Finite Group Databasebeta

← Group #10713265

Character table — Group #10713265

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order1222223444466666888812121212242424241616161624244848484848484848448812121212242424244488161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ91111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−ii−ii−i11-1-11-1i−i
χ101111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i−ii−ii-1-111-11−ii
χ111111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iiii−ii−i11-1-1-11−ii
χ121111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iii−ii−ii-1-1111-1i−i
χ131111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iiii−ii−i-1-111-11i−i
χ141111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iii−ii−ii11-1-11-1−ii
χ151111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−ii−ii−i-1-1111-1−ii
χ161111-1-111-11-1111-1-11-1-111-11-1-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−i−ii−ii11-1-1-11i−i
χ172222222222222222-2-2-2-22222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ182222222222222222-2-2-2-22222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ19222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ21222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ22222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ232222-2-222-22-2222-2-2-222-22-22-222220000-2-2000000000000000000002i−2i−2i2i00000000
χ242222-2-222-22-2222-2-2-222-22-22-222220000-2-200000000000000000000−2i2i2i−2i00000000
χ252222-2-2-12-22-2-1-1-1112-2-22-11-1111112i2i−2i−2i-1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii000000000000
χ262222-2-2-12-22-2-1-1-1112-2-22-11-1111112i2i−2i−2i-1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i000000000000
χ272222-2-2-12-22-2-1-1-1112-2-22-11-111111−2i−2i2i2i-1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i000000000000
χ282222-2-2-12-22-2-1-1-1112-2-22-11-111111−2i−2i2i2i-1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii000000000000
χ2922-2-22-22-222-2-22-22-22-22-2-222-2-2-2222-22-22-222-2-222-2-2000000000000000000000000
χ3022-2-22-22-222-2-22-22-22-22-2-222-2-2-222-22-222-2-2-222-2-222000000000000000000000000
χ3122-2-22-22-222-2-22-22-2-22-22-222-222-2-20000-220000000000000000000000002-22-20000
χ3222-2-22-22-222-2-22-22-2-22-22-222-222-2-20000-22000000000000000000000000-22-220000
χ3322-2-22-2-1-222-21-11-112-22-21-1-1111-1-12-22-2-11-1-111-1-11100003−33−33−33−3000000000000
χ3422-2-22-2-1-222-21-11-112-22-21-1-1111-1-12-22-2-11-1-111-1-1110000−33−33−33−33000000000000
χ3522-2-22-2-1-222-21-11-112-22-21-1-1111-1-1-22-22-1111-1-111-1-100003−33−3−33−33000000000000
χ3622-2-22-2-1-222-21-11-112-22-21-1-1111-1-1-22-22-1111-1-111-1-10000−33−333−33−3000000000000
χ3722-2-2-222-2-222-22-2-2222-2-2-2-22222-2-22i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3822-2-2-222-2-222-22-2-2222-2-2-2-22222-2-2−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3922-2-2-222-2-222-22-2-22-2-222-2-222-2-2220000-220000000000000000000000002-2-220000
χ4022-2-2-222-2-222-22-2-22-2-222-2-222-2-2220000-22000000000000000000000000-222-20000
χ4122-2-2-22-1-2-2221-111-122-2-211-1-1-1-1112i−2i−2i2i-11−i−iiiii−i−i00003−3−33i3−i3−i3i3000000000000
χ4222-2-2-22-1-2-2221-111-122-2-211-1-1-1-1112i−2i−2i2i-11−i−iiiii−i−i0000−333−3−i3i3i3−i3000000000000
χ4322-2-2-22-1-2-2221-111-122-2-211-1-1-1-111−2i2i2i−2i-11ii−i−i−i−iii00003−3−33−i3i3i3−i3000000000000
χ4422-2-2-22-1-2-2221-111-122-2-211-1-1-1-111−2i2i2i−2i-11ii−i−i−i−iii0000−333−3i3−i3−i3i3000000000000
χ454444444-4-4-4-4444440000-4-4-4-4000000000000000000000000000000000000000000
χ46444444-24444-2-2-2-2-2-4-4-4-4-2-2-2-2222200002200000000000000000000000000000000
χ47444444-2-4-4-4-4-2-2-2-2-20000222200000000006−66−66−66−6000000000000000000000000
χ48444444-2-4-4-4-4-2-2-2-2-2000022220000000000−66−66−66−66000000000000000000000000
χ494444-4-44-44-44444-4-40000-44-44000000000000000000000000000000000000000000
χ504444-4-4-24-44-4-2-2-222-444-4-22-22-2-2-2-200002200000000000000000000000000000000
χ514444-4-4-2-44-44-2-2-22200002-22-20000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ524444-4-4-2-44-44-2-2-22200002-22-20000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ5344-4-44-444-4-44-44-44-400004-4-44000000000000000000000000000000000000000000
χ5444-4-44-4-24-4-442-22-220000-222-200000000006−6−666−6−66000000000000000000000000
χ5544-4-44-4-24-4-442-22-220000-222-20000000000−666−6−666−6000000000000000000000000
χ5644-4-44-4-2-444-42-22-22-44-442-2-22-2-22200002-200000000000000000000000000000000
χ5744-4-4-44444-4-4-44-4-44000044-4-4000000000000000000000000000000000000000000
χ5844-4-4-44-244-4-42-222-20000-2-2220000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ5944-4-4-44-244-4-42-222-20000-2-2220000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ6044-4-4-44-2-4-4442-222-2-4-44422-2-222-2-200002-200000000000000000000000000000000
χ618-88-800800008-8-80000000000000000000000000000000000000000000000000000
χ628-88-800-40000-44400000000002i6−2i62i6−2i600000000000000000000000000000000000000
χ638-88-800-40000-4440000000000−2i62i6−2i62i600000000000000000000000000000000000000
χ648-8-880080000-8-880000000000000000000000000000000000000000000000000000
χ658-8-8800-4000044-400000000002i6−2i6−2i62i600000000000000000000000000000000000000
χ668-8-8800-4000044-40000000000−2i62i62i6−2i600000000000000000000000000000000000000

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