Finite Group Databasebeta

← Group #69592

Character table — Group #69592

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order12222234444666666644444444121212121212121212121212441212121212121212224444448888
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
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1
χ91-11-1-1111-11-1-1-1-1111-1ii−i−i11-1-111-1-11111-1-1-1-1i−iii−i−iii−i−i1-1i−i1-1i−i1-1i−i
χ101-11-1-1111-11-1-1-1-1111-1ii−i−i11-1-111-1-11111-1-1-1-1i−iii−i−iii−i−i-11−ii-11−ii-11−ii
χ111-11-1-1111-11-1-1-1-1111-1ii−i−i-1-11111-1-1-1-1-1-11111−iiii−i−i−i−iii1-1i−i1-1i−i-11−ii
χ121-11-1-1111-11-1-1-1-1111-1ii−i−i-1-11111-1-1-1-1-1-11111−iiii−i−i−i−iii-11−ii-11−ii1-1i−i
χ131-11-1-1111-11-1-1-1-1111-1−i−iii11-1-111-1-11111-1-1-1-1−ii−i−iii−i−iii1-1−ii1-1−ii1-1−ii
χ141-11-1-1111-11-1-1-1-1111-1−i−iii11-1-111-1-11111-1-1-1-1−ii−i−iii−i−iii-11i−i-11i−i-11i−i
χ151-11-1-1111-11-1-1-1-1111-1−i−iii-1-11111-1-1-1-1-1-11111i−i−i−iiiii−i−i1-1−ii1-1−ii-11i−i
χ161-11-1-1111-11-1-1-1-1111-1−i−iii-1-11111-1-1-1-1-1-11111i−i−i−iiiii−i−i-11i−i-11i−i1-1−ii
χ172222222-2-2-2-222222222-22-20000-2-2-2-200000000002-22-20000000000000000
χ182222222-2-2-2-22222222-22-220000-2-2-2-20000000000-22-220000000000000000
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
χ23222222-1-2-2-2-2-1-1-1-1-1-1-12-22-200001111−i3−i3i3i3−i3−i3i3i300-11-11−i3i3−i3i3000000000000
χ24222222-1-2-2-2-2-1-1-1-1-1-1-12-22-200001111i3i3−i3−i3i3i3−i3−i300-11-11i3−i3i3−i3000000000000
χ25222222-1-2-2-2-2-1-1-1-1-1-1-1-22-2200001111−i3−i3i3i3−i3−i3i3i3001-11-1i3−i3i3−i3000000000000
χ26222222-1-2-2-2-2-1-1-1-1-1-1-1-22-2200001111i3i3−i3−i3i3i3−i3−i3001-11-1−i3i3−i3i3000000000000
χ272222-2-222-2-222-2-22-2-22000000002-22-20000000000000000002200-2-2000000
χ282222-2-222-2-222-2-22-2-22000000002-22-2000000000000000000-2-20022000000
χ292222-2-22-222-22-2-22-2-2200000000-22-22000000000000000000002200-2-20000
χ302222-2-22-222-22-2-22-2-2200000000-22-2200000000000000000000-2-200220000
χ312-22-22-2222-2-2-2222-2-2-2000000002-2-220000000000000000002-200-22000000
χ322-22-22-2222-2-2-2222-2-2-2000000002-2-22000000000000000000-22002-2000000
χ332-22-22-22-2-222-2222-2-2-200000000-222-2000000000000000000002i−2i00−2i2i0000
χ342-22-22-22-2-222-2222-2-2-200000000-222-200000000000000000000−2i2i002i−2i0000
χ352-22-2-222-22-22-2-2-2222-22i−2i−2i2i0000-2-22200000000002i−2i−2i2i0000000000000000
χ362-22-2-222-22-22-2-2-2222-2−2i2i2i−2i0000-2-2220000000000−2i2i2i−2i0000000000000000
χ372-22-2-22-12-22-2111-1-1-112i2i−2i−2i22-2-2-1-111-1-1-1-111112i−2i−i−iii−i−iii000000000000
χ382-22-2-22-12-22-2111-1-1-112i2i−2i−2i-2-222-1-1111111-1-1-1-1−2i2i−i−iiiii−i−i000000000000
χ392-22-2-22-12-22-2111-1-1-11−2i−2i2i2i22-2-2-1-111-1-1-1-11111−2i2iii−i−iii−i−i000000000000
χ402-22-2-22-12-22-2111-1-1-11−2i−2i2i2i-2-222-1-1111111-1-1-1-12i−2iii−i−i−i−iii000000000000
χ412-22-2-22-1-22-22111-1-1-112i−2i−2i2i000011-1-1−i3−i3i3i3i3i3−i3−i300−iii−i3−3−33000000000000
χ422-22-2-22-1-22-22111-1-1-112i−2i−2i2i000011-1-1i3i3−i3−i3−i3−i3i3i300−iii−i−333−3000000000000
χ432-22-2-22-1-22-22111-1-1-11−2i2i2i−2i000011-1-1−i3−i3i3i3i3i3−i3−i300i−i−ii−333−3000000000000
χ442-22-2-22-1-22-22111-1-1-11−2i2i2i−2i000011-1-1i3i3−i3−i3−i3−i3i3i300i−i−ii3−3−33000000000000
χ454444-4-4-24-4-44-222-222-200000000-22-22000000000000000000000000000000
χ464444-4-4-2-444-4-222-222-2000000002-22-2000000000000000000000000000000
χ4744-4-40040000400-400-400002-22-200002-22-22-22-20000000000000000000000
χ4844-4-40040000400-400-40000-22-220000-22-22-22-220000000000000000000000
χ4944-4-400-20000-2−2i32i32−2i32i3200002-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000
χ5044-4-400-20000-2−2i32i32−2i32i320000-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000
χ5144-4-400-20000-22i3−2i322i3−2i3200002-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000
χ5244-4-400-20000-22i3−2i322i3−2i320000-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000
χ534-44-44-4-244-4-42-2-2-222200000000-222-2000000000000000000000000000000
χ544-44-44-4-2-4-4442-2-2-2222000000002-2-22000000000000000000000000000000
χ554-4-440040000-400-400400002-2-2200002-22-2-22-220000000000000000000000
χ564-4-440040000-400-40040000-222-20000-22-222-22-20000000000000000000000
χ574-4-4400-200002−2i32i322i3−2i3-200002-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000
χ584-4-4400-200002−2i32i322i3−2i3-20000-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000
χ594-4-4400-2000022i3−2i32−2i32i3-200002-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000
χ604-4-4400-2000022i3−2i32−2i32i3-20000-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000

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