Finite Group Databasebeta

← Group #69685

Character table — Group #69685

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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1
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
χ1322222222-12222-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-122-2-2-1-1-1-11111000000000000
χ1422222222-12222-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-1-2-2221111-1-1-1-1000000000000
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
χ19222-2-2-22-2222-2-222-2-2-2-2200000000000022-2-2002-200002-22-2000000000000
χ20222-2-2-22-2222-2-222-2-2-2-2200000000000022-2-200-220000-22-22000000000000
χ21222-2-2-22-22-2-22222-2-2-2-22000000000000-2-2222i−2i002i−2i2i−2i0000000000000000
χ22222-2-2-22-22-2-22222-2-2-2-22000000000000-2-222−2i2i00−2i2i−2i2i0000000000000000
χ23222-2-2-22-2-122-2-2-1-11111-1000033−3−333−3−3-1-111002-23−3−33-11-11000000000000
χ24222-2-2-22-2-122-2-2-1-11111-1000033−3−333−3−3-1-11100-22−333−31-11-1000000000000
χ25222-2-2-22-2-122-2-2-1-11111-10000−3−333−3−333-1-111002-2−333−3-11-11000000000000
χ26222-2-2-22-2-122-2-2-1-11111-10000−3−333−3−333-1-11100-223−3−331-11-1000000000000
χ27222-2-2-22-2-1-2-222-1-11111-1000033−3−3−3−33311-1-12i−2i00−ii−ii−i3i3i3−i3000000000000
χ28222-2-2-22-2-1-2-222-1-11111-1000033−3−3−3−33311-1-1−2i2i00i−ii−ii3−i3−i3i3000000000000
χ29222-2-2-22-2-1-2-222-1-11111-10000−3−33333−3−311-1-12i−2i00−ii−iii3−i3−i3i3000000000000
χ30222-2-2-22-2-1-2-222-1-11111-10000−3−33333−3−311-1-1−2i2i00i−ii−i−i3i3i3−i3000000000000
χ3122-22-2-2-22200002-222-2-2-2002-200002-22-20000000000000000−i2−i2i2i2−i2−i2i2i20000
χ3222-22-2-2-22200002-222-2-2-2002-200002-22-20000000000000000i2i2−i2−i2i2i2−i2−i20000
χ3322-22-2-2-22200002-222-2-2-200-220000-22-220000000000000000−i2−i2i2i2i2i2−i2−i20000
χ3422-22-2-2-22200002-222-2-2-200-220000-22-220000000000000000i2i2−i2−i2−i2−i2i2i20000
χ352-22-22-2-2220000-222-22-2-22-2002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ362-22-22-2-2220000-222-22-2-22-2002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ372-22-22-2-2220000-222-22-2-2-2200-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ382-22-22-2-2220000-222-22-2-2-2200-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ392-2-222-22-222-22-2-2-2-222-220000000000002-22-2000000000000000000002i−2i00
χ402-2-222-22-222-22-2-2-2-222-220000000000002-22-200000000000000000000−2i2i00
χ412-2-222-22-22-22-22-2-2-222-22000000000000-22-2200000000000000000000002i−2i
χ422-2-222-22-22-22-22-2-2-222-22000000000000-22-220000000000000000000000−2i2i
χ432-2-2-2-222222-2-22-2-22-2-2220000000000002-2-2200000000000000002-2-220000
χ442-2-2-2-222222-2-22-2-22-2-2220000000000002-2-220000000000000000-222-20000
χ452-2-2-2-22222-222-2-2-22-2-222000000000000-222-20000000000002-2-2200000000
χ462-2-2-2-22222-222-2-2-22-2-222000000000000-222-2000000000000-222-200000000
χ4744-44-4-4-44-20000-22-2-2222004-40000-22-220000000000000000000000000000
χ4844-44-4-4-44-20000-22-2-222200-4400002-22-20000000000000000000000000000
χ4944-4-444-4-4400004-4-4-444-40000000000000000000000000000000000000000
χ5044-4-444-4-4-20000-2222-2-220000000023−23−23230000000000000000000000000000
χ5144-4-444-4-4-20000-2222-2-2200000000−232323−230000000000000000000000000000
χ524-444-44-4-440000-44-44-44-40000000000000000000000000000000000000000
χ534-444-44-4-4-200002-22-22-22000023−23−232300000000000000000000000000000000
χ544-444-44-4-4-200002-22-22-220000−232323−2300000000000000000000000000000000
χ554-44-44-4-44-200002-2-22-2224-400-22-2200000000000000000000000000000000
χ564-44-44-4-44-200002-2-22-222-44002-22-200000000000000000000000000000000
χ574-4-444-44-4-24-44-4222-2-22-2000000000000-22-22000000000000000000000000
χ584-4-444-44-4-2-44-44222-2-22-20000000000002-22-2000000000000000000000000
χ594-4-4-4-4444-24-4-4422-222-2-2000000000000-222-2000000000000000000000000
χ604-4-4-4-4444-2-444-422-222-2-20000000000002-2-22000000000000000000000000

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