Finite Group Databasebeta

← Group #69595

Character table — Group #69595

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order1222222222366666664444444466661212121212121212441212121212121212224444444444
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1
χ911-1-11-1-111-111-1-111-1-1i−ii−iii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1i−i1-11-1i−ii−ii−i1-1
χ1011-1-11-1-111-111-1-111-1-1i−ii−iii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1i−i-11-11−ii−ii−ii-11
χ1111-1-11-1-111-111-1-111-1-1i−ii−i−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111i−i1-11-1i−ii−i−ii-11
χ1211-1-11-1-111-111-1-111-1-1i−ii−i−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111i−i-11-11−ii−iii−i1-1
χ1311-1-11-1-111-111-1-111-1-1−ii−iiii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−ii1-11-1−ii−iii−i-11
χ1411-1-11-1-111-111-1-111-1-1−ii−iiii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−ii-11-11i−ii−i−ii1-1
χ1511-1-11-1-111-111-1-111-1-1−ii−ii−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−ii1-11-1−ii−ii−ii1-1
χ1611-1-11-1-111-111-1-111-1-1−ii−ii−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−ii-11-11i−ii−ii−i-11
χ172222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ182222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-11111-1-1000000000000
χ192222222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ202222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112211-1-1-1-111000000000000
χ2122222-2-2-2-2222-2-2-2-222000000002-22-200000000000000000022-2-200000000
χ2222222-2-2-2-2222-2-2-2-222000000002-22-2000000000000000000-2-22200000000
χ232222-22-22-2-22222222222-2-20000-2-2-2-20000000000220000-2-2000000000000
χ242222-22-22-2-222222222-2-2220000-2-2-2-20000000000-2-2000022000000000000
χ252222-22-22-2-2-1-1-1-1-1-1-1-122-2-200001111−i3−i3i3i3−i3−i3i3i300-1-1−i3i3−i3i311000000000000
χ262222-22-22-2-2-1-1-1-1-1-1-1-122-2-200001111i3i3−i3−i3i3i3−i3−i300-1-1i3−i3i3−i311000000000000
χ272222-22-22-2-2-1-1-1-1-1-1-1-1-2-22200001111−i3−i3i3i3−i3−i3i3i30011i3−i3i3−i3-1-1000000000000
χ282222-22-22-2-2-1-1-1-1-1-1-1-1-2-22200001111i3i3−i3−i3i3i3−i3−i30011−i3i3−i3i3-1-1000000000000
χ292222-2-22-22-222-2-2-2-22200000000-22-22000000000000000000000022-2-20000
χ302222-2-22-22-222-2-2-2-22200000000-22-220000000000000000000000-2-2220000
χ3122-2-2222-2-2-22222-2-2-2-2000000002-2-220000000000000000002-2-2200000000
χ3222-2-2222-2-2-22222-2-2-2-2000000002-2-22000000000000000000-222-200000000
χ3322-2-22-2-222-2-1-111-1-1112i−2i2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii2-2−ii-1-111−ii000000000000
χ3422-2-22-2-222-2-1-111-1-1112i−2i2i−2i−2i−2i2i2i-1-111iiii−i−i−i−i-22−ii11-1-1−ii000000000000
χ3522-2-22-2-222-2-1-111-1-111−2i2i−2i2i2i2i−2i−2i-1-111−i−i−i−iiiii-22i−i11-1-1i−i000000000000
χ3622-2-22-2-222-2-1-111-1-111−2i2i−2i2i−2i−2i2i2i-1-111iiii−i−i−i−i2-2i−i-1-111i−i000000000000
χ3722-2-2-22-2-2222222-2-2-2-200000000-222-200000000000000000000002i−2i−2i2i0000
χ3822-2-2-22-2-2222222-2-2-2-200000000-222-20000000000000000000000−2i2i2i−2i0000
χ3922-2-2-2-222-2222-2-222-2-22i−2i−2i2i0000-2-22200000000002i−2i0000−2i2i000000000000
χ4022-2-2-2-222-2222-2-222-2-2−2i2i2i−2i0000-2-2220000000000−2i2i00002i−2i000000000000
χ4122-2-2-2-222-22-1-111-1-1112i−2i−2i2i000011-1-133−3−3−3−33300−ii−i3i3i3−i3i−i000000000000
χ4222-2-2-2-222-22-1-111-1-1112i−2i−2i2i000011-1-1−3−33333−3−300−iii3−i3−i3i3i−i000000000000
χ4322-2-2-2-222-22-1-111-1-111−2i2i2i−2i000011-1-133−3−3−3−33300i−ii3−i3−i3i3−ii000000000000
χ4422-2-2-2-222-22-1-111-1-111−2i2i2i−2i000011-1-1−3−33333−3−300i−i−i3i3i3−i3−ii000000000000
χ4544444-4-4-4-44-2-22222-2-200000000-22-22000000000000000000000000000000
χ464444-4-44-44-4-2-22222-2-2000000002-22-2000000000000000000000000000000
χ4744-4-4444-4-4-4-2-2-2-2222200000000-222-2000000000000000000000000000000
χ4844-4-4-44-4-444-2-2-2-22222000000002-2-22000000000000000000000000000000
χ494-44-40000004-400004-400002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ504-44-40000004-400004-40000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ514-44-4000000-22−2i32i3−2i32i3-2200002i−2i2i−2i00002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ524-44-4000000-22−2i32i3−2i32i3-220000−2i2i−2i2i0000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ534-44-4000000-222i3−2i32i3−2i3-2200002i−2i2i−2i00002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ544-44-4000000-222i3−2i32i3−2i3-220000−2i2i−2i2i0000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ554-4-440000004-40000-4400002-2-2200002-22-2-22-220000000000000000000000
χ564-4-440000004-40000-440000-222-20000-22-222-22-20000000000000000000000
χ574-4-44000000-22−2i32i32i3−2i32-200002-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000
χ584-4-44000000-22−2i32i32i3−2i32-20000-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000
χ594-4-44000000-222i3−2i3−2i32i32-200002-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000
χ604-4-44000000-222i3−2i3−2i32i32-20000-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000

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