Finite Group Databasebeta

← Group #72341821

Character table — Group #72341821

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122446666888812121212121212121212121212121212121216161616161616161616323232323232323232323232484848486464646464646464
order1222444422448888222244444444444444334466666612121212242424242424242444881212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ31111111111111111111111111111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ4111111111111-1-1-1-111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ5111111111111-1-1-1-1111111111111111111−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ6111111111111-1-1-1-1111111111111111111−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ7111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1
χ8111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1111+i321+i321+i321+i321−i321−i321−i321−i32
χ9111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1111−i321−i321−i321−i321+i321+i321+i321+i32
χ10111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ12111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-1-11i−i1-1-1111-1-111-1-111-1-1iiiii−i−i−i−i−i11i−i11-1-1-1-1-1-11111-1-111-1-1i−i1-1i−ii−ii−ii−i
χ1411-1-1-11i−i1-1-1111-1-111-1-111-1-1iiiii−i−i−i−i−i−1−i32−1+i32i−i−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32i−i1-1ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ14
χ1511-1-1-11i−i1-1-1111-1-111-1-111-1-1iiiii−i−i−i−i−i−1+i32−1−i32i−i−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32i−i1-1ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ22
χ1611-1-1-11i−i1-1-11-1-11111-1-111-1-1iiiii−i−i−i−i−i11−ii11-1-1-1-1-1-111-1-111-1-111−ii-11i−i−iii−i−ii
χ1711-1-1-11i−i1-1-11-1-11111-1-111-1-1iiiii−i−i−i−i−i−1−i32−1+i32−ii−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−ii-11ζ22−ζ22−ζ22ζ22ζ14−ζ14−ζ14ζ14
χ1811-1-1-11i−i1-1-11-1-11111-1-111-1-1iiiii−i−i−i−i−i−1+i32−1−i32−ii−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−ii-11ζ14−ζ14−ζ14ζ14ζ22−ζ22−ζ22ζ22
χ1911-1-1-11−ii1-1-1111-1-111-1-111-1-1−i−i−i−i−iiiiii11−ii11-1-1-1-1-1-11111-1-111-1-1−ii1-1−ii−ii−ii−ii
χ2011-1-1-11−ii1-1-1111-1-111-1-111-1-1−i−i−i−i−iiiiii−1−i32−1+i32−ii−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−ii1-1−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ14
χ2111-1-1-11−ii1-1-1111-1-111-1-111-1-1−i−i−i−i−iiiiii−1+i32−1−i32−ii−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−ii1-1−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ22
χ2211-1-1-11−ii1-1-11-1-11111-1-111-1-1−i−i−i−i−iiiiii11i−i11-1-1-1-1-1-111-1-111-1-111i−i-11−iii−i−iii−i
χ2311-1-1-11−ii1-1-11-1-11111-1-111-1-1−i−i−i−i−iiiiii−1−i32−1+i32i−i−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32i−i-11−ζ22ζ22ζ22−ζ22−ζ14ζ14ζ14−ζ14
χ2411-1-1-11−ii1-1-11-1-11111-1-111-1-1−i−i−i−i−iiiiii−1+i32−1−i32i−i−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32i−i-11−ζ14ζ14ζ14−ζ14−ζ22ζ22ζ22−ζ22
χ252222-2-20022-2-200002-22-22-22-200000000002200222222-2-2-2-200000000000000000000
χ262222-2-20022-2-200002-22-22-22-20000000000−1−i3−1+i300−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31−i31+i31−i300000000000000000000
χ272222-2-20022-2-200002-22-22-22-20000000000−1+i3−1−i300−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31+i31−i31+i300000000000000000000
χ2822-2-22-2002-22-200002-2-222-2-220000000000220022-2-2-2-222-2-200000000000000000000
χ2922-2-22-2002-22-200002-2-222-2-220000000000−1−i3−1+i300−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i31+i31−i300000000000000000000
χ3022-2-22-2002-22-200002-2-222-2-220000000000−1+i3−1−i300−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i31−i31+i300000000000000000000
χ313333333333333333-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-10033000000000000000000-1-1-1-100000000
χ32333333333333-3-3-3-3-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-100-3-3000000000000000000111100000000
