Finite Group Databasebeta

← Group #72342120

Character table — Group #72342120

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122446666888812121212121212121212121212121212121216161616161616161616323232323232323232323232484848486464646464646464
order12442424224488882222222224444444442334661212121266121224242424242424244488666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111−1−i32−1+i321−1−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
χ311111111111111111111111111111111111−1+i32−1−i321−1+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
χ4111111111111-1-1-1-1111111111111111111-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ5111111111111-1-1-1-1111111111111111111-1−1−i32−1+i32-1−1−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−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ6111111111111-1-1-1-1111111111111111111-1−1+i32−1−i32-1−1+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+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ7111111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-111-1111111111111111111-1-111-1-1-1-1-1-1-1-1
χ8111111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1−1−i32−1+i32-1−1−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
χ9111111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1−1+i32−1−i32-1−1+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
χ10111111-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-11-11-11-11
χ11111111-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-11−1−i32−1+i321−1−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+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ12111111-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-11−1+i32−1−i321−1+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−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-1-1-111-1-11-1111-1-111-1-1111-1-111-1-111-1-1-1111-111-1-1-1-1-1-11111-1-111-1-11-11-11111-1-1-1-1
χ1411-1-1-111-1-11-1111-1-111-1-1111-1-111-1-111-1-1-11−1−i32−1+i32-1−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1511-1-1-111-1-11-1111-1-111-1-1111-1-111-1-111-1-1-11−1+i32−1−i32-1−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1611-1-1-111-1-11-11-1-11111-1-1111-1-111-1-111-1-1-1-111111-1-1-1-1-1-111-1-111-1-111-11-111-11-1-11-11
χ1711-1-1-111-1-11-11-1-11111-1-1111-1-111-1-111-1-1-1-1−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ1811-1-1-111-1-11-11-1-11111-1-1111-1-111-1-111-1-1-1-1−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ1911-1-1-11-11-11-1111-1-111-1-1-1-1-11111-1-1-1-1111-111111-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-1-11111
χ2011-1-1-11-11-11-1111-1-111-1-1-1-1-11111-1-1-1-1111-1−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ2111-1-1-11-11-11-1111-1-111-1-1-1-1-11111-1-1-1-1111-1−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ2211-1-1-11-11-11-11-1-11111-1-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-1-111-1-111-1-1111-1-11-11-111-11-1
χ2311-1-1-11-11-11-11-1-11111-1-1-1-1-11111-1-1-1-11111−1−i32−1+i32-1−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1-111+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ2411-1-1-11-11-11-11-1-11111-1-1-1-1-11111-1-1-1-11111−1+i32−1−i32-1−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1-111−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ252222-2-200-222-200002-22-2000002-22-2000000220222222-2-2-2-200000000000000000000
χ262222-2-200-222-200002-22-2000002-22-2000000−1−i3−1+i30−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31−i31+i31−i300000000000000000000
χ272222-2-200-222-200002-22-2000002-22-2000000−1+i3−1−i30−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31+i31−i31+i300000000000000000000
χ2822-2-22-20022-2-200002-2-22000002-2-2200000022022-2-2-2-222-2-200000000000000000000
χ2922-2-22-20022-2-200002-2-22000002-2-22000000−1−i3−1+i30−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i31+i31−i300000000000000000000
χ3022-2-22-20022-2-200002-2-22000002-2-22000000−1+i3−1−i30−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i31−i31+i300000000000000000000
