Finite Group Databasebeta

← Group #69694

Character table — Group #69694

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order12222234444666666644441212121212121212121212124444121212121212121222448888
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
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-11-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-11-1111-1-1
χ92222222-2-2-2-22222222000000000000-2-2-2-22-20022-2-2000000000000
χ102222222-2-2-2-22222222000000000000-2-2-2-2-2200-2-222000000000000
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
χ13222222-12222-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-122-2-2-1-1-1-1111100000000
χ14222222-12222-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-1-2-2221111-1-1-1-100000000
χ15222222-1-2-2-2-2-1-1-1-1-1-1-10000−i3−i3−i3−i3i3i3i3i311112-200-1-111−i3−i3i3i300000000
χ16222222-1-2-2-2-2-1-1-1-1-1-1-10000−i3−i3−i3−i3i3i3i3i31111-220011-1-1i3i3−i3−i300000000
χ17222222-1-2-2-2-2-1-1-1-1-1-1-10000i3i3i3i3−i3−i3−i3−i311112-200-1-111i3i3−i3−i300000000
χ18222222-1-2-2-2-2-1-1-1-1-1-1-10000i3i3i3i3−i3−i3−i3−i31111-220011-1-1−i3−i3i3i300000000
χ192222-2-222-22-22-2-2-2-22200000000000022-2-2000000000000020-20000
χ202222-2-222-22-22-2-2-2-22200000000000022-2-20000000000000-2020000
χ212222-2-22-22-222-2-2-2-222000000000000-2-22200000000000020-200000
χ222222-2-22-22-222-2-2-2-222000000000000-2-222000000000000-20200000
χ232-2-222-2222-2-2-222-2-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-200000000000000000000
χ242-2-222-2222-2-2-222-2-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-200000000000000000000
χ252-2-222-22-2-222-222-2-2-22000000000000-22-22002-200002-22-200000000
χ262-2-222-22-2-222-222-2-2-22000000000000-22-2200-220000-22-2200000000
χ272-2-222-2-122-2-21-1-1111-12i2i−2i−2i−i−iii−i−iii-11-1100003−33−3−i3i3i3−i300000000
χ282-2-222-2-122-2-21-1-1111-12i2i−2i−2i−i−iii−i−iii-11-110000−33−33i3−i3−i3i300000000
χ292-2-222-2-122-2-21-1-1111-1−2i−2i2i2iii−i−iii−i−i-11-1100003−33−3i3−i3−i3i300000000
χ302-2-222-2-122-2-21-1-1111-1−2i−2i2i2iii−i−iii−i−i-11-110000−33−33−i3i3i3−i300000000
χ312-2-222-2-1-2-2221-1-1111-1000033−3−3−3−3331-11-1002-23−3−33-11-1100000000
χ322-2-222-2-1-2-2221-1-1111-1000033−3−3−3−3331-11-100-22−333−31-11-100000000
χ332-2-222-2-1-2-2221-1-1111-10000−3−33333−3−31-11-1002-2−333−3-11-1100000000
χ342-2-222-2-1-2-2221-1-1111-10000−3−33333−3−31-11-100-223−3−331-11-100000000
χ352-2-22-2222-2-22-2-2-222-220000000000002-2-220000000000000000002-2
χ362-2-22-2222-2-22-2-2-222-220000000000002-2-22000000000000000000-22
χ372-2-22-222-222-2-2-2-222-22000000000000-222-200000000000000002-200
χ382-2-22-222-222-2-2-2-222-22000000000000-222-20000000000000000-2200
χ394444-4-4-24-44-4-22222-2-2000000000000-2-22200000000000000000000
χ404444-4-4-2-44-44-22222-2-200000000000022-2-200000000000000000000
χ4144-4-4004000040000-4-42-22-22-22-22-22-2000000000000000000000000
χ4244-4-4004000040000-4-4-22-22-22-22-22-22000000000000000000000000
χ4344-4-400-20000-2−2i32i3−2i32i3222-22-2−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000000000000000000000000
χ4444-4-400-20000-2−2i32i3−2i32i322-22-221+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000000000000000000000000
χ4544-4-400-20000-22i3−2i32i3−2i3222-22-2−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000000000000000000000000
χ4644-4-400-20000-22i3−2i32i3−2i322-22-221−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000000000000000000000000
χ474-44-40040000-400004-42i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ484-44-40040000-400004-4−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ494-44-400-200002−2i32i32i3−2i3-222i−2i−2i2i2ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7000000000000000000000000
χ504-44-400-200002−2i32i32i3−2i3-22−2i2i2i−2i−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7000000000000000000000000
χ514-44-400-2000022i3−2i3−2i32i3-222i−2i−2i2i2ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11000000000000000000000000
χ524-44-400-2000022i3−2i3−2i32i3-22−2i2i2i−2i−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11000000000000000000000000
χ534-4-44-44-24-4-44222-2-22-2000000000000-222-200000000000000000000
χ544-4-44-44-2-444-4222-2-22-20000000000002-2-2200000000000000000000

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