Finite Group Databasebeta

← Group #68805

Character table — Group #68805

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
χ91-1-1-111-11111-1-11-1-1-111-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-11-1ii−i−ii−i1-1
χ101-1-1-111-11111-1-11-1-1-111-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-11−i−iii−ii-11
χ111-1-1-111-11111-1-11-1-1-111-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii1-11-1ii−i−i−ii-11
χ121-1-1-111-11111-1-11-1-1-111-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11-11−i−iiii−i1-1
χ131-1-1-111-11111-1-11-1-1-111-1−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-11-1−i−iii−ii1-1
χ141-1-1-111-11111-1-11-1-1-111-1−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-11ii−i−ii−i-11
χ151-1-1-111-11111-1-11-1-1-111-1−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i1-11-1−i−iiii−i-11
χ161-1-1-111-11111-1-11-1-1-111-1−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11-11ii−i−i−ii1-1
χ17222222222-2-2-2-222222220000-2-2-2-20000000000000000000022-2-200000000
χ18222222222-2-2-2-222222220000-2-2-2-200000000000000000000-2-22200000000
χ1922222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ23222-22-2-2-222-22-2-222-22-2-22-22-22-2-2222-2-222-2-2000000000000000000000000
χ24222-22-2-2-222-22-2-222-22-2-2-22-222-2-22-2-222-2-222000000000000000000000000
χ25222-22-2-2-22-22-22-222-22-2-20000-222-20000000000000000000000002-22-20000
χ26222-22-2-2-22-22-22-222-22-2-20000-222-2000000000000000000000000-22-220000
χ27222-22-2-2-2-12-22-21-1-11-1112-22-2-111-1-1-111-1-11100003−33−33−33−3000000000000
χ28222-22-2-2-2-12-22-21-1-11-1112-22-2-111-1-1-111-1-1110000−33−33−33−33000000000000
χ29222-22-2-2-2-12-22-21-1-11-111-22-22-111-111-1-111-1-100003−33−3−33−33000000000000
χ30222-22-2-2-2-12-22-21-1-11-111-22-22-111-111-1-111-1-10000−33−333−33−3000000000000
χ312-2-222-22-222-2-22-2-2-222-222i−2i−2i2i2-22-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322-2-222-22-222-2-22-2-2-222-22−2i2i2i−2i2-22-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332-2-222-22-22-222-2-2-2-222-220000-22-220000000000000000000000002i−2i−2i2i0000
χ342-2-222-22-22-222-2-2-2-222-220000-22-22000000000000000000000000−2i2i2i−2i0000
χ352-2-222-22-2-12-2-22111-1-11-12i−2i−2i2i-11-11−i−iiiii−i−i00003−3−33i3−i3−i3i3000000000000
χ362-2-222-22-2-12-2-22111-1-11-12i−2i−2i2i-11-11−i−iiiii−i−i0000−333−3−i3i3i3−i3000000000000
χ372-2-222-22-2-12-2-22111-1-11-1−2i2i2i−2i-11-11ii−i−i−i−iii00003−3−33−i3i3i3−i3000000000000
χ382-2-222-22-2-12-2-22111-1-11-1−2i2i2i−2i-11-11ii−i−i−i−iii0000−333−3i3−i3−i3i3000000000000
χ392-2-2-222-222-2-2222-2-2-222-20000-2-222000000000000000000002-2-2200000000
χ402-2-2-222-222-2-2222-2-2-222-20000-2-22200000000000000000000-222-200000000
χ412-2-2-222-22-122-2-2-1111-1-112i2i−2i−2i-1-111−i−i−i−iiiii2-22i−2i-1-111−i−iii000000000000
χ422-2-2-222-22-122-2-2-1111-1-112i2i−2i−2i-1-111−i−i−i−iiiii-22−2i2i11-1-1ii−i−i000000000000
χ432-2-2-222-22-122-2-2-1111-1-11−2i−2i2i2i-1-111iiii−i−i−i−i2-2−2i2i-1-111ii−i−i000000000000
χ442-2-2-222-22-122-2-2-1111-1-11−2i−2i2i2i-1-111iiii−i−i−i−i-222i−2i11-1-1−i−iii000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ46444-44-4-4-4-2-44-442-2-22-22200002-2-2200000000000000000000000000000000
χ4744-44-44-4-440000-44-44-44-40000000000000000000000000000000000000000
χ4844-44-44-4-4-200002-22-22-22000000006−66−66−66−6000000000000000000000000
χ4944-44-44-4-4-200002-22-22-2200000000−66−66−66−66000000000000000000000000
χ5044-4-4-4-4444000044-4-4-4-440000000000000000000000000000000000000000
χ5144-4-4-4-444-20000-2-22222-2000000006−6−666−6−66000000000000000000000000
χ5244-4-4-4-444-20000-2-22222-200000000−666−6−666−6000000000000000000000000
χ534-444-4-4-44400004-444-4-4-40000000000000000000000000000000000000000
χ544-444-4-4-44-20000-22-2-222200000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ554-444-4-4-44-20000-22-2-222200000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ564-44-4-444-440000-4-44-4-4440000000000000000000000000000000000000000
χ574-44-4-444-4-2000022-222-2-200000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ584-44-4-444-4-2000022-222-2-200000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ594-4-444-44-4-2-444-4222-2-22-200002-22-200000000000000000000000000000000
χ604-4-4-444-44-2-4-444-2222-2-22000022-2-200000000000000000000000000000000

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