Finite Group Databasebeta

← Group #69692

Character table — Group #69692

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order12222234444666666644444444121212121212121212121212441212121212121212222244448888
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ91-1-111-1111-1-111-1-1-1-1111-1-1ii−i−iiiii−i−i−i−i11-1-1i−iii−i−i11-1-11-11-11-11-1i−ii−i
χ101-1-111-1111-1-111-1-1-1-1111-1-1ii−i−iiiii−i−i−i−i11-1-1i−iii−i−i11-1-1-11-11-11-11−ii−ii
χ111-1-111-1111-1-111-1-1-1-1111-1-1−i−iii−i−i−i−iiiii11-1-1−ii−i−iii11-1-11-11-11-11-1−ii−ii
χ121-1-111-1111-1-111-1-1-1-1111-1-1−i−iii−i−i−i−iiiii11-1-1−ii−i−iii11-1-1-11-11-11-11i−ii−i
χ131-1-111-1111-1-111-1-1-1-11-1-111ii−i−iiiii−i−i−i−i11-1-1−ii−i−iii-1-1111-1-111-1-11i−i−ii
χ141-1-111-1111-1-111-1-1-1-11-1-111ii−i−iiiii−i−i−i−i11-1-1−ii−i−iii-1-111-111-1-111-1−iii−i
χ151-1-111-1111-1-111-1-1-1-11-1-111−i−iii−i−i−i−iiiii11-1-1i−iii−i−i-1-1111-1-111-1-11−iii−i
χ161-1-111-1111-1-111-1-1-1-11-1-111−i−iii−i−i−i−iiiii11-1-1i−iii−i−i-1-111-111-1-111-1i−i−ii
χ172222222-2-2-2-222222222-22-2000000000000-2-2-2-20000002-22-2000000000000
χ182222222-2-2-2-22222222-22-22000000000000-2-2-2-2000000-22-22000000000000
χ19222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-2-21111-1-1-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-122-1-1-1-11111000000000000
χ23222222-1-2-2-2-2-1-1-1-1-1-1-12-22-20000−i3−i3i3i3−i3−i3i3i3111100−i3i3−i3i3-11-11000000000000
χ24222222-1-2-2-2-2-1-1-1-1-1-1-12-22-20000i3i3−i3−i3i3i3−i3−i3111100i3−i3i3−i3-11-11000000000000
χ25222222-1-2-2-2-2-1-1-1-1-1-1-1-22-220000−i3−i3i3i3−i3−i3i3i3111100i3−i3i3−i31-11-1000000000000
χ26222222-1-2-2-2-2-1-1-1-1-1-1-1-22-220000i3i3−i3−i3i3i3−i3−i3111100−i3i3−i3i31-11-1000000000000
χ272222-2-222-22-2-2-22-2-22200000000000000002-22-20000000000002200-2-20000
χ282222-2-222-22-2-2-22-2-22200000000000000002-22-2000000000000-2-200220000
χ292222-2-22-22-22-2-22-2-2220000000000000000-22-2200000000002200-2-2000000
χ302222-2-22-22-22-2-22-2-2220000000000000000-22-220000000000-2-20022000000
χ312-2-222-22-2-22222-2-2-2-222-2-22000000000000-2-2220000002-2-22000000000000
χ322-2-222-22-2-22222-2-2-2-22-222-2000000000000-2-222000000-222-2000000000000
χ332-2-222-2-122-2-2-1-11111-122-2-22i2i−2i−2i−i−i−i−iiiii-1-1112i−2i−i−iii-1-111000000000000
χ342-2-222-2-122-2-2-1-11111-122-2-2−2i−2i2i2iiiii−i−i−i−i-1-111−2i2iii−i−i-1-111000000000000
χ352-2-222-2-122-2-2-1-11111-1-2-2222i2i−2i−2i−i−i−i−iiiii-1-111−2i2iii−i−i11-1-1000000000000
χ362-2-222-2-122-2-2-1-11111-1-2-222−2i−2i2i2iiiii−i−i−i−i-1-1112i−2i−i−iii11-1-1000000000000
χ372-2-222-2-1-2-222-1-11111-12-2-22000033−3−3−3−33311-1-1003−3−33-111-1000000000000
χ382-2-222-2-1-2-222-1-11111-12-2-220000−3−33333−3−311-1-100−333−3-111-1000000000000
χ392-2-222-2-1-2-222-1-11111-1-222-2000033−3−3−3−33311-1-100−333−31-1-11000000000000
χ402-2-222-2-1-2-222-1-11111-1-222-20000−3−33333−3−311-1-1003−3−331-1-11000000000000
χ412-2-22-2222-2-22-2-2-222-2200000000000000002-2-220000000000002-200-220000
χ422-2-22-2222-2-22-2-2-222-2200000000000000002-2-22000000000000-22002-20000
χ432-2-22-222-222-2-2-2-222-220000000000000000-222-200000000002-200-22000000
χ442-2-22-222-222-2-2-2-222-220000000000000000-222-20000000000-22002-2000000
χ454444-4-4-24-44-422-222-2-20000000000000000-22-220000000000000000000000
χ464444-4-4-2-44-4422-222-2-200000000000000002-22-20000000000000000000000
χ4744-4-4004000000400-4-400002-22-22-22-22-22-200000000000000000000000000
χ4844-4-4004000000400-4-40000-22-22-22-22-22-2200000000000000000000000000
χ4944-4-400-20000−2i32i3-2−2i32i32200002-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ5044-4-400-20000−2i32i3-2−2i32i3220000-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ5144-4-400-200002i3−2i3-22i3−2i32200002-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ5244-4-400-200002i3−2i3-22i3−2i3220000-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ534-44-4004000000-4004-400002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ544-44-4004000000-4004-40000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ554-44-400-20000−2i32i322i3−2i3-2200002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ564-44-400-20000−2i32i322i3−2i3-220000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ574-44-400-200002i3−2i32−2i32i3-2200002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ584-44-400-200002i3−2i32−2i32i3-220000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ594-4-44-44-24-4-44222-2-22-20000000000000000-222-20000000000000000000000
χ604-4-44-44-2-444-4222-2-22-200000000000000002-2-220000000000000000000000

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