Finite Group Databasebeta

← Group #10695813

Character table — Group #10695813

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222234444666224466661212121212124444612121212121212121244881212121224242424888888884488
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
χ51111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ922222222222222-2-2-2-222-2-22222-2-20000-20000-2000000000000000022-2-200000000
χ1022222222222222-2-2-2-222-2-22222-2-20000-20000-20000000000000000-2-22200000000
χ112222222-2-2-2-222222-2-22222-2-2-2-2-2-2000020000-2000000000000000000002i2i−2i−2i0000
χ122222222-2-2-2-222222-2-22222-2-2-2-2-2-2000020000-200000000000000000000−2i−2i2i2i0000
χ132222222-2-2-2-2222-2-22222-2-2-2-2-2-22222-2-2-222222-2-2-2-2000000000000000000000000
χ142222222-2-2-2-2222-2-22222-2-2-2-2-2-222-2-222-2-2-2-2-222222000000000000000000000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-1111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-11111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-21-1-1-1-1-111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ20222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-21-1-1-1-1-111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ21222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-22211111-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000
χ22222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-22211111-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000
χ232222-2-2222-2-22222-22-2-2-22222-2-2220000-20000-200002-2002-22-20000000000000000
χ242222-2-2222-2-22222-22-2-2-22222-2-2220000-20000-20000-2200-22-220000000000000000
χ252222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-200002000020000000000000000000000002-200
χ262222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-20000200002000000000000000000000000-2200
χ272222-2-22-2-2222222-2-22-2-222-2-222-2-20000-200002000000000000000000000000002-2
χ282222-2-22-2-2222222-2-22-2-222-2-222-2-20000-20000200000000000000000000000000-22
χ292222-2-22-2-222222-222-2-2-2-2-2-2-22222000020000-20000002-200002-22-2000000000000
χ302222-2-22-2-222222-222-2-2-2-2-2-2-22222000020000-2000000-220000-22-22000000000000
χ312222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-100001−i3−i3i3i31−i3−i3i3i32-200-11-11−i3i3i3−i3000000000000
χ322222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-100001−i3−i3i3i31−i3−i3i3i3-22001-11-1i3−i3−i3i3000000000000
χ332222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-100001i3i3−i3−i31i3i3−i3−i32-200-11-11i3−i3−i3i3000000000000
χ342222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-100001i3i3−i3−i31i3i3−i3−i3-22001-11-1−i3i3i3−i3000000000000
χ352222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-10000-1−i3−i3i3i31i3i3−i3−i3002-2−i3i3i3−i3-11-11000000000000
χ362222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-10000-1−i3−i3i3i31i3i3−i3−i300-22i3−i3−i3i31-11-1000000000000
χ372222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-10000-1i3i3−i3−i31−i3−i3i3i3002-2i3−i3−i3i3-11-11000000000000
χ382222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-10000-1i3i3−i3−i31−i3−i3i3i300-22−i3i3i3−i31-11-1000000000000
χ39444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200002000020000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-244-4-4-2-2-2-22222220000-2000020000000000000000000000000000
χ414444-4-4-244-4-4-2-2-2-44-442222-2-222220000-20000-20000000000000000000000000000
χ424444-4-4-2-4-444-2-2-24-4-4422-2-222-2-222000020000-20000000000000000000000000000
χ4344-4-44-4400004-4-400004-400000000000000000000000000000000000022−2200000000
χ4444-4-44-4400004-4-400004-4000000000000000000000000000000000000−222200000000
χ4544-4-4-44400004-4-40000-44000000000000000000000000000000000022−220000000000
χ4644-4-4-44400004-4-40000-440000000000000000000000000000000000−22220000000000
χ474-44-4004004i−4i-44-400000000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ484-44-4004004i−4i-44-400000000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ494-44-400400−4i4i-44-40000000000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ504-44-400400−4i4i-44-40000000000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ514-4-440044-400-4-44000000004-400002i−2i2i−2i02i−2i2i−2i02i−2i2i−2i000000000000000000000000
χ524-4-440044-400-4-44000000004-40000−2i2i−2i2i0−2i2i−2i2i0−2i2i−2i2i000000000000000000000000
χ534-4-44004-4400-4-4400000000-4400002i−2i−2i2i02i−2i2i−2i0−2i2i−2i2i000000000000000000000000
χ544-4-44004-4400-4-4400000000-440000−2i2i2i−2i0−2i2i−2i2i02i−2i2i−2i000000000000000000000000
χ554-4-4400-24-40022-2000000−2i32i3-2200−2i32i32i−2i2i−2i02ζ14−2ζ142ζ22−2ζ2202ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ564-4-4400-24-40022-2000000−2i32i3-2200−2i32i3−2i2i−2i2i0−2ζ142ζ14−2ζ222ζ220−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ574-4-4400-24-40022-20000002i3−2i3-22002i3−2i32i−2i2i−2i02ζ22−2ζ222ζ14−2ζ1402ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ584-4-4400-24-40022-20000002i3−2i3-22002i3−2i3−2i2i−2i2i0−2ζ222ζ22−2ζ142ζ140−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ594-4-4400-2-440022-2000000−2i32i32-2002i3−2i32i−2i−2i2i02ζ22−2ζ222ζ14−2ζ140−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ604-4-4400-2-440022-2000000−2i32i32-2002i3−2i3−2i2i2i−2i0−2ζ222ζ22−2ζ142ζ1402ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ614-4-4400-2-440022-20000002i3−2i32-200−2i32i32i−2i−2i2i02ζ14−2ζ142ζ22−2ζ220−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ624-4-4400-2-440022-20000002i3−2i32-200−2i32i3−2i2i2i−2i0−2ζ142ζ14−2ζ222ζ2202ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ6388-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000
χ6488-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000
χ658-88-800-4008i−8i4-440000000000−4i4i0000000000000000000000000000000000000000
χ668-88-800-400−8i8i4-4400000000004i−4i0000000000000000000000000000000000000000

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