Finite Group Databasebeta

← Group #10708182

Character table — Group #10708182

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size111122222244444444888888888888161616161616161616161616161616242424242424242448484848
order12222236664444446644121212121212121212124888812122424242424242424222244444488
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-11111111-1-1-1-11111-111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ611111111111-1-1-1-11111111-1-1-1-11111-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ711111111111-1-1-1-11111111-1-1-1-11111-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ811111111111-1-1-1-11111111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ9222222222222222222-2-2222222-2-2-2-2-20000-2-200000000000000000000
χ1022222222222-2-2-2-2222-2-222-2-2-2-2-2-2-2-2200002200000000000000000000
χ112222222222-20000-2222-2-2-2000022-2-20000000000000002200-2-2000000
χ122222222222-20000-2222-2-2-2000022-2-2000000000000000-2-20022000000
χ132222222222-20000-222-22-2-20000-2-222000000000000000002200-2-20000
χ142222222222-20000-222-22-2-20000-2-22200000000000000000-2-200220000
χ15222222-1-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1000000000000
χ16222222-1-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-12-2-2-2-2-1-111111111000000000000
χ17222222-1-1-1-1222222-1-1-2-2-1-1-1-1-1-11111-200001133−3−333−3−3000000000000
χ18222222-1-1-1-1222222-1-1-2-2-1-1-1-1-1-11111-2000011−3−333−3−333000000000000
χ19222222-1-1-1-12-2-2-2-22-1-122-1-11111-1-1-1-1-222-2-211-1-1-1-11111000000000000
χ20222222-1-1-1-12-2-2-2-22-1-122-1-11111-1-1-1-1-2-2-222111111-1-1-1-1000000000000
χ21222222-1-1-1-12-2-2-2-22-1-1-2-2-1-11111111120000-1-133−3−3−3−333000000000000
χ22222222-1-1-1-12-2-2-2-22-1-1-2-2-1-11111111120000-1-1−3−33333−3−3000000000000
χ2322-2-2-222-22-2222-2-2-2-22002-222-2-200000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000
χ2422-2-2-222-22-2222-2-2-2-22002-222-2-200000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000
χ2522-2-2-222-22-22-2-222-2-22002-2-2-22200000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000
χ2622-2-2-222-22-22-2-222-2-22002-2-2-22200000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000
χ2722-2-2-22-11-11222-2-2-21-100-11-1-1113−33−30−i2i2−i2i23−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ2822-2-2-22-11-11222-2-2-21-100-11-1-1113−33−30i2−i2i2−i23−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ2922-2-2-22-11-11222-2-2-21-100-11-1-111−33−330−i2i2−i2i2−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ3022-2-2-22-11-11222-2-2-21-100-11-1-111−33−330i2−i2i2−i2−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ3122-2-2-22-11-112-2-222-21-100-1111-1-13−33−30−i2i2i2−i2−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ3222-2-2-22-11-112-2-222-21-100-1111-1-13−33−30i2−i2−i2i2−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ3322-2-2-22-11-112-2-222-21-100-1111-1-1−33−330−i2i2i2−i23−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ3422-2-2-22-11-112-2-222-21-100-1111-1-1−33−330i2−i2−i2i23−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ35444444-2-2-2-2-40000-4-2-24-4220000-2-222000000000000000000000000000
χ36444444-2-2-2-2-40000-4-2-2-4422000022-2-2000000000000000000000000000
χ374444-4-44444000000-4-4000000000000000000000000000000000002-200
χ384444-4-44444000000-4-400000000000000000000000000000000000-2200
χ3944-4-44-44-44-40000004-400000000000000000000000000000000000002-2
χ4044-4-44-44-44-40000004-40000000000000000000000000000000000000-22
χ4144-4-4-444-44-4-400004-4400-4400000000000000000000000000000000000
χ4244-4-4-44-22-22-4000042-2002-2000023−23−2323000000000000000000000000000
χ4344-4-4-44-22-22-4000042-2002-20000−232323−23000000000000000000000000000
χ444-44-40044-4-402-22-200000002-22-2000000000000000000000002i−2i2i−2i0000
χ454-44-40044-4-402-22-200000002-22-200000000000000000000000−2i2i−2i2i0000
χ464-44-40044-4-40-22-220000000-22-22000000000000000000000002i−2i−2i2i0000
χ474-44-40044-4-40-22-220000000-22-2200000000000000000000000−2i2i2i−2i0000
χ484-4-44004-4-4402-2-2200000002-2-2200000000000000000002-22-200000000
χ494-4-44004-4-4402-2-2200000002-2-220000000000000000000-22-2200000000
χ504-4-44004-4-440-222-20000000-222-200000000000000000002-2-2200000000
χ514-4-44004-4-440-222-20000000-222-20000000000000000000-222-200000000
χ528888-8-8-4-4-4-400000044000000000000000000000000000000000000000
χ5388-8-88-8-44-44000000-44000000000000000000000000000000000000000
χ548-88-800-4-44404-44-40000000-22-220000000000000000000000000000000
χ558-88-800-4-4440-44-4400000002-22-20000000000000000000000000000000
χ568-8-8800-444-404-4-440000000-222-20000000000000000000000000000000
χ578-8-8800-444-40-444-400000002-2-220000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.