Finite Group Databasebeta

← Group #69596

Character table — Group #69596

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order1222222222366666664444666612121212121212124444121212121212121222444444
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-11-1-1-111
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11-1111-1-1
χ92222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ102222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ112222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-11111-1-100000000
χ122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-22211-1-1-1-11100000000
χ1322222-2-22-2-2222222220000-2-2-2-2000000002-200220000-2-200000000
χ1422222-2-22-2-2222222220000-2-2-2-200000000-2200-2-200002200000000
χ1522222-2-22-2-2-1-1-1-1-1-1-1-100001111−i3−i3−i3−i3i3i3i3i32-200-1-1−i3−i3i3i31100000000
χ1622222-2-22-2-2-1-1-1-1-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3-220011i3i3−i3−i3-1-100000000
χ1722222-2-22-2-2-1-1-1-1-1-1-1-100001111i3i3i3i3−i3−i3−i3−i32-200-1-1i3i3−i3−i31100000000
χ1822222-2-22-2-2-1-1-1-1-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3-220011−i3−i3i3i3-1-100000000
χ192222-22-2-22-222-2-22-2-22000022-2-200000000000000000000020-20000
χ202222-22-2-22-222-2-22-2-22000022-2-2000000000000000000000-2020000
χ212222-2-22-2-2222-2-22-2-220000-2-2220000000000000000000020-200000
χ222222-2-22-2-2222-2-22-2-220000-2-22200000000000000000000-20200000
χ232-2-2222-2-2-222222-2-2-2-200002-22-2000000000000000000000000002i−2i
χ242-2-2222-2-2-222222-2-2-2-200002-22-200000000000000000000000000−2i2i
χ252-2-222-22-22-22222-2-2-2-20000-22-220000000000000000000000002i−2i00
χ262-2-222-22-22-22222-2-2-2-20000-22-22000000000000000000000000−2i2i00
χ272-2-22-2222-2-222-2-2-222-22i2i−2i−2i2-2-222i2i−2i−2i2i2i−2i−2i00000000000000000000
χ282-2-22-2222-2-222-2-2-222-2−2i−2i2i2i2-2-22−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ292-2-22-2222-2-2-1-1111-1-112i2i−2i−2i-111-1−i−iii−i−iii00003−3−i3i3−i3i33−300000000
χ302-2-22-2222-2-2-1-1111-1-112i2i−2i−2i-111-1−i−iii−i−iii0000−33i3−i3i3−i3−3300000000
χ312-2-22-2222-2-2-1-1111-1-11−2i−2i2i2i-111-1ii−i−iii−i−i00003−3i3−i3i3−i33−300000000
χ322-2-22-2222-2-2-1-1111-1-11−2i−2i2i2i-111-1ii−i−iii−i−i0000−33−i3i3−i3i3−3300000000
χ332-2-22-2-2-222222-2-2-222-20000-222-200000000002-2002-2-220000000000
χ342-2-22-2-2-222222-2-2-222-20000-222-20000000000-2200-222-20000000000
χ352-2-22-2-2-2222-1-1111-1-1100001-1-1133−3−3−3−333002-23−3-111-1−3300000000
χ362-2-22-2-2-2222-1-1111-1-1100001-1-1133−3−3−3−33300-22−331-1-113−300000000
χ372-2-22-2-2-2222-1-1111-1-1100001-1-11−3−33333−3−3002-2−33-111-13−300000000
χ382-2-22-2-2-2222-1-1111-1-1100001-1-11−3−33333−3−300-223−31-1-11−3300000000
χ394444-44-4-44-4-2-222-222-20000-2-2220000000000000000000000000000
χ404444-4-44-4-44-2-222-222-2000022-2-20000000000000000000000000000
χ4144-4-40000004-400400-42i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4244-4-40000004-400400-4−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4344-4-4000000-22−2i32i3-2−2i32i322i−2i2i−2i00002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ1100000000000000000000
χ4444-4-4000000-22−2i32i3-2−2i32i32−2i2i−2i2i0000−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ1100000000000000000000
χ4544-4-4000000-222i3−2i3-22i3−2i322i−2i2i−2i00002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ700000000000000000000
χ4644-4-4000000-222i3−2i3-22i3−2i32−2i2i−2i2i0000−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ700000000000000000000
χ474-44-40000004-400-40042-2-2200002-2-222-2-2200000000000000000000
χ484-44-40000004-400-4004-222-20000-222-2-222-200000000000000000000
χ494-44-4000000-22−2i32i322i3−2i3-22-2-220000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i300000000000000000000
χ504-44-4000000-22−2i32i322i3−2i3-2-222-200001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i300000000000000000000
χ514-44-4000000-222i3−2i32−2i32i3-22-2-220000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i300000000000000000000
χ524-44-4000000-222i3−2i32−2i32i3-2-222-200001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i300000000000000000000
χ534-4-4444-4-4-44-2-2-2-222220000-22-220000000000000000000000000000
χ544-4-444-44-44-4-2-2-2-2222200002-22-20000000000000000000000000000

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