Finite Group Databasebeta

← Group #10713620

Character table — Group #10713620

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order122223444466688668881212121224242424161616162424484848484848484822446666121212124488161616162488
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
χ9111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−ii−ii−i11-1-11-1i−i
χ10111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i−ii−ii-1-111-11−ii
χ11111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iiii−ii−i11-1-1-11−ii
χ12111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iii−ii−ii-1-1111-1i−i
χ13111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iiii−ii−i-1-111-11i−i
χ14111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii−ii−ii11-1-11-1−ii
χ15111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−ii−ii−i-1-1111-1−ii
χ16111-1-1111-1-11-1-1111-1-1-111-1-1111-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−i−ii−ii11-1-1-11i−i
χ172222222222222-2-222-2-2-22222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ182222222222222-2-222-2-2-22222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ1922222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ2222222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ23222-2-2222-2-22-2-2-2-22-222-22-2-22-2-2220000-22000000000000000000002i−2i−2i2i00000000
χ24222-2-2222-2-22-2-2-2-22-222-22-2-22-2-2220000-2200000000000000000000−2i2i2i−2i00000000
χ25222-2-2-122-2-2-11122-11-2-22-111-1-1-1112i2i−2i−2i-11−i−i−i−iiiii2-22i−2i-1-111−i−iii000000000000
χ26222-2-2-122-2-2-11122-11-2-22-111-1-1-1112i2i−2i−2i-11−i−i−i−iiiii-22−2i2i11-1-1ii−i−i000000000000
χ27222-2-2-122-2-2-11122-11-2-22-111-1-1-111−2i−2i2i2i-11iiii−i−i−i−i2-2−2i2i-1-111ii−i−i000000000000
χ28222-2-2-122-2-2-11122-11-2-22-111-1-1-111−2i−2i2i2i-11iiii−i−i−i−i-222i−2i11-1-1−i−iii000000000000
χ2922-22-22-22-2222222-2-2-22-2-22-2222222-22-2-2-222-2-222-2-2000000000000000000000000
χ3022-22-22-22-2222222-2-2-22-2-22-222222-22-22-2-2-2-222-2-222000000000000000000000000
χ3122-22-22-22-22222-2-2-2-22-22-22-22-2-2-2-20000220000000000000000000000002-22-20000
χ3222-22-22-22-22222-2-2-2-22-22-22-22-2-2-2-2000022000000000000000000000000-22-220000
χ3322-22-2-1-22-22-1-1-12211-22-21-11-1-1-1-1-12-22-211-1-111-1-1110000−i3i3−i3i3−i3i3−i3i3000000000000
χ3422-22-2-1-22-22-1-1-12211-22-21-11-1-1-1-1-12-22-211-1-111-1-1110000i3−i3i3−i3i3−i3i3−i3000000000000
χ3522-22-2-1-22-22-1-1-12211-22-21-11-1-1-1-1-1-22-221111-1-111-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ3622-22-2-1-22-22-1-1-12211-22-21-11-1-1-1-1-1-22-221111-1-111-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ3722-2-222-222-22-2-222-222-2-2-2-22222-2-22i−2i−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3822-2-222-222-22-2-222-222-2-2-2-22222-2-2−2i2i2i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3922-2-222-222-22-2-2-2-2-22-222-2-222-2-22200002-20000000000000000000000002-2-220000
χ4022-2-222-222-22-2-2-2-2-22-222-2-222-2-22200002-2000000000000000000000000-222-20000
χ4122-2-22-1-222-2-111221-12-2-211-1-1-1-1112i−2i−2i2i1-1−i−iiiii−i−i0000−i3i3i3−i33−3−33000000000000
χ4222-2-22-1-222-2-111221-12-2-211-1-1-1-1112i−2i−2i2i1-1−i−iiiii−i−i0000i3−i3−i3i3−333−3000000000000
χ4322-2-22-1-222-2-111221-12-2-211-1-1-1-111−2i2i2i−2i1-1ii−i−i−i−iii0000−i3i3i3−i3−333−3000000000000
χ4422-2-22-1-222-2-111221-12-2-211-1-1-1-111−2i2i2i−2i1-1ii−i−i−i−iii0000i3−i3−i3i33−3−33000000000000
χ45444444-4-4-4-44440044000-4-4-4-4000000000000000000000000000000000000000000
χ4644444-24444-2-2-2-4-4-2-2-4-4-4-2-2-2-2222200002200000000000000000000000000000000
χ4744444-2-4-4-4-4-2-2-200-2-200022220000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ4844444-2-4-4-4-4-2-2-200-2-200022220000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ49444-4-44-4-4444-4-4004-4000-444-4000000000000000000000000000000000000000000
χ50444-4-4-244-4-4-222-4-4-2244-4-222-222-2-200002-200000000000000000000000000000000
χ51444-4-4-2-4-444-22200-220002-2-2200000000006−66−6−66−66000000000000000000000000
χ52444-4-4-2-4-444-22200-220002-2-220000000000−66−666−66−6000000000000000000000000
χ5344-44-444-44-444400-4-40004-44-4000000000000000000000000000000000000000000
χ5444-44-4-24-44-4-2-2-20022000-22-220000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ5544-44-4-24-44-4-2-2-20022000-22-220000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ5644-44-4-2-44-44-2-2-2-4-4224-442-22-222220000-2-200000000000000000000000000000000
χ5744-4-4444-4-444-4-400-4400044-4-4000000000000000000000000000000000000000000
χ5844-4-44-24-4-44-222002-2000-2-22200000000006−6−66−666−6000000000000000000000000
χ5944-4-44-24-4-44-222002-2000-2-2220000000000−666−66−6−66000000000000000000000000
χ6044-4-44-2-444-4-222-4-42-2-44422-2-222-2-20000-2200000000000000000000000000000000
χ618-800080000-80042−4200000000042−420000000000000000000000000000000000000000
χ628-800080000-800−4242000000000−42420000000000000000000000000000000000000000
χ638-8000-400004−4i34i342−42000000000−22222i6−2i600000000000000000000000000000000000000
χ648-8000-400004−4i34i3−424200000000022−22−2i62i600000000000000000000000000000000000000
χ658-8000-4000044i3−4i342−42000000000−2222−2i62i600000000000000000000000000000000000000
χ668-8000-4000044i3−4i3−424200000000022−222i6−2i600000000000000000000000000000000000000

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