χ33333333-3-333333333-1-1-1-1-1-1-1-1-31111-3111100-3-300000000000000000011-1-100000000
χ34333333-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-31111-311110033000000000000000000-1-11100000000
χ3533-3-3-333i−3i3-3-3333-3-3-1-111-1-1113i−i−i−i−i−3iiiii003i−3i000000000000000000−ii-1100000000
χ3633-3-3-333i−3i3-3-33-3-333-1-111-1-1113i−i−i−i−i−3iiiii00−3i3i000000000000000000i−i1-100000000
χ3733-3-3-33−3i3i3-3-3333-3-3-1-111-1-111−3iiiii3i−i−i−i−i00−3i3i000000000000000000i−i-1100000000
χ3833-3-3-33−3i3i3-3-33-3-333-1-111-1-111−3iiiii3i−i−i−i−i003i−3i000000000000000000−ii1-100000000
χ3966666666-2-2-2-200002-22-2-22-22-222-2-2-222-2-20000000000000000000000000000000000
χ4066666666-2-2-2-20000-22-222-22-2-2-2-222-2-2-2220000000000000000000000000000000000
χ41666666-6-6-2-2-2-200002-22-2-22-222-2-2222-2-2220000000000000000000000000000000000
χ42666666-6-6-2-2-2-20000-22-222-22-2222-2-2222-2-20000000000000000000000000000000000
χ436666-6-60066-6-60000-22-22-22-2200000000000000000000000000000000000000000000
χ446666-6-600-2-22200002222-2-2-2-204-40004-4000000000000000000000000000000000000
χ456666-6-600-2-22200002222-2-2-2-20-44000-44000000000000000000000000000000000000
χ466666-6-600-2-2220000-2-2-2-222220004-40004-40000000000000000000000000000000000
χ476666-6-600-2-2220000-2-2-2-22222000-44000-440000000000000000000000000000000000
χ4866-6-66-6006-66-60000-222-2-222-200000000000000000000000000000000000000000000
χ4966-6-66-600-22-22000022-2-2-2-22204i−4i000−4i4i000000000000000000000000000000000000
χ5066-6-66-600-22-22000022-2-2-2-2220−4i4i0004i−4i000000000000000000000000000000000000
χ5166-6-66-600-22-220000-2-22222-2-20004i−4i000−4i4i0000000000000000000000000000000000
χ5266-6-66-600-22-220000-2-22222-2-2000−4i4i0004i−4i0000000000000000000000000000000000
χ5366-6-6-666i−6i-222-200002-2-22-222-2−2i2i2i−2i−2i2i−2i−2i2i2i0000000000000000000000000000000000
χ5466-6-6-666i−6i-222-20000-222-22-2-22−2i−2i−2i2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ5566-6-6-66−6i6i-222-200002-2-22-222-22i−2i−2i2i2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ5666-6-6-66−6i6i-222-20000-222-22-2-222i2i2i−2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ578-88-800000000−2i22i2−2i22i20000000000000000002200-2-22-22-20000−i2i2−i2i2−i2i2−i2i2000000000000
χ588-88-800000000−2i22i2−2i22i2000000000000000000−1−i3−1+i3001+i31−i3−1−i31+i3−1+i31−i30000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23000000000000
χ598-88-800000000−2i22i2−2i22i2000000000000000000−1+i3−1−i3001−i31+i3−1+i31−i3−1−i31+i30000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000000000
χ608-88-8000000002i2−2i22i2−2i20000000000000000002200-2-22-22-20000i2−i2i2−i2i2−i2i2−i2000000000000
χ618-88-8000000002i2−2i22i2−2i2000000000000000000−1−i3−1+i3001+i31−i3−1−i31+i3−1+i31−i30000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23000000000000
χ628-88-8000000002i2−2i22i2−2i2000000000000000000−1+i3−1−i3001−i31+i3−1+i31−i3−1−i31+i30000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13000000000000
χ638-8-8800000000−2i22i22i2−2i20000000000000000002200-2-2-22-220000−i2i2i2−i2−i2i2i2−i2000000000000
χ648-8-8800000000−2i22i22i2−2i2000000000000000000−1−i3−1+i3001+i31−i31+i3−1−i31−i3−1+i30000ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23000000000000
χ658-8-8800000000−2i22i22i2−2i2000000000000000000−1+i3−1−i3001−i31+i31−i3−1+i31+i3−1−i30000ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13000000000000
χ668-8-88000000002i2−2i2−2i22i20000000000000000002200-2-2-22-220000i2−i2−i2i2i2−i2−i2i2000000000000
χ678-8-88000000002i2−2i2−2i22i2000000000000000000−1−i3−1+i3001+i31−i31+i3−1−i31−i3−1+i30000−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23000000000000
χ688-8-88000000002i2−2i2−2i22i2000000000000000000−1+i3−1−i3001−i31+i31−i3−1+i31+i3−1−i30000−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13000000000000

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