Finite Group Databasebeta

← Group #10714584

Character table — Group #10714584

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order1244222344466612121212668888121244881212121224242424242424244488121212122424242416161616161616162244
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
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111-11-1
χ922222222222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2000000000000000000000000
χ112222222-1222-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ122222222-1222-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ132222222-1222-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-211111111-1-1-1-122-2-2-1-1-1-11111000000000000
χ142222222-1222-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-211111111-1-1-1-1-2-2221111-1-1-1-1000000000000
χ152222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1111111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ162222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1111111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ172222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2221111-1-1-1-111110000−i3−i3i3i3i3i3−i3−i3000000000000
χ182222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2221111-1-1-1-111110000i3i3−i3−i3−i3−i3i3i3000000000000
χ1922222-2-22-22-22-2-222-2-22-22-22-2-2200000000000022-2-200000000000000002i2i−2i−2i0000
χ2022222-2-22-22-22-2-222-2-22-22-22-2-2200000000000022-2-20000000000000000−2i−2i2i2i0000
χ2122222-2-22-22-22-2-222-2-22-2-22-22-22000000000000-2-2220000000000002i2i−2i−2i00000000
χ2222222-2-22-22-22-2-222-2-22-2-22-22-22000000000000-2-222000000000000−2i−2i2i2i00000000
χ232222-22-222-2-22-2-222-2-2-2200002-22-20022-2-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ242222-22-222-2-22-2-222-2-2-2200002-22-20022-2-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ252222-22-222-2-22-2-222-2-2-2200002-2-2200-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ262222-22-222-2-22-2-222-2-2-2200002-2-2200-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ272222-2-222-2-222222222-2-20000-2-2002-2000022-2-200000000000000002−2−222−2−220000
χ282222-2-222-2-222222222-2-20000-2-2002-2000022-2-20000000000000000−222−2−222−20000
χ292222-2-222-2-222222222-2-20000-2-200-220000-2-22200000000000000002−2−22−222−20000
χ302222-2-222-2-222222222-2-20000-2-200-220000-2-2220000000000000000−222−22−2−220000
χ3122-2-2-22-22-2222-2-2-2-222-222-2-22-220000000000002-22-20000000000000000000020-20
χ3222-2-2-22-22-2222-2-2-2-222-222-2-22-220000000000002-22-200000000000000000000-2020
χ3322-2-2-22-22-2222-2-2-2-222-22-222-2-22000000000000-22-2200000000000000000000020-2
χ3422-2-2-22-22-2222-2-2-2-222-22-222-2-22000000000000-22-22000000000000000000000-202
χ3522-2-2-2-22222-2222-2-2-2-2-2-222-2-2220000000000002-2-22002i−2i00002i−2i2i−2i000000000000
χ3622-2-2-2-22222-2222-2-2-2-2-2-222-2-2220000000000002-2-2200−2i2i0000−2i2i−2i2i000000000000
χ3722-2-2-2-22222-2222-2-2-2-2-2-2-2-22222000000000000-222-22-2002-22-20000000000000000
χ3822-2-2-2-22222-2222-2-2-2-2-2-2-2-22222000000000000-222-2-2200-22-220000000000000000
χ3922-2-2-2-22-122-2-1-1-111111122-2-2-1-100003−33−33−33−3-111-1002i−2i−i3i3i3−i3−ii−ii000000000000
χ4022-2-2-2-22-122-2-1-1-111111122-2-2-1-100003−33−33−33−3-111-100−2i2ii3−i3−i3i3i−ii−i000000000000
χ4122-2-2-2-22-122-2-1-1-111111122-2-2-1-10000−33−33−33−33-111-1002i−2ii3−i3−i3i3−ii−ii000000000000
χ4222-2-2-2-22-122-2-1-1-111111122-2-2-1-10000−33−33−33−33-111-100−2i2i−i3i3i3−i3i−ii−i000000000000
χ4322-2-2-2-22-122-2-1-1-1111111-2-222-1-100003−33−3−33−331-1-112-200-11-113−3−33000000000000
χ4422-2-2-2-22-122-2-1-1-1111111-2-222-1-100003−33−3−33−331-1-11-22001-11-1−333−3000000000000
χ4522-2-2-2-22-122-2-1-1-1111111-2-222-1-10000−33−333−33−31-1-112-200-11-11−333−3000000000000
χ4622-2-2-2-22-122-2-1-1-1111111-2-222-1-10000−33−333−33−31-1-11-22001-11-13−3−33000000000000
χ4744444-4-4-2-44-4-222-2-222-224-44-42-2000000000000-2-222000000000000000000000000
χ4844444-4-4-2-44-4-222-2-222-22-44-442-200000000000022-2-2000000000000000000000000
χ494444-44-4-24-4-4-222-2-2222-20000-224-400-2-22200000000000000000000000000000000
χ504444-44-4-24-4-4-222-2-2222-20000-22-440022-2-200000000000000000000000000000000
χ514444-4-44-2-4-44-2-2-2-2-2-2-222000022004-40000-2-2220000000000000000000000000000
χ524444-4-44-2-4-44-2-2-2-2-2-2-22200002200-44000022-2-20000000000000000000000000000
χ5344-4-44444-4-4-4444-4-4-4-4440000-4-40000000000000000000000000000000000000000
χ5444-4-4444-2-4-4-4-2-2-22222-2-20000220000000023−23−23230000000000000000000000000000
χ5544-4-4444-2-4-4-4-2-2-22222-2-200002200000000−232323−230000000000000000000000000000
χ5644-4-44-4-444-444-4-4-4-4444-400004-40000000000000000000000000000000000000000
χ5744-4-44-4-4-24-44-22222-2-2-220000-22000023−23−232300000000000000000000000000000000
χ5844-4-44-4-4-24-44-22222-2-2-220000-220000−232323−2300000000000000000000000000000000
χ5944-4-4-44-4-2-444-22222-2-22-24-4-442-2000000000000-22-22000000000000000000000000
χ6044-4-4-44-4-2-444-22222-2-22-2-444-42-20000000000002-22-2000000000000000000000000
χ618-88i−8i0008000-8008i−8i00000000000000000000000000000000000000000000000000
χ628-88i−8i000-40004−4i34i3−4i4i43−43000000000000000000000000000000000000000000000000
χ638-88i−8i000-400044i3−4i3−4i4i−4343000000000000000000000000000000000000000000000000
χ648-8−8i8i0008000-800−8i8i00000000000000000000000000000000000000000000000000
χ658-8−8i8i000-40004−4i34i34i−4i−4343000000000000000000000000000000000000000000000000
χ668-8−8i8i000-400044i3−4i34i−4i43−43000000000000000000000000000000000000000000000000

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