2i−2i2i−2i−2i2i2i1iiii−i−i−i−i2-2ii−i−i-1-111000000000000
χ412222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-112i−2i−2i2i00001−i3−i3i3i3i3i3−i3−i300−iii−i−333−3000000000000
χ422222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-112i−2i−2i2i00001i3i3−i3−i3−i3−i3i3i300−iii−i3−3−33000000000000
χ432222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-11−2i2i2i−2i00001−i3−i3i3i3i3i3−i3−i300i−i−ii3−3−33000000000000
χ442222-1-2-2-1-1-1-222-22-2-1-1-1-11111-1-11−2i2i2i−2i00001i3i3−i3−i3−i3−i3i3i300i−i−ii−333−3000000000000
χ454444-244-2-2-24-4-4-44-4222222-2-2-2-2-2000000002000000000000000000000000000000
χ464444-244-2-2-2-4-444-4-422-2-2-2-2-2-2222000000002000000000000000000000000000000
χ474444-2-4-4-2-2-24-44-4-4422-2-2222222-200000000-2000000000000000000000000000000
χ484444-2-4-4-2-2-2-4-4-44442222-2-222-2-2200000000-2000000000000000000000000000000
χ4944-4-444-44-4-40000000000004-400000002i−2i2i−2i02i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ5044-4-444-44-4-40000000000004-40000000−2i2i−2i2i0−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ5144-4-44-444-4-4000000000000-4400000002-2-2202-22-2-22-220000000000000000000000
χ5244-4-44-444-4-4000000000000-440000000-222-20-22-222-22-20000000000000000000000
χ5344-4-4-24-4-2220000000023−2323−23-2200000002i−2i2i−2i0−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ5444-4-4-24-4-2220000000023−2323−23-220000000−2i2i−2i2i0ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ5544-4-4-24-4-22200000000−2323−2323-2200000002i−2i2i−2i0ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ5644-4-4-24-4-22200000000−2323−2323-220000000−2i2i−2i2i0−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ5744-4-4-2-44-2220000000023−23−23232-200000002-2-220−1+31−3−1−31+31−3−1+31+3−1−30000000000000000000000
χ5844-4-4-2-44-2220000000023−23−23232-20000000-222-201−3−1+31+3−1−3−1+31−3−1−31+30000000000000000000000
χ5944-4-4-2-44-22200000000−232323−232-200000002-2-220−1−31+3−1+31−31+3−1−31−3−1+30000000000000000000000
χ6044-4-4-2-44-22200000000−232323−232-20000000-222-201+3−1−31−3−1+3−1−31+3−1+31−30000000000000000000000
χ618-88-8800-88-800000000000000000000000000000000000000000000000000000000
χ628-88-8-4004-440000000000000043−430000000000000000000000000000000000000000
χ638-88-8-4004-4400000000000000−43430000000000000000000000000000000000000000
χ648-8-88800-8-8800000000000000000000000000000000000000000000000000000000
χ658-8-88-40044-400000043−43000000000000000000000000000000000000000000000000
χ668-8-88-40044-4000000−4343000000000000000000000000000000000000000000000000

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