Finite Group Databasebeta

← Group #10711079

Character table — Group #10711079

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222222244444444444444888888888888888888888881616161616161616242424242424242448484848
order122344612122224444466612121224466888812121212121224242424242424244461212121212222244444444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1111111-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111-1-1111111-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111-1-1111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111
χ8111111111111111-1-1111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1
χ91111-1-11-1-1-1-1-1111111-1-111-1-11-1-1-1ii−i−i1111-1-1iiii−i−i−i−ii−i-11ii−i−i1-11-11-11-1i−ii−i
χ101111-1-11-1-1-1-1-1111111-1-111-1-11-1-1-1ii−i−i1111-1-1iiii−i−i−i−ii−i-11ii−i−i-11-11-11-11−ii−ii
χ111111-1-11-1-1-1-1-1111111-1-111-1-11-1-1-1−i−iii1111-1-1−i−i−i−iiiii−ii-11−i−iii1-11-11-11-1−ii−ii
χ121111-1-11-1-1-1-1-1111111-1-111-1-11-1-1-1−i−iii1111-1-1−i−i−i−iiiii−ii-11−i−iii-11-11-11-11i−ii−i
χ131111-1-11-1-1-1-1-1111-1-11-1-111-11-11-1-1ii−i−i11-1-111iiii−i−i−i−i−ii1-1−i−iii1-1-111-1-11i−i−ii
χ141111-1-11-1-1-1-1-1111-1-11-1-111-11-11-1-1ii−i−i11-1-111iiii−i−i−i−i−ii1-1−i−iii-111-1-111-1−iii−i
χ151111-1-11-1-1-1-1-1111-1-11-1-111-11-11-1-1−i−iii11-1-111−i−i−i−iiiiii−i1-1ii−i−i1-1-111-1-11−iii−i
χ161111-1-11-1-1-1-1-1111-1-11-1-111-11-11-1-1−i−iii11-1-111−i−i−i−iiiiii−i1-1ii−i−i-111-1-111-1i−i−ii
χ172222222222-2-22-2-222222222-2-22-2-20000-2-222220000000000-2-20000000000000000
χ182222222222-2-22-2-2-2-222222222-2-2-20000-2-2-2-2-2-20000000000220000000000000000
χ19222222222-22-2-22-2002-2-2-2-220002-200002-200000000000000000000002200-2-20000
χ20222222222-22-2-22-2002-2-2-2-220002-200002-20000000000000000000000-2-200220000
χ21222222222-2-22-2-22002-2-2-2-22000-220000-22000000000000000000002200-2-2000000
χ22222222222-2-22-2-22002-2-2-2-22000-220000-2200000000000000000000-2-20022000000
χ232222-2-22-2-222-2-2-2200222-2-2-20002-20000-22000000000000000000002-200-22000000
χ242222-2-22-2-222-2-2-2200222-2-2-20002-20000-2200000000000000000000-22002-2000000
χ252222-2-22-2-22-22-22-200222-2-2-2000-2200002-200000000000000000000002-200-220000
χ262222-2-22-2-22-22-22-200222-2-2-2000-2200002-20000000000000000000000-22002-20000
χ272222-2-22-2-2-2222-2-2222-2-222-22-2-2220000-2-222-2-200000000002-20000000000000000
χ282222-2-22-2-2-2222-2-2-2-22-2-222-2-222220000-2-2-2-2220000000000-220000000000000000
χ29222-122-1-1-122222222-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ30222-122-1-1-122222222-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-1-11111000000000000
χ31222-122-1-1-1222222-2-2-1-1-1-1-1-1-2-2-2-1-12222-1-11111-1-1-1-1-1-1-1-1-2-2111111000000000000
χ32222-122-1-1-1222222-2-2-1-1-1-1-1-1-2-2-2-1-1-2-2-2-2-1-11111111111112211-1-1-1-1000000000000
χ33222-122-1-1-12-2-22-2-222-1-1-1-1-1-1-2-2211000011-1-1-1-1−i3−i3i3i3−i3−i3i3i30011−i3i3−i3i3000000000000
χ34222-122-1-1-12-2-22-2-222-1-1-1-1-1-1-2-2211000011-1-1-1-1i3i3−i3−i3i3i3−i3−i30011i3−i3i3−i3000000000000
