Finite Group Databasebeta

← Group #10708321

Character table — Group #10708321

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size111122222244448888888888888888161616161616161616161616161624242424484848484848
order12222236662266224444666666121212128888121224242424242424244444444444
χ1111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ511111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1111-1-1
χ611111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111-1-1-111
χ711111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1111
χ811111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111111-1-1-1
χ92222222222222222-2-2-2-2222222-2-2-2-20000-2-2000000000000000000
χ1022222222222222-2-222-2-222-2-2-2-2-2-2-2-2000022000000000000000000
χ112222222222-2-22200002-2-2-2000022-2-2000000000000002200000-200
χ122222222222-2-22200002-2-2-2000022-2-200000000000000-2-200000200
χ132222222222-2-2220000-22-2-20000-2-222000000000000000022-200000
χ142222222222-2-2220000-22-2-20000-2-2220000000000000000-2-2200000
χ15222222-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000000
χ16222222-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000000
χ17222222-1-1-1-122-1-122-2-2-2-2-1-1-1-1-1-1111100001133−3−333−3−30000000000
χ18222222-1-1-1-122-1-122-2-2-2-2-1-1-1-1-1-11111000011−3−333−3−3330000000000
χ19222222-1-1-1-122-1-1-2-222-2-2-1-1111111110000-1-133−3−3−3−3330000000000
χ20222222-1-1-1-122-1-1-2-222-2-2-1-1111111110000-1-1−3−33333−3−30000000000
χ21222222-1-1-1-122-1-1-2-2-2-222-1-11111-1-1-1-122-2-211-1-1-1-111110000000000
χ22222222-1-1-1-122-1-1-2-2-2-222-1-11111-1-1-1-1-2-222111111-1-1-1-10000000000
χ2322-2-22-222-2-2-222-2002i−2i002-2000000002−2−i2i22i−2i2−22−2−i2i2−i2i20000000000
χ2422-2-22-222-2-2-222-2002i−2i002-200000000−22i2−i22i−2i−22−22i2−i2i2−i20000000000
χ2522-2-22-222-2-2-222-200−2i2i002-2000000002−2i2−i2−2i2i2−22−2i2−i2i2−i20000000000
χ2622-2-22-222-2-2-222-200−2i2i002-200000000−22−i2i2−2i2i−22−22−i2i2−i2i20000000000
χ2722-2-22-2-1-111-22-11002i−2i00-11−i3−i3i3i33−33−32−2−i2i2−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ2822-2-22-2-1-111-22-11002i−2i00-11−i3−i3i3i33−33−3−22i2−i2−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ2922-2-22-2-1-111-22-11002i−2i00-11i3i3−i3−i3−33−332−2−i2i2−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ3022-2-22-2-1-111-22-11002i−2i00-11i3i3−i3−i3−33−33−22i2−i2−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ3122-2-22-2-1-111-22-1100−2i2i00-11−i3−i3i3i3−33−332−2i2−i2i−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ3222-2-22-2-1-111-22-1100−2i2i00-11−i3−i3i3i3−33−33−22−i2i2i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ3322-2-22-2-1-111-22-1100−2i2i00-11i3i3−i3−i33−33−32−2i2−i2i−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ3422-2-22-2-1-111-22-1100−2i2i00-11i3i3−i3−i33−33−3−22−i2i2i−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ35444444-2-2-2-2-4-4-2-200004-4220000-2-222000000000000000000000000
χ36444444-2-2-2-2-4-4-2-20000-4422000022-2-2000000000000000000000000
χ374444-4-4444400-4-4000000000000000000000000000000000002-2000
χ384444-4-4444400-4-400000000000000000000000000000000000-22000
χ3944-4-44-444-4-44-44-4000000-4400000000000000000000000000000000
χ4044-4-44-4-2-2224-4-220000002-2000023−23−2323000000000000000000000000
χ4144-4-44-4-2-2224-4-220000002-20000−232323−23000000000000000000000000
χ4244-4-4-4444-4-400-44000000000000000000000000000000000000002i−2i
χ4344-4-4-4444-4-400-4400000000000000000000000000000000000000−2i2i
χ444-44-4004-44-400002-20000002-22-20000000000000000002i−2i2i−2i000000
χ454-44-4004-44-400002-20000002-22-2000000000000000000−2i2i−2i2i000000
χ464-44-4004-44-40000-22000000-22-220000000000000000002i−2i−2i2i000000
χ474-44-4004-44-40000-22000000-22-22000000000000000000−2i2i2i−2i000000
χ488888-8-8-4-4-4-400440000000000000000000000000000000000000000
χ4988-8-8-88-4-444004-40000000000000000000000000000000000000000
χ508-88-800-44-4400004-4000000-22-220000000000000000000000000000
χ518-88-800-44-440000-440000002-22-20000000000000000000000000000
χ528-8-88008-8-8800000000000000000000000000000000000000000000
χ538-8-8800-444-4000000000000−2i32i32i3−2i30000000000000000000000000000
χ548-8-8800-444-40000000000002i3−2i3−2i32i30000000000000000000000000000

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