Finite Group Databasebeta

← Group #10696764

Character table — Group #10696764

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122234444666244446612121212121212128888121224242424242424242444661212121212128888248888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1
χ9222222222222-22-2-2-2-2-22222-2-2-2-200002-2000000000000000000000000002-200
χ10222222222222-22-2-2-2-2-22222-2-2-2-200002-200000000000000000000000000-2200
χ112222222-2-22222-2-22-22222-2-2-2-2220000-2-200000000002-2000022-2-20000000000
χ122222222-2-22222-2-22-22222-2-2-2-2220000-2-20000000000-220000-2-2220000000000
χ132222222-2-2222-2-22-22-2-222-2-222-2-20000-220000000000000000000000002-20000
χ142222222-2-2222-2-22-22-2-222-2-222-2-20000-22000000000000000000000000-220000
χ1522222-2-2222222-2-2-2222-2-222-2-2-2-20000-2200000000000000000000000000002-2
χ1622222-2-2222222-2-2-2222-2-222-2-2-2-20000-220000000000000000000000000000-22
χ1722222-2-222222-2-222-2-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000
χ1822222-2-222222-2-222-2-2-2-2-2222222-2-222-2-2-2-2-2-222220000000000000000000000
χ1922222-2-2-2-2222222-2-222-2-2-2-222-2-200002-2000000000000000000002i2i−2i−2i000000
χ2022222-2-2-2-2222222-2-222-2-2-2-222-2-200002-200000000000000000000−2i−2i2i2i000000
χ2122222-2-2-2-2222-22-222-2-2-2-2-2-2-2-222000022000000002-20022-2-200000000000000
χ2222222-2-2-2-2222-22-222-2-2-2-2-2-2-2-22200002200000000-2200-2-22200000000000000
χ232222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ242222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-111110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-10000000000
χ272222-122-2-2-1-1-12-2-22-2-1-1-1-11111-1-1000011−i3−i3i3i3−i3−i3i3i3002-2−i3i3−i3i3-1-1110000000000
χ282222-122-2-2-1-1-12-2-22-2-1-1-1-11111-1-1000011−i3−i3i3i3−i3−i3i3i300-22i3−i3i3−i311-1-10000000000
χ292222-122-2-2-1-1-12-2-22-2-1-1-1-11111-1-1000011i3i3−i3−i3i3i3−i3−i3002-2i3−i3i3−i3-1-1110000000000
χ302222-122-2-2-1-1-12-2-22-2-1-1-1-11111-1-1000011i3i3−i3−i3i3i3−i3−i300-22−i3i3−i3i311-1-10000000000
χ312222-1-2-222-1-1-1-2-222-21111-1-1-1-1-1-122-2-211-1-1-1-111110000−i3i3i3−i3−i3i3−i3i30000000000
χ322222-1-2-222-1-1-1-2-222-21111-1-1-1-1-1-122-2-211-1-1-1-111110000i3−i3−i3i3i3−i3i3−i30000000000
χ332222-1-2-222-1-1-1-2-222-21111-1-1-1-1-1-1-2-222111111-1-1-1-10000−i3i3i3−i3i3−i3i3−i30000000000
χ342222-1-2-222-1-1-1-2-222-21111-1-1-1-1-1-1-2-222111111-1-1-1-10000i3−i3−i3i3−i3i3−i3i30000000000
χ352222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i32-200-1-111−i3i3i3−i30000000000
χ362222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i3-220011-1-1i3−i3−i3i30000000000
χ372222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i32-200-1-111i3−i3−i3i30000000000
χ382222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i3-220011-1-1−i3i3i3−i30000000000
χ394444-24444-2-2-2-44-4-4-422-2-2-2-222220000-22000000000000000000000000000000
χ404444-244-4-4-2-2-2-4-44-4422-2-222-2-22200002-2000000000000000000000000000000
χ414444-2-4-444-2-2-24-4-4-44-2-222-2-2222200002-2000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2444-4-4-2-22222-2-2220000-22000000000000000000000000000000
χ4344-4-44004i−4i4-4-40000000004i−4i0000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ4444-4-44004i−4i4-4-40000000004i−4i000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ4544-4-4400−4i4i4-4-4000000000−4i4i000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ4644-4-4400−4i4i4-4-4000000000−4i4i0000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ474-44-444-400-44-400000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ484-44-444-400-44-400000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ494-44-44-4400-44-40000000-440000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ504-44-44-4400-44-40000000-44000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ514-44-4-24-4002-2200000−2i32i3-220000−2i32i32i−2i2i−2i002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000
χ524-44-4-24-4002-2200000−2i32i3-220000−2i32i3−2i2i−2i2i00−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000
χ534-44-4-24-4002-22000002i3−2i3-2200002i3−2i32i−2i2i−2i002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000
χ544-44-4-24-4002-22000002i3−2i3-2200002i3−2i3−2i2i−2i2i00−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000
χ554-44-4-2-44002-2200000−2i32i32-200002i3−2i32i−2i−2i2i002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000
χ564-44-4-2-44002-2200000−2i32i32-200002i3−2i3−2i2i2i−2i00−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000
χ574-44-4-2-44002-22000002i3−2i32-20000−2i32i32i−2i−2i2i002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000
χ584-44-4-2-44002-22000002i3−2i32-20000−2i32i3−2i2i2i−2i00−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000
χ5988-8-8-4008i−8i-444000000000−4i4i0000000000000000000000000000000000000000
χ6088-8-8-400−8i8i-4440000000004i−4i0000000000000000000000000000000000000000
χ618-8-8880000-8-88000000000000000000000000000000000000000000000000000
χ628-8-88-4000044-40000000000043−4300000000000000000000000000000000000000
χ638-8-88-4000044-400000000000−434300000000000000000000000000000000000000

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