χ35222-122-1-1-12-2-22-2-2-2-2-1-1-1-1-1-122-2110000111111−i3−i3i3i3−i3−i3i3i300-1-1i3−i3i3−i3000000000000
χ36222-122-1-1-12-2-22-2-2-2-2-1-1-1-1-1-122-2110000111111i3i3−i3−i3i3i3−i3−i300-1-1−i3i3−i3i3000000000000
χ37222-1-2-2-111-2222-2-222-111-1-112-2-2-1-1000011-1-11133−3−3−3−33300-113−3−33000000000000
χ38222-1-2-2-111-2222-2-222-111-1-112-2-2-1-1000011-1-111−3−33333−3−300-11−333−3000000000000
χ39222-1-2-2-111-2222-2-2-2-2-111-1-11-222-1-100001111-1-133−3−3−3−333001-1−333−3000000000000
χ40222-1-2-2-111-2222-2-2-2-2-111-1-11-222-1-100001111-1-1−3−33333−3−3001-13−3−33000000000000
χ41222-1-2-2-111-2-2-222222-111-1-11-22-2112i2i−2i−2i-1-1-1-111−i−i−i−iiiii2i−2i1-1−i−iii000000000000
χ42222-1-2-2-111-2-2-222222-111-1-11-22-211−2i−2i2i2i-1-1-1-111iiii−i−i−i−i−2i2i1-1ii−i−i000000000000
χ43222-1-2-2-111-2-2-2222-2-2-111-1-112-22112i2i−2i−2i-1-111-1-1−i−i−i−iiiii−2i2i-11ii−i−i000000000000
χ44222-1-2-2-111-2-2-2222-2-2-111-1-112-2211−2i−2i2i2i-1-111-1-1iiii−i−i−i−i2i−2i-11−i−iii000000000000
χ45444-244-2-2-2-44-4-44-400-22222-2000-220000-2200000000000000000000000000000000
χ46444-244-2-2-2-4-44-4-4400-22222-20002-200002-200000000000000000000000000000000
χ47444-2-4-4-22244-4-4-4400-2-2-2222000-2200002-200000000000000000000000000000000
χ48444-2-4-4-2224-44-44-400-2-2-22220002-20000-2200000000000000000000000000000000
χ4944-444-44-4-400000000-400004000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ5044-444-44-4-400000000-40000400000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ5144-44-4444400000000-40000-4000002-2-220000002-22-2-22-2200000000000000000000
χ5244-44-4444400000000-40000-400000-222-2000000-22-222-22-200000000000000000000
χ5344-4-24-4-222000000002−2i32i3−2i32i3-2000002i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ5444-4-24-4-222000000002−2i32i3−2i32i3-200000−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ5544-4-24-4-2220000000022i3−2i32i3−2i3-2000002i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000
χ5644-4-24-4-2220000000022i3−2i32i3−2i3-200000−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000
χ5744-4-2-44-2-2-2000000002−2i32i32i3−2i32000002-2-22000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000
χ5844-4-2-44-2-2-2000000002−2i32i32i3−2i3200000-222-20000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000
χ5944-4-2-44-2-2-20000000022i3−2i3−2i32i32000002-2-22000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000
χ6044-4-2-44-2-2-20000000022i3−2i3−2i32i3200000-222-20000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000
χ618-80800-8000000004-4000000000000000004-4000000000000000000000000000000
χ628-80800-800000000-4400000000000000000-44000000000000000000000000000000
χ638-80-400443−430000004-400000000000000000-2223−230000000000000000000000000000
χ648-80-400443−43000000-44000000000000000002-2−23230000000000000000000000000000
χ658-80-4004−43430000004-400000000000000000-22−23230000000000000000000000000000
χ668-80-4004−4343000000-44000000000000000002-223−230000000000000000000000000000

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