Finite Group Databasebeta

← Group #69987

Character table — Group #69987

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order124422234446661212121222446666661212121212128888242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111
χ6111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1
χ7111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ92222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ102222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ112222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1111122-2-2-1-1-1-1111100000000
χ122222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-11111-2-2221111-1-1-1-100000000
χ1322222-2-222-2-222222220000-2-20000-2-20000002-2000022-2-200000000
χ1422222-2-222-2-222222220000-2-20000-2-2000000-220000-2-22200000000
χ1522222-2-2-12-2-2-1-1-1-1-1-1-1000011−i3−i3i3i311−i3−i3i3i3002-2−i3−i3i3i3-1-11100000000
χ1622222-2-2-12-2-2-1-1-1-1-1-1-1000011−i3−i3i3i311−i3−i3i3i300-22i3i3−i3−i311-1-100000000
χ1722222-2-2-12-2-2-1-1-1-1-1-1-1000011i3i3−i3−i311i3i3−i3−i3002-2i3i3−i3−i3-1-11100000000
χ1822222-2-2-12-2-2-1-1-1-1-1-1-1000011i3i3−i3−i311i3i3−i3−i300-22−i3−i3i3i311-1-100000000
χ192222-22-22-22-2-2-2222-2-200002-200002-200000000000000000000002-2
χ202222-22-22-22-2-2-2222-2-200002-200002-20000000000000000000000-22
χ212222-2-222-2-22-2-2222-2-20000-220000-22000000000000000000002-200
χ222222-2-222-2-22-2-2222-2-20000-220000-2200000000000000000000-2200
χ2322-2-22222-2-2-2222-2-2-2-222-2-2222222-2-2-2-2-2-200000000000000000000
χ2422-2-22222-2-2-2222-2-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000
χ2522-2-2222-1-2-2-2-1-1-1111122-2-2-1-1-1-1-1-111111100003−33−33−33−300000000
χ2622-2-2222-1-2-2-2-1-1-1111122-2-2-1-1-1-1-1-11111110000−33−33−33−3300000000
χ2722-2-2222-1-2-2-2-1-1-11111-2-222-1-1111111-1-1-1-100003−33−3−33−3300000000
χ2822-2-2222-1-2-2-2-1-1-11111-2-222-1-1111111-1-1-1-10000−33−333−33−300000000
χ2922-2-22-2-22-222222-2-2-2-20000-2-200002200002i−2i002i−2i−2i2i000000000000
χ3022-2-22-2-22-222222-2-2-2-20000-2-20000220000−2i2i00−2i2i2i−2i000000000000
χ3122-2-22-2-2-1-222-1-1-11111000011−i3−i3i3i3-1-1i3i3−i3−i32i−2i00−iii−i3−3−3300000000
χ3222-2-22-2-2-1-222-1-1-11111000011−i3−i3i3i3-1-1i3i3−i3−i3−2i2i00i−i−ii−333−300000000
χ3322-2-22-2-2-1-222-1-1-11111000011i3i3−i3−i3-1-1−i3−i3i3i32i−2i00−iii−i−333−300000000
χ3422-2-22-2-2-1-222-1-1-11111000011i3i3−i3−i3-1-1−i3−i3i3i3−2i2i00i−i−ii3−3−3300000000
χ3522-2-2-22-222-22-2-22-2-22200002-20000-220000000000000000002i−2i0000
χ3622-2-2-22-222-22-2-22-2-22200002-20000-22000000000000000000−2i2i0000
χ3722-2-2-2-22222-2-2-22-2-2220000-2200002-200000000000000002i−2i000000
χ3822-2-2-2-22222-2-2-22-2-2220000-2200002-20000000000000000−2i2i000000
χ394444-44-4-2-44-422-2-2-2220000-220000-22000000000000000000000000
χ404444-4-44-2-4-4422-2-2-22200002-200002-2000000000000000000000000
χ4144-4-4-44-4-24-4422-222-2-20000-2200002-2000000000000000000000000
χ4244-4-4-4-44-244-422-222-2-200002-20000-22000000000000000000000000
χ434-44i−4i000400000-44i−4i002-22i−2i002-22-2002i−2i2i−2i00000000000000000000
χ444-44i−4i000400000-44i−4i00-22−2i2i00-22-2200−2i2i−2i2i00000000000000000000
χ454-44i−4i000-2000−2i32i32−2i2i23−232-22i−2i00−1−i31+i3−1+i31−i3002ζ11−2ζ112ζ7−2ζ700000000000000000000
χ464-44i−4i000-2000−2i32i32−2i2i23−23-22−2i2i001+i3−1−i31−i3−1+i300−2ζ112ζ11−2ζ72ζ700000000000000000000
χ474-44i−4i000-20002i3−2i32−2i2i−23232-22i−2i00−1+i31−i3−1−i31+i3002ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ484-44i−4i000-20002i3−2i32−2i2i−2323-22−2i2i001−i3−1+i31+i3−1−i300−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ494-4−4i4i000400000-4−4i4i002-2−2i2i002-22-200−2i2i−2i2i00000000000000000000
χ504-4−4i4i000400000-4−4i4i00-222i−2i00-22-22002i−2i2i−2i00000000000000000000
χ514-4−4i4i000-2000−2i32i322i−2i−23232-2−2i2i00−1−i31+i3−1+i31−i300−2ζ112ζ11−2ζ72ζ700000000000000000000
χ524-4−4i4i000-2000−2i32i322i−2i−2323-222i−2i001+i3−1−i31−i3−1+i3002ζ11−2ζ112ζ7−2ζ700000000000000000000
χ534-4−4i4i000-20002i3−2i322i−2i23−232-2−2i2i00−1+i31−i3−1−i31+i300−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ544-4−4i4i000-20002i3−2i322i−2i23−23-222i−2i001−i3−1+i31+i3−1−i3002ζ7−2ζ72ζ11−2ζ1100000000000000000000

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