χ313333333333333333-1-1-1-13-1-1-1-1-1-1-1-1-1-13-1-13003000000000000000000-1-1-1-100000000
χ32333333333333-3-3-3-3-1-1-1-13-1-1-1-1-1-1-1-1-1-13-1-1-300-3000000000000000000111100000000
χ33333333-3-333333333-1-1-1-1-31111-1-1-1-111-311-300-300000000000000000011-1-100000000
χ34333333-3-33333-3-3-3-3-1-1-1-1-31111-1-1-1-111-3113003000000000000000000-1-11100000000
χ3533-3-3-333-3-33-3333-3-3-1-1113-1-111-1-111-1-1-311300-3000000000000000000-11-1100000000
χ3633-3-3-333-3-33-33-3-333-1-1113-1-111-1-111-1-1-311-30030000000000000000001-11-100000000
χ3733-3-3-33-33-33-3333-3-3-1-111-311-1-1-1-111113-1-1-30030000000000000000001-1-1100000000
χ3833-3-3-33-33-33-33-3-333-1-111-311-1-1-1-111113-1-1300-3000000000000000000-111-100000000
χ3966666666-2-2-2-200002-2-22-222-2-2-222-2-2-2-2220000000000000000000000000000000000
χ4066666666-2-2-2-20000-222-2-2-2-2222-2-2222-2-2-20000000000000000000000000000000000
χ41666666-6-6-2-2-2-200002-2-222-2-222-222-2222-2-20000000000000000000000000000000000
χ42666666-6-6-2-2-2-20000-222-2222-2-22-2-22-2-22220000000000000000000000000000000000
χ436666-6-6002-2-22000022-2-204-400-2-2220004-40000000000000000000000000000000000
χ446666-6-6002-2-22000022-2-20-4400-2-222000-440000000000000000000000000000000000
χ456666-6-6002-2-220000-2-2220004-422-2-24-40000000000000000000000000000000000000
χ466666-6-6002-2-220000-2-222000-4422-2-2-440000000000000000000000000000000000000
χ476666-6-600-666-60000-22-2200000-22-22000000000000000000000000000000000000000
χ4866-6-66-60066-6-60000-222-200000-222-2000000000000000000000000000000000000000
χ4966-6-66-600-2-2220000222204-400-2-2-2-2000-440000000000000000000000000000000000
χ5066-6-66-600-2-222000022220-4400-2-2-2-20004-40000000000000000000000000000000000
χ5166-6-66-600-2-2220000-2-2-2-20004-42222-440000000000000000000000000000000000000
χ5266-6-66-600-2-2220000-2-2-2-2000-4422224-40000000000000000000000000000000000000
χ5366-6-6-666-62-22-200002-22-2-22222-22-22-2-22-2-20000000000000000000000000000000000
χ5466-6-6-666-62-22-20000-22-22-2-2-2-2-22-22-2222220000000000000000000000000000000000
χ5566-6-6-66-662-22-200002-22-22-2-2-2-2-22-2222-2220000000000000000000000000000000000
χ5666-6-6-66-662-22-20000-22-22222222-22-2-2-2-2-2-20000000000000000000000000000000000
χ578-88i−8i0000000022−22−2i22i20000000000000000000220-2-22i−2i2i−2i00002−2−i2i22−2−i2i2000000000000
χ588-88i−8i0000000022−22−2i22i20000000000000000000−1−i3−1+i301+i31−i32ζ22−2ζ222ζ14−2ζ140000−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ23000000000000
χ598-88i−8i0000000022−22−2i22i20000000000000000000−1+i3−1−i301−i31+i32ζ14−2ζ142ζ22−2ζ220000ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000000000
χ608-88i−8i00000000−22222i2−2i20000000000000000000220-2-22i−2i2i−2i0000−22i2−i2−22i2−i2000000000000
χ618-88i−8i00000000−22222i2−2i20000000000000000000−1−i3−1+i301+i31−i32ζ22−2ζ222ζ14−2ζ140000ζ7−ζ13−ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+ζ23000000000000
χ628-88i−8i00000000−22222i2−2i20000000000000000000−1+i3−1−i301−i31+i32ζ14−2ζ142ζ22−2ζ220000−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ7−ζ13−ζ7+ζ13−ζ7−ζ13ζ7+ζ13000000000000
χ638-8−8i8i0000000022−222i2−2i20000000000000000000220-2-2−2i2i−2i2i00002−2i2−i22−2i2−i2000000000000
χ648-8−8i8i0000000022−222i2−2i20000000000000000000−1−i3−1+i301+i31−i3−2ζ222ζ22−2ζ142ζ140000−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ23000000000000
χ658-8−8i8i0000000022−222i2−2i20000000000000000000−1+i3−1−i301−i31+i3−2ζ142ζ14−2ζ222ζ220000ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ13000000000000
χ668-8−8i8i00000000−2222−2i22i20000000000000000000220-2-2−2i2i−2i2i0000−22−i2i2−22−i2i2000000000000
χ678-8−8i8i00000000−2222−2i22i20000000000000000000−1−i3−1+i301+i31−i3−2ζ222ζ22−2ζ142ζ140000ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ23000000000000
χ688-8−8i8i00000000−2222−2i22i20000000000000000000−1+i3−1−i301−i31+i3−2ζ142ζ14−2ζ222ζ220000−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ13000000000000

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