Finite Group Databasebeta

← Group #69643

Character table — Group #69643

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order1222223444466666664444121212121212121212121212224466661212121244448888
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
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1-1-111
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1111-1-1
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ92222222-2-2-2-222222220000-2-2-2-200000000002-2000022-2-200000000
χ102222222-2-2-2-222222220000-2-2-2-20000000000-220000-2-22200000000
χ11222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ12222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ13222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-1111100000000
χ14222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-100000000
χ15222222-1-2-2-2-2-1-1-1-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3002-2−i3−i3i3i3-1-11100000000
χ16222222-1-2-2-2-2-1-1-1-1-1-1-100001111−i3−i3−i3−i3i3i3i3i300-22i3i3−i3−i311-1-100000000
χ17222222-1-2-2-2-2-1-1-1-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-11100000000
χ18222222-1-2-2-2-2-1-1-1-1-1-1-100001111i3i3i3i3−i3−i3−i3−i300-22−i3−i3i3i311-1-100000000
χ192222-2-222-22-22-2-22-2-22000022-2-200000000000000000000020-20000
χ202222-2-222-22-22-2-22-2-22000022-2-2000000000000000000000-2020000
χ212222-2-22-22-222-2-22-2-220000-2-2220000000000000000000020-200000
χ222222-2-22-22-222-2-22-2-220000-2-22200000000000000000000-20200000
χ2322-2-22-2222-2-2-2222-2-2-200002-22-2000000002-2002-22-2000000000000
χ2422-2-22-2222-2-2-2222-2-2-200002-22-200000000-2200-22-22000000000000
χ2522-2-22-22-2-222-2222-2-2-22i2i−2i−2i-22-222i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622-2-22-22-2-222-2222-2-2-2−2i−2i2i2i-22-22−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722-2-22-2-122-2-21-1-1-11110000-11-1133−3−3−3−3332-200-11-113−33−300000000
χ2822-2-22-2-122-2-21-1-1-11110000-11-1133−3−3−3−333-22001-11-1−33−3300000000
χ2922-2-22-2-122-2-21-1-1-11110000-11-11−3−33333−3−32-200-11-11−33−3300000000
χ3022-2-22-2-122-2-21-1-1-11110000-11-11−3−33333−3−3-22001-11-13−33−300000000
χ3122-2-22-2-1-2-2221-1-1-11112i2i−2i−2i1-11-1−i−iii−i−iii0000−i3i3i3−i33−3−3300000000
χ3222-2-22-2-1-2-2221-1-1-11112i2i−2i−2i1-11-1−i−iii−i−iii0000i3−i3−i3i3−333−300000000
χ3322-2-22-2-1-2-2221-1-1-1111−2i−2i2i2i1-11-1ii−i−iii−i−i0000−i3i3i3−i3−333−300000000
χ3422-2-22-2-1-2-2221-1-1-1111−2i−2i2i2i1-11-1ii−i−iii−i−i0000i3−i3−i3i33−3−3300000000
χ3522-2-2-2222-2-22-2-2-2222-200002-2-220000000000000000000000002i−2i00
χ3622-2-2-2222-2-22-2-2-2222-200002-2-22000000000000000000000000−2i2i00
χ3722-2-2-222-222-2-2-2-2222-20000-222-2000000000000000000000000002i−2i
χ3822-2-2-222-222-2-2-2-2222-20000-222-200000000000000000000000000−2i2i
χ394444-4-4-24-44-4-222-222-20000-2-2220000000000000000000000000000
χ404444-4-4-2-44-44-222-222-2000022-2-20000000000000000000000000000
χ4144-4-4-44-24-4-44222-2-2-220000-222-20000000000000000000000000000
χ4244-4-4-44-2-444-4222-2-2-2200002-2-220000000000000000000000000000
χ434-44-40040000400-400-42i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ444-44-40040000400-400-4−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ454-44-400-20000-2−2i32i32−2i32i322i−2i2i−2i00002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ1100000000000000000000
χ464-44-400-20000-2−2i32i32−2i32i32−2i2i−2i2i0000−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ1100000000000000000000
χ474-44-400-20000-22i3−2i322i3−2i322i−2i2i−2i00002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ700000000000000000000
χ484-44-400-20000-22i3−2i322i3−2i32−2i2i−2i2i0000−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ700000000000000000000
χ494-4-440040000-400-40042-2-2200002-2-222-2-2200000000000000000000
χ504-4-440040000-400-4004-222-20000-222-2-222-200000000000000000000
χ514-4-4400-200002−2i32i322i3−2i3-22-2-220000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i300000000000000000000
χ524-4-4400-200002−2i32i322i3−2i3-2-222-200001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i300000000000000000000
χ534-4-4400-2000022i3−2i32−2i32i3-22-2-220000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i300000000000000000000
χ544-4-4400-2000022i3−2i32−2i32i3-2-222-200001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i300000000000000000000

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