Finite Group Databasebeta

← Group #69585

Character table — Group #69585

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order12222222344446666666444412121212121212121212121244441212121212121212888888882244
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
χ9222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ10222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ1122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ1422222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ1522222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111-1-1-1-111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ1622222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111-1-1-1-111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ1722222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22211111111-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000
χ1822222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22211111111-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000
χ1922-22-2-22-2222-2-22-2-22-2-22000022-2-20000000000000000000000000000002i−2i
χ2022-22-2-22-2222-2-22-2-22-2-22000022-2-2000000000000000000000000000000−2i2i
χ2122-22-2-22-22-2-2222-2-22-2-220000-2-22200000000000000000000000000002-200
χ2222-22-2-22-22-2-2222-2-22-2-220000-2-2220000000000000000000000000000-2200
χ2322-2-22-2-222000022-2-22-2-2002-20000000022-2-2000000000000−i2−i2i2i2−i2−i2i2i20000
χ2422-2-22-2-222000022-2-22-2-2002-20000000022-2-2000000000000i2i2−i2−i2i2i2−i2−i20000
χ2522-2-22-2-222000022-2-22-2-200-2200000000-2-222000000000000−i2−i2i2i2i2i2−i2−i20000
χ2622-2-22-2-222000022-2-22-2-200-2200000000-2-222000000000000i2i2−i2−i2−i2−i2i2i20000
χ272-222-2-2-2222-22-2-2222-2-2-200002-22-20000000000000000000000002i−2i2i−2i0000
χ282-222-2-2-2222-22-2-2222-2-2-200002-22-2000000000000000000000000−2i2i−2i2i0000
χ292-222-2-2-222-22-22-2222-2-2-20000-22-22000000000000000000002i−2i2i−2i00000000
χ302-222-2-2-222-22-22-2222-2-2-20000-22-2200000000000000000000−2i2i−2i2i00000000
χ312-2-2222-2-222-2-22-2-2-2222-200002-2-22000000002i−2i002i−2i2i−2i0000000000000000
χ322-2-2222-2-222-2-22-2-2-2222-200002-2-2200000000−2i2i00−2i2i−2i2i0000000000000000
χ332-2-2222-2-22-222-2-2-2-2222-20000-222-200000000002i−2i00002i−2i2i−2i000000000000
χ342-2-2222-2-22-222-2-2-2-2222-20000-222-20000000000−2i2i0000−2i2i−2i2i000000000000
χ352-2-2222-2-2-12-2-22111-1-1-110000-111-1−i3−i3i3i3−i3i3−i3i32i−2i00−ii−ii3−3−33000000000000
χ362-2-2222-2-2-12-2-22111-1-1-110000-111-1−i3−i3i3i3−i3i3−i3i3−2i2i00i−ii−i−333−3000000000000
χ372-2-2222-2-2-12-2-22111-1-1-110000-111-1i3i3−i3−i3i3−i3i3−i32i−2i00−ii−ii−333−3000000000000
χ382-2-2222-2-2-12-2-22111-1-1-110000-111-1i3i3−i3−i3i3−i3i3−i3−2i2i00i−ii−i3−3−33000000000000
χ392-2-2222-2-2-1-222-2111-1-1-1100001-1-11−i3−i3i3i3i3−i3i3−i3002i−2i3−3−33−ii−ii000000000000
χ402-2-2222-2-2-1-222-2111-1-1-1100001-1-11−i3−i3i3i3i3−i3i3−i300−2i2i−333−3i−ii−i000000000000
χ412-2-2222-2-2-1-222-2111-1-1-1100001-1-11i3i3−i3−i3−i3i3−i3i3002i−2i−333−3−ii−ii000000000000
χ422-2-2222-2-2-1-222-2111-1-1-1100001-1-11i3i3−i3−i3−i3i3−i3i300−2i2i3−3−33i−ii−i000000000000
χ432-2-2-2-222220000-22-2-2-2222-20000002-22-200000000000000002−2−222−2−220000
χ442-2-2-2-222220000-22-2-2-2222-20000002-22-20000000000000000−222−2−222−20000
χ452-2-2-2-222220000-22-2-2-222-22000000-22-2200000000000000002−2−22−222−20000
χ462-2-2-2-222220000-22-2-2-222-22000000-22-220000000000000000−222−22−2−220000
χ47444-4-44-4-4400004-44-4-44-40000000000000000000000000000000000000000
χ48444-4-44-4-4-20000-22-222-2200000000−2i32i32i3−2i30000000000000000000000000000
χ49444-4-44-4-4-20000-22-222-22000000002i3−2i3−2i32i30000000000000000000000000000
χ5044-44-4-44-4-244-4-4-222-222-20000-2-22200000000000000000000000000000000
χ5144-44-4-44-4-2-4-444-222-222-2000022-2-200000000000000000000000000000000
χ5244-4-44-4-44-20000-2-222-222004-400000000-2-222000000000000000000000000
χ5344-4-44-4-44-20000-2-222-22200-440000000022-2-2000000000000000000000000
χ544-444-4-4-44-24-44-42-2-2-22220000-22-2200000000000000000000000000000000
χ554-444-4-4-44-2-44-442-2-2-222200002-22-200000000000000000000000000000000
χ564-44-44-44-440000-4-44-44-440000000000000000000000000000000000000000
χ574-44-44-44-4-2000022-22-22-2000000000000−2i32i32i3−2i3000000000000000000000000
χ584-44-44-44-4-2000022-22-22-20000000000002i3−2i3−2i32i3000000000000000000000000
χ594-4-4-4-4444-200002-2222-2-24-4000000-22-220000000000000000000000000000
χ604-4-4-4-4444-200002-2222-2-2-440000002-22-20000000000000000000000000000

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