Finite Group Databasebeta

← Group #69621

Character table — Group #69621

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order12222222344446666666444412121212121212121212121244441212121212121212888888884444
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91-1-11-111-111-11-11-1-11-11-1i−ii−i11-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ101-1-11-111-111-11-11-1-11-11-1i−ii−i11-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ111-1-11-111-111-11-11-1-11-11-1i−ii−i11-1-1ii−i−iii−i−i-11−ii-1-111−i−iii11-1-1ii−i−i-11−ii
χ121-1-11-111-111-11-11-1-11-11-1i−ii−i11-1-1ii−i−iii−i−i-11−ii-1-111−i−iii-1-111−i−iii1-1i−i
χ131-1-11-111-111-11-11-1-11-11-1−ii−ii11-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ141-1-11-111-111-11-11-1-11-11-1−ii−ii11-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii-1-111ii−i−i-11i−i
χ151-1-11-111-111-11-11-1-11-11-1−ii−ii11-1-1−i−iii−i−iii-11i−i-1-111ii−i−i11-1-1−i−iii-11i−i
χ161-1-11-111-111-11-11-1-11-11-1−ii−ii11-1-1−i−iii−i−iii-11i−i-1-111ii−i−i-1-111ii−i−i1-1−ii
χ17222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ1922222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ2322222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ2422222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ2522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22211111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ2622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22211111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ272222-2-2-2-222-2-22-2222-2-2-200002-22-20000000000000000000000002-22-20000
χ282222-2-2-2-222-2-22-2222-2-2-200002-22-2000000000000000000000000-22-220000
χ292222-2-2-2-22-222-2-2222-2-2-20000-22-22000000000000000000002-22-200000000
χ302222-2-2-2-22-222-2-2222-2-2-20000-22-2200000000000000000000-22-2200000000
χ312-2-222-2-22222-2-2-2-2-222-2200002-2-220000000000000000000000002i−2i−2i2i0000
χ322-2-222-2-22222-2-2-2-2-222-2200002-2-22000000000000000000000000−2i2i2i−2i0000
χ332-2-222-2-222-2-222-2-2-222-220000-222-2000000000000000000002-2-2200000000
χ342-2-222-2-222-2-222-2-2-222-220000-222-200000000000000000000-222-200000000
χ352-2-22-222-22-22-222-2-22-22-22i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362-2-22-222-22-22-222-2-22-22-2−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372-2-22-222-2-12-22-2-111-11-112i−2i2i−2i-1-111−i−iii−i−iii2-22i−2i-1-111−i−iii000000000000
χ382-2-22-222-2-12-22-2-111-11-112i−2i2i−2i-1-111−i−iii−i−iii-22−2i2i11-1-1ii−i−i000000000000
χ392-2-22-222-2-12-22-2-111-11-11−2i2i−2i2i-1-111ii−i−iii−i−i2-2−2i2i-1-111ii−i−i000000000000
χ402-2-22-222-2-12-22-2-111-11-11−2i2i−2i2i-1-111ii−i−iii−i−i-222i−2i11-1-1−i−iii000000000000
χ412-2-22-222-2-1-22-22-111-11-112i−2i−2i2i11-1-1−i−iiiii−i−i0000−i3i3i3−i33−3−33000000000000
χ422-2-22-222-2-1-22-22-111-11-112i−2i−2i2i11-1-1−i−iiiii−i−i0000i3−i3−i3i3−333−3000000000000
χ432-2-22-222-2-1-22-22-111-11-11−2i2i2i−2i11-1-1ii−i−i−i−iii0000−i3i3i3−i3−333−3000000000000
χ442-2-22-222-2-1-22-22-111-11-11−2i2i2i−2i11-1-1ii−i−i−i−iii0000i3−i3−i3i33−3−33000000000000
χ454444-4-4-4-4-24-4-442-2-2-22220000-22-2200000000000000000000000000000000
χ464444-4-4-4-4-2-444-42-2-2-222200002-22-200000000000000000000000000000000
χ4744-4-444-4-440000-44-4-444-40000000000000000000000000000000000000000
χ4844-4-444-4-4-200002-222-2-2200000000000023−2323−23000000000000000000000000
χ4944-4-444-4-4-200002-222-2-22000000000000−2323−2323000000000000000000000000
χ5044-4-4-4-4444000044-4-4-4-440000000000000000000000000000000000000000
χ5144-4-4-4-444-20000-2-22222-20000000023−2323−230000000000000000000000000000
χ5244-4-4-4-444-20000-2-22222-200000000−2323−23230000000000000000000000000000
χ534-44-44-44-4400004-44-44-4-40000000000000000000000000000000000000000
χ544-44-44-44-4-20000-22-22-22200000000−2i32i32i3−2i30000000000000000000000000000
χ554-44-44-44-4-20000-22-22-222000000002i3−2i3−2i32i30000000000000000000000000000
χ564-44-4-44-4440000-4-44-4-4440000000000000000000000000000000000000000
χ574-44-4-44-44-2000022-222-2-2000000000000−2i32i32i3−2i3000000000000000000000000
χ584-44-4-44-44-2000022-222-2-20000000000002i3−2i3−2i32i3000000000000000000000000
χ594-4-444-4-44-244-4-4222-2-22-20000-222-200000000000000000000000000000000
χ604-4-444-4-44-2-4-444222-2-22-200002-2-2200000000000000000000000000000000

Here i is the imaginary unit (i² = −1).