Finite Group Databasebeta

← Group #10696701

Character table — Group #10696701

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order1222344444466624446612121212121212128888121224242424242424242244666612121212888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ922222222-2-22222-2-22-2-2-2-2-22222220000-2-200000000002-2000022-2-2000000000000
χ1022222222-2-22222-2-22-2-2-2-2-22222220000-2-20000000000-220000-2-222000000000000
χ112222222-222-2222-2-2-22-2-22222-2-2-2-200002-20000000000000000000022-2-200000000
χ122222222-222-2222-2-2-22-2-22222-2-2-2-200002-200000000000000000000-2-22200000000
χ132222222-2-2-2-222222-2-222-2-222-2-2-2-20000-220000000000000000000000002i2i−2i−2i0000
χ142222222-2-2-2-222222-2-222-2-222-2-2-2-20000-22000000000000000000000000−2i−2i2i2i0000
χ1522222-2-22222222-22-2-2-2-222-2-222-2-20000-2200000000000000000000000000002-200
χ1622222-2-22222222-22-2-2-2-222-2-222-2-20000-220000000000000000000000000000-2200
χ1722222-2-22-2-222222-2-2222-2-2-2-222-2-200002-20000000000000000000000000000002-2
χ1822222-2-22-2-222222-2-2222-2-2-2-222-2-200002-2000000000000000000000000000000-22
χ1922222-2-2-222-22222-22-22222-2-2-2-2220000-2-2000000002-20022-2-20000000000000000
χ2022222-2-2-222-22222-22-22222-2-2-2-2220000-2-200000000-2200-2-2220000000000000000
χ2122222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2000000000000000000000000
χ2222222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222000000000000000000000000
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ252222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ262222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ272222-1222-2-22-1-1-1-2-22-21111-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3002-2−i3i3−i3i3-1-111000000000000
χ282222-1222-2-22-1-1-1-2-22-21111-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300-22i3−i3i3−i311-1-1000000000000
χ292222-1222-2-22-1-1-1-2-22-21111-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3002-2i3−i3i3−i3-1-111000000000000
χ302222-1222-2-22-1-1-1-2-22-21111-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300-22−i3i3−i3i311-1-1000000000000
χ312222-1-2-2-222-2-1-1-12-22-2-1-1-1-11111-1-1000011−i3−i3i3i3i3i3−i3−i32-200-1-111−i3i3−i3i3000000000000
χ322222-1-2-2-222-2-1-1-12-22-2-1-1-1-11111-1-1000011−i3−i3i3i3i3i3−i3−i3-220011-1-1i3−i3i3−i3000000000000
χ332222-1-2-2-222-2-1-1-12-22-2-1-1-1-11111-1-1000011i3i3−i3−i3−i3−i3i3i32-200-1-111i3−i3i3−i3000000000000
χ342222-1-2-2-222-2-1-1-12-22-2-1-1-1-11111-1-1000011i3i3−i3−i3−i3−i3i3i3-220011-1-1−i3i3−i3i3000000000000
χ352222-1-2-2-2-2-2-2-1-1-1-222211111111-1-122-2-2-1-1-1-1-1-111110000−i3i3i3−i3−i3i3i3−i3000000000000
χ362222-1-2-2-2-2-2-2-1-1-1-222211111111-1-122-2-2-1-1-1-1-1-111110000i3−i3−i3i3i3−i3−i3i3000000000000
χ372222-1-2-2-2-2-2-2-1-1-1-222211111111-1-1-2-222-1-11111-1-1-1-10000−i3i3i3−i3i3−i3−i3i3000000000000
χ382222-1-2-2-2-2-2-2-1-1-1-222211111111-1-1-2-222-1-11111-1-1-1-10000i3−i3−i3i3−i3i3i3−i3000000000000
χ394444-244-444-4-2-2-2-4-4-4422-2-2-2-222220000-2200000000000000000000000000000000
χ404444-244-4-4-4-4-2-2-244-4-4-2-222-2-2222200002-200000000000000000000000000000000
χ414444-2-4-44444-2-2-2-44-4-422-2-222-2-22200002-200000000000000000000000000000000
χ424444-2-4-44-4-44-2-2-24-4-44-2-22222-2-2220000-2200000000000000000000000000000000
χ4344-4-444-40000-44-4000000004-400000000000000000000000000000000−2i22i200000000
χ4444-4-444-40000-44-4000000004-4000000000000000000000000000000002i2−2i200000000
χ4544-4-44-440000-44-400000000-44000000000000000000000000000000−2i22i20000000000
χ4644-4-44-440000-44-400000000-440000000000000000000000000000002i2−2i20000000000
χ474-44-440004-404-4-40000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ484-44-440004-404-4-40000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ494-44-44000-4404-4-4000000-440000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ504-44-44000-4404-4-4000000-44000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ514-44-4-20004-40-2220000−2i32i3-220000−2i32i32i−2i2i−2i002ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ524-44-4-20004-40-2220000−2i32i3-220000−2i32i3−2i2i−2i2i00−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ534-44-4-20004-40-22200002i3−2i3-2200002i3−2i32i−2i2i−2i002ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ544-44-4-20004-40-22200002i3−2i3-2200002i3−2i3−2i2i−2i2i00−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ554-44-4-2000-440-2220000−2i32i32-200002i3−2i32i−2i−2i2i002ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ564-44-4-2000-440-2220000−2i32i32-200002i3−2i3−2i2i2i−2i00−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ574-44-4-2000-440-22200002i3−2i32-20000−2i32i32i−2i−2i2i002ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ584-44-4-2000-440-22200002i3−2i32-20000−2i32i3−2i2i2i−2i00−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ594-4-44400400-4-4-4400000000004-4000000000000000000000000000000002i−2i2i−2i0000
χ604-4-44400400-4-4-4400000000004-400000000000000000000000000000000−2i2i−2i2i0000
χ614-4-44400-4004-4-440000000000-44000000000000000000000000000000002-2-220000
χ624-4-44400-4004-4-440000000000-4400000000000000000000000000000000-222-20000
χ6388-8-8-48-800004-4400000000-44000000000000000000000000000000000000000000
χ6488-8-8-4-8800004-44000000004-4000000000000000000000000000000000000000000
χ658-8-88-400800-844-40000000000-440000000000000000000000000000000000000000
χ668-8-88-400-800844-400000000004-40000000000000000000000000000000000000000

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