Finite Group Databasebeta

← Group #68809

Character table — Group #68809

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order12222222344446666666888812121212242424242424242444441212121212121212444488884444
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
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ9222222222-2-2-2-222222220000-2-2-2-20000000000000000000022-2-200000000
χ10222222222-2-2-2-222222220000-2-2-2-200000000000000000000-2-22200000000
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
χ1522-222-2-2-2222-2-22-2-2-222-2000022-2-2000000002-20022-2-20000000000000000
χ1622-222-2-2-2222-2-22-2-2-222-2000022-2-200000000-2200-2-2220000000000000000
χ1722-222-2-2-22-2-2222-2-2-222-20000-2-2220000000000000000000000000000002i−2i
χ1822-222-2-2-22-2-2222-2-2-222-20000-2-222000000000000000000000000000000−2i2i
χ1922-222-2-2-2-122-2-2-1111-1-110000-1-1113333−3−3−3−32-200-1-11133−3−3000000000000
χ2022-222-2-2-2-122-2-2-1111-1-110000-1-1113333−3−3−3−3-220011-1-1−3−333000000000000
χ2122-222-2-2-2-122-2-2-1111-1-110000-1-111−3−3−3−333332-200-1-111−3−333000000000000
χ2222-222-2-2-2-122-2-2-1111-1-110000-1-111−3−3−3−33333-220011-1-133−3−3000000000000
χ2322-2-2-222-22000022-2-2-2-22−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i20000000000002-200−i2−i2i2i20000
χ2422-2-2-222-22000022-2-2-2-22−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2000000000000-2200i2i2−i2−i20000
χ2522-2-2-222-22000022-2-2-2-22i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i20000000000002-200i2i2−i2−i20000
χ2622-2-2-222-22000022-2-2-2-22i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2000000000000-2200−i2−i2i2i20000
χ272-222-2-22-222-22-2-222-22-2-200002-22-200000000000000000000000000002-200
χ282-222-2-22-222-22-2-222-22-2-200002-22-20000000000000000000000000000-2200
χ292-222-2-22-22-22-22-222-22-2-20000-22-2200000000002i−2i00002i−2i2i−2i000000000000
χ302-222-2-22-22-22-22-222-22-2-20000-22-220000000000−2i2i0000−2i2i−2i2i000000000000
χ312-222-2-22-2-1-22-221-1-11-11100001-11-1−i3i3−i3i3−i3i3−i3i3002i−2i3−33−3−ii−ii000000000000
χ322-222-2-22-2-1-22-221-1-11-11100001-11-1−i3i3−i3i3−i3i3−i3i300−2i2i−33−33i−ii−i000000000000
χ332-222-2-22-2-1-22-221-1-11-11100001-11-1i3−i3i3−i3i3−i3i3−i3002i−2i−33−33−ii−ii000000000000
χ342-222-2-22-2-1-22-221-1-11-11100001-11-1i3−i3i3−i3i3−i3i3−i300−2i2i3−33−3i−ii−i000000000000
χ352-22-222-2-220000-2-22-2-2222−22−200002−2−22−222−2000000000000002i−2i−i2i2−i2i20000
χ362-22-222-2-220000-2-22-2-2222−22−200002−2−22−222−200000000000000−2i2ii2−i2i2−i20000
χ372-22-222-2-220000-2-22-2-222−22−220000−222−22−2−22000000000000002i−2ii2−i2i2−i20000
χ382-22-222-2-220000-2-22-2-222−22−220000−222−22−2−2200000000000000−2i2i−i2i2−i2i20000
χ392-2-22-22-2222-2-22-2-2-222-2200002-2-220000000000000000000000002-2-220000
χ402-2-22-22-2222-2-22-2-2-222-2200002-2-22000000000000000000000000-222-20000
χ412-2-22-22-222-222-2-2-2-222-222i−2i−2i2i-222-22i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ422-2-22-22-222-222-2-2-2-222-22−2i2i2i−2i-222-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ432-2-22-22-22-1-222-2111-1-11-12i−2i−2i2i1-1-11−ii−iii−ii−i00003−3−33i3−i3−i3i3000000000000
χ442-2-22-22-22-1-222-2111-1-11-12i−2i−2i2i1-1-11−ii−iii−ii−i0000−333−3−i3i3i3−i3000000000000
χ452-2-22-22-22-1-222-2111-1-11-1−2i2i2i−2i1-1-11i−ii−i−ii−ii00003−3−33−i3i3i3−i3000000000000
χ462-2-22-22-22-1-222-2111-1-11-1−2i2i2i−2i1-1-11i−ii−i−ii−ii0000−333−3i3−i3−i3i3000000000000
χ4744444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ48444-4-4-4-44400004-444-4-4-40000000000000000000000000000000000000000
χ49444-4-4-4-44-20000-22-2-222200000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ50444-4-4-4-44-20000-22-2-222200000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ5144-444-4-4-4-2-4-444-2222-2-22000022-2-200000000000000000000000000000000
χ5244-4-4-444-4-20000-2-22222-2−2i2−2i22i22i20000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5344-4-4-444-4-20000-2-22222-22i22i2−2i2−2i20000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ544-444-4-44-4-24-44-42-2-22-2220000-22-2200000000000000000000000000000000
χ554-44-444-4-4-2000022-222-2-222−2222−220000−222−22−2−22000000000000000000000000
χ564-44-444-4-4-2000022-222-2-2−2222−222200002−2−22−222−2000000000000000000000000
χ574-4-44-44-44-24-4-44222-2-22-20000-222-200000000000000000000000000000000
χ584-4-4-44-44440000-44-44-44-40000000000000000000000000000000000000000
χ594-4-4-44-444-200002-22-22-22000000006−6−666−6−66000000000000000000000000
χ604-4-4-44-444-200002-22-22-2200000000−666−6−666−6000000000000000000000000

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