Finite Group Databasebeta

← Group #69684

Character table — Group #69684

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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ9222222222-2-2-2-2222222222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ10222222222-2-2-2-22222222-2-222-2-2-2-22222-2-2-2-2000000000000000000000000
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
χ1322222222-12222-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-122-2-21111-1-1-1-1000000000000
χ1422222222-12222-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-1-2-222-1-1-1-11111000000000000
χ1522222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-1-1-1-1111111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ1622222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-1-1-1-1111111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ1722222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2221111-1-1-1-111110000−i3−i3i3i3i3i3−i3−i3000000000000
χ1822222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2221111-1-1-1-111110000i3i3−i3−i3−i3−i3i3i3000000000000
χ19222-22-2-2-22000022-22-2-2-2002-2000022-2-2000000000000000022−2−222−2−20000
χ20222-22-2-2-22000022-22-2-2-2002-2000022-2-20000000000000000−2−222−2−2220000
χ21222-22-2-2-22000022-22-2-2-200-220000-2-222000000000000000022−2−2−2−2220000
χ22222-22-2-2-22000022-22-2-2-200-220000-2-2220000000000000000−2−22222−2−20000
χ2322-22-22-2-2200002-22-22-2-22-20022-2-2000000000000000000002−22−22−22−20000
χ2422-22-22-2-2200002-22-22-2-22-20022-2-200000000000000000000−22−22−22−220000
χ2522-22-22-2-2200002-22-22-2-2-2200-2-222000000000000000000002−22−2−22−220000
χ2622-22-22-2-2200002-22-22-2-2-2200-2-22200000000000000000000−22−222−22−20000
χ2722-2-2-2-22222-22-22-2-2-2-22200000000000022-2-200000000000000002-2-220000
χ2822-2-2-2-22222-22-22-2-2-2-22200000000000022-2-20000000000000000-222-20000
χ2922-2-2-2-2222-22-222-2-2-2-222000000000000-2-2220000000000002-2-2200000000
χ3022-2-2-2-2222-22-222-2-2-2-222000000000000-2-222000000000000-222-200000000
χ312-222-2-22-2222-2-2-222-2-2-220000000000002-22-22-20000002-22-2000000000000
χ322-222-2-22-2222-2-2-222-2-2-220000000000002-22-2-22000000-22-22000000000000
χ332-222-2-22-22-2-222-222-2-2-22000000000000-22-22002i−2i2i−2i2i−2i0000000000000000
χ342-222-2-22-22-2-222-222-2-2-22000000000000-22-2200−2i2i−2i2i−2i2i0000000000000000
χ352-222-2-22-2-122-2-21-1-1111-100003−33−33−33−3-11-112-2003−3−33-11-11000000000000
χ362-222-2-22-2-122-2-21-1-1111-100003−33−33−33−3-11-11-2200−333−31-11-1000000000000
χ372-222-2-22-2-122-2-21-1-1111-10000−33−33−33−33-11-112-200−333−3-11-11000000000000
χ382-222-2-22-2-122-2-21-1-1111-10000−33−33−33−33-11-11-22003−3−331-11-1000000000000
χ392-222-2-22-2-1-2-2221-1-1111-100003−33−3−33−331-11-1002i−2i−ii−ii−i3i3i3−i3000000000000
χ402-222-2-22-2-1-2-2221-1-1111-100003−33−3−33−331-11-100−2i2ii−ii−ii3−i3−i3i3000000000000
χ412-222-2-22-2-1-2-2221-1-1111-10000−33−333−33−31-11-1002i−2i−ii−iii3−i3−i3i3000000000000
χ422-222-2-22-2-1-2-2221-1-1111-10000−33−333−33−31-11-100−2i2ii−ii−i−i3i3i3−i3000000000000
χ432-2-2-2222-222-2-22-2-2-222-220000000000002-2-2200000000000000000000002i−2i
χ442-2-2-2222-222-2-22-2-2-222-220000000000002-2-220000000000000000000000−2i2i
χ452-2-2-2222-22-222-2-2-2-222-22000000000000-222-2000000000000000000002i−2i00
χ462-2-2-2222-22-222-2-2-2-222-22000000000000-222-200000000000000000000−2i2i00
χ47444-44-4-4-4-20000-2-22-2222004-40000-2-2220000000000000000000000000000
χ48444-44-4-4-4-20000-2-22-222200-44000022-2-20000000000000000000000000000
χ4944-44-44-4-4-20000-22-22-2224-400-2-22200000000000000000000000000000000
χ5044-44-44-4-4-20000-22-22-222-440022-2-200000000000000000000000000000000
χ5144-4-4-4-444-24-44-4-22222-2-2000000000000-2-222000000000000000000000000
χ5244-4-4-4-444-2-44-44-22222-2-200000000000022-2-2000000000000000000000000
χ534-44-4-44-4440000-44-4-444-40000000000000000000000000000000000000000
χ544-44-4-44-44-200002-222-2-220000000023−23−23230000000000000000000000000000
χ554-44-4-44-44-200002-222-2-2200000000−232323−230000000000000000000000000000
χ564-4-444-4-4440000-4-444-44-40000000000000000000000000000000000000000
χ574-4-444-4-44-2000022-2-22-22000023−23−232300000000000000000000000000000000
χ584-4-444-4-44-2000022-2-22-220000−232323−2300000000000000000000000000000000
χ594-4-4-4444-4-24-4-44222-2-22-2000000000000-222-2000000000000000000000000
χ604-4-4-4444-4-2-444-4222-2-22-20000000000002-2-22000000000000000000000000

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