Finite Group Databasebeta

← Group #68765

Character table — Group #68765

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order1222223444466612121212444444446612121212121212121212881212121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ91-1-11-11111-1-11-1-111-1-1ii−i−i11-1-1-111-11111-1-1-1-1i−iii−i−iii−i−iii−i−i11-1-11-1i−i
χ101-1-11-11111-1-11-1-111-1-1ii−i−i11-1-1-111-11111-1-1-1-1i−iii−i−iii−i−i−i−iii-1-111-11−ii
χ111-1-11-11111-1-11-1-111-1-1ii−i−i-1-111-111-1-1-1-1-11111−iiii−i−i−i−iiiii−i−i11-1-1-11−ii
χ121-1-11-11111-1-11-1-111-1-1ii−i−i-1-111-111-1-1-1-1-11111−iiii−i−i−i−iii−i−iii-1-1111-1i−i
χ131-1-11-11111-1-11-1-111-1-1−i−iii11-1-1-111-11111-1-1-1-1−ii−i−iii−i−iiiii−i−i-1-111-11i−i
χ141-1-11-11111-1-11-1-111-1-1−i−iii11-1-1-111-11111-1-1-1-1−ii−i−iii−i−iii−i−iii11-1-11-1−ii
χ151-1-11-11111-1-11-1-111-1-1−i−iii-1-111-111-1-1-1-1-11111i−i−i−iiiii−i−iii−i−i-1-1111-1−ii
χ161-1-11-11111-1-11-1-111-1-1−i−iii-1-111-111-1-1-1-1-11111i−i−i−iiiii−i−i−i−iii11-1-1-11i−i
χ172222222-2-2-2-2222-2-2-2-20000000022-2-200000000000000000000002-22-20000
χ182222222-2-2-2-2222-2-2-2-20000000022-2-20000000000000000000000-22-220000
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
χ20222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-1-1-11111000000000000
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
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111221111-1-1-1-1000000000000
χ232222-2-222-22-2222222200000000-2-2-2-20000000000000000002-22-200000000
χ242222-2-222-22-2222222200000000-2-2-2-2000000000000000000-22-2200000000
χ252222-2-22-22-22222-2-2-2-22-22-20000-2-22200000000002-22-20000000000000000
χ262222-2-22-22-22222-2-2-2-2-22-220000-2-2220000000000-22-220000000000000000
χ272222-2-2-1-22-22-1-1-111112-22-2000011-1-133−3−333−3−300-11-113−33−3000000000000
χ282222-2-2-1-22-22-1-1-111112-22-2000011-1-1−3−333−3−33300-11-11−33−33000000000000
χ292222-2-2-1-22-22-1-1-11111-22-22000011-1-133−3−333−3−3001-11-1−33−33000000000000
χ302222-2-2-1-22-22-1-1-11111-22-22000011-1-1−3−333−3−333001-11-13−33−3000000000000
χ312-2-222-222-2-222-2-222-2-2000000002-2-220000000000000000002i−2i−2i2i00000000
χ322-2-222-222-2-222-2-222-2-2000000002-2-22000000000000000000−2i2i2i−2i00000000
χ332-2-222-22-222-22-2-2-2-2222i−2i−2i2i00002-22-200000000002i−2i−2i2i0000000000000000
χ342-2-222-22-222-22-2-2-2-222−2i2i2i−2i00002-22-20000000000−2i2i2i−2i0000000000000000
χ352-2-222-2-1-222-2-11111-1-12i−2i−2i2i0000-11-1133−3−3−3−33300−iii−ii3−i3−i3i3000000000000
χ362-2-222-2-1-222-2-11111-1-12i−2i−2i2i0000-11-11−3−33333−3−300−iii−i−i3i3i3−i3000000000000
χ372-2-222-2-1-222-2-11111-1-1−2i2i2i−2i0000-11-1133−3−3−3−33300i−i−ii−i3i3i3−i3000000000000
χ382-2-222-2-1-222-2-11111-1-1−2i2i2i−2i0000-11-11−3−33333−3−300i−i−iii3−i3−i3i3000000000000
χ392-2-22-222-2-2222-2-2-2-22200000000-22-2200000000000000000000002-2-220000
χ402-2-22-222-2-2222-2-2-2-22200000000-22-220000000000000000000000-222-20000
χ412-2-22-22-122-2-2-111-1-1112i2i−2i−2i22-2-21-1-11-1-1-1-111112i−2i−i−iii−i−iii000000000000
χ422-2-22-22-122-2-2-111-1-1112i2i−2i−2i-2-2221-1-111111-1-1-1-1−2i2i−i−iiiii−i−i000000000000
χ432-2-22-22-122-2-2-111-1-111−2i−2i2i2i22-2-21-1-11-1-1-1-11111−2i2iii−i−iii−i−i000000000000
χ442-2-22-22-122-2-2-111-1-111−2i−2i2i2i-2-2221-1-111111-1-1-1-12i−2iii−i−i−i−iii000000000000
χ45444444-2-4-4-4-4-2-2-2222200000000-2-222000000000000000000000000000000
χ464444-4-4-24-44-4-2-2-2-2-2-2-2000000002222000000000000000000000000000000
χ4744-4-40040000-44-4000000002-22-200002-22-22-22-20000000000000000000000
χ4844-4-40040000-44-400000000-22-220000-22-22-22-220000000000000000000000
χ4944-4-400-200002-2223−2323−2300002-22-20000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ5044-4-400-200002-2223−2323−230000-22-2200001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ5144-4-400-200002-22−2323−232300002-22-20000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ5244-4-400-200002-22−2323−23230000-22-2200001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ534-44-40040000-4-44000000002-2-2200002-22-2-22-220000000000000000000000
χ544-44-40040000-4-4400000000-222-20000-22-222-22-20000000000000000000000
χ554-44-400-2000022-223−23−232300002-2-220000−1+31−3−1−31+31−3−1+31+3−1−30000000000000000000000
χ564-44-400-2000022-223−23−23230000-222-200001−3−1+31+3−1−3−1+31−3−1−31+30000000000000000000000
χ574-44-400-2000022-2−232323−2300002-2-220000−1−31+3−1+31−31+3−1−31−3−1+30000000000000000000000
χ584-44-400-2000022-2−232323−230000-222-200001+3−1−31−3−1+3−1−31+3−1+31−30000000000000000000000
χ594-4-444-4-24-4-44-222-2-22200000000-222-2000000000000000000000000000000
χ604-4-44-44-2-4-444-22222-2-2000000002-22-2000000000000000000000000000000

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