Finite Group Databasebeta

← Group #70360

Character table — Group #70360

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order12222234444666121212124444661212121212121212121224668812122424242444444488
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1111-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-1-111
χ92222222-2-2-2-2222-2-2-2-2000022-2-20000000000000000000002-200000
χ102222222-2-2-2-2222-2-2-2-2000022-2-2000000000000000000000-2200000
χ11222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000
χ12222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000
χ13222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-2-2-1-1111100000000
χ14222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2112211-1-1-1-100000000
χ152222-2-222-22-222222220000-2-2-2-200000000000000000000200-20000
χ162222-2-222-22-222222220000-2-2-2-200000000000000000000-20020000
χ172222-2-22-22-22222-2-2-2-20000-2-222000000002-22200-2-2000000000000
χ182222-2-22-22-22222-2-2-2-20000-2-22200000000-22-2-20022000000000000
χ192222-2-2-1-22-22-1-1-11111000011-1-13333−3−3−3−32-2-1-1001133−3−300000000
χ202222-2-2-1-22-22-1-1-11111000011-1-13333−3−3−3−3-221100-1-1−3−33300000000
χ212222-2-2-1-22-22-1-1-11111000011-1-1−3−3−3−333332-2-1-10011−3−33300000000
χ222222-2-2-1-22-22-1-1-11111000011-1-1−3−3−3−33333-221100-1-133−3−300000000
χ232-22-22-222-2-22-2-2222-2-22i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i00000000000000000000
χ242-22-22-222-2-22-2-2222-2-2−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ252-22-22-22-222-2-2-22-2-22200002-2-220000000000000000000000002i−2i00
χ262-22-22-22-222-2-2-22-2-22200002-2-22000000000000000000000000−2i2i00
χ272-22-22-2-12-2-2211-1-1-1112i2i−2i−2i-11-11−i−iii−i−iii00−i3i300−i3i33−33−300000000
χ282-22-22-2-12-2-2211-1-1-1112i2i−2i−2i-11-11−i−iii−i−iii00i3−i300i3−i3−33−3300000000
χ292-22-22-2-12-2-2211-1-1-111−2i−2i2i2i-11-11ii−i−iii−i−i00−i3i300−i3i3−33−3300000000
χ302-22-22-2-12-2-2211-1-1-111−2i−2i2i2i-11-11ii−i−iii−i−i00i3−i300i3−i33−33−300000000
χ312-22-2-22222-2-2-2-2222-2-20000-22-22000000000000000000000000002i−2i
χ322-22-2-22222-2-2-2-2222-2-20000-22-2200000000000000000000000000−2i2i
χ332-22-2-222-2-222-2-22-2-2220000-222-20000000000002-2002-2-2200000000
χ342-22-2-222-2-222-2-22-2-2220000-222-2000000000000-2200-222-200000000
χ352-22-2-22-1-2-22211-111-1-100001-1-11−i3−i3i3i3i3i3−i3−i300−i3i32-2i3−i3-111-100000000
χ362-22-2-22-1-2-22211-111-1-100001-1-11−i3−i3i3i3i3i3−i3−i300i3−i3-22−i3i31-1-1100000000
χ372-22-2-22-1-2-22211-111-1-100001-1-11i3i3−i3−i3−i3−i3i3i300−i3i3-22i3−i31-1-1100000000
χ382-22-2-22-1-2-22211-111-1-100001-1-11i3i3−i3−i3−i3−i3i3i300i3−i32-2−i3i3-111-100000000
χ39444444-2-4-4-4-4-2-2-222220000-2-2220000000000000000000000000000
χ404444-4-4-24-44-4-2-2-2-2-2-2-2000022220000000000000000000000000000
χ4144-4-400400004-4-400002-22-200002-22-22-22-200000000000000000000
χ4244-4-400400004-4-40000-22-220000-22-22-22-2200000000000000000000
χ4344-4-400-20000-22223−2323−232-22-20000−1+31−3−1+31−3−1−31+3−1−31+300000000000000000000
χ4444-4-400-20000-22223−2323−23-22-2200001−3−1+31−3−1+31+3−1−31+3−1−300000000000000000000
χ4544-4-400-20000-222−2323−23232-22-20000−1−31+3−1−31+3−1+31−3−1+31−300000000000000000000
χ4644-4-400-20000-222−2323−2323-22-2200001+3−1−31+3−1−31−3−1+31−3−1+300000000000000000000
χ474-44-44-4-2-444-422-222-2-20000-222-20000000000000000000000000000
χ484-44-4-44-244-4-422-2-2-22200002-22-20000000000000000000000000000
χ494-4-440040000-44-400002i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ504-4-440040000-44-40000−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ514-4-4400-200002-2223−23−23232i−2i−2i2i0000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000
χ524-4-4400-200002-2223−23−2323−2i2i2i−2i0000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000
χ534-4-4400-200002-22−232323−232i−2i−2i2i0000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000
χ544-4-4400-200002-22−232323−23−2i2i2i−2i0000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000

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