Finite Group Databasebeta

← Group #10704590

Character table — Group #10704590

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222444444444444666688888888888812121212121216161616161616161616161616162424242448484848
order12222236664444444444664444441212121212121212121222444488881212242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1111111-1-1111111-1-1-1-1111111ii−i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ61111111111111111-1-1-1-1111111-1-1111111-1-1-1-1111111−i−iii-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i1111−i−iii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii1111ii−i−i
χ9111111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-11-11-1-1-111-1-111-1-111-1-11-11-1
χ10111111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-11-11
χ11111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-111111-11-1-1-111-1-111-1-1-1-111-11-11
χ12111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-11111-11-11-1-1-1-111-1-111-1-1111-11-1
χ13111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1i−i−ii11ii−i−i−i−iii-1-111i−i−ii
χ14111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1−iii−i11−i−iiiii−i−i-1-111−iii−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111i−i−ii11ii−i−i−i−iii11-1-1−iii−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−iii−i11−i−iiiii−i−i11-1-1i−i−ii
χ172222222222-2-2000022-2-222222200-2-2000022-2-2-2-20000000000000000002-2000000
χ182222222222-2-2000022-2-222-2-2-2-200-2-2000022-2-222000000000000000000-22000000
χ192222222222-2-20000-2-22222222200-2-20000-2-222-2-2000000000000000000-22000000
χ202222222222-2-20000-2-22222-2-2-2-200-2-20000-2-222220000000000000000002-2000000
χ21222222-1-1-1-12222222222-1-1000022-1-1-1-1-1-1-1-1-1-10000002222-1-1-1-1-1-1-1-1-1-100000000
χ22222222-1-1-1-12222222222-1-1000022-1-1-1-1-1-1-1-1-1-1000000-2-2-2-2-1-11111111100000000
χ23222222-1-1-1-1222222-2-2-2-2-1-10000-2-2-1-1-1-1-1-111110000002i2i−2i−2i11−i−i−i−iiiii00000000
χ24222222-1-1-1-1222222-2-2-2-2-1-10000-2-2-1-1-1-1-1-11111000000−2i−2i2i2i11iiii−i−i−i−i00000000
χ25222222-1-1-1-122-2-2-2-22222-1-10000-2-2-1-11111-1-1-1-10000002-22-211-1-111-1-11100000000
χ26222222-1-1-1-122-2-2-2-22222-1-10000-2-2-1-11111-1-1-1-1000000-22-221111-1-111-1-100000000
χ27222222-1-1-1-122-2-2-2-2-2-2-2-2-1-1000022-1-1111111110000002i−2i−2i2i-1-1−i−iiiii−i−i00000000
χ28222222-1-1-1-122-2-2-2-2-2-2-2-2-1-1000022-1-111111111000000−2i2i2i−2i-1-1ii−i−i−i−iii00000000
χ2922-2-2-222-22-22-200002i−2i2i−2i-220000002-200002i−2i2i−2i0022-2-200000000000000002i−2i0000
χ3022-2-2-222-22-22-200002i−2i2i−2i-220000002-200002i−2i2i−2i00-2-2220000000000000000−2i2i0000
χ3122-2-2-222-22-22-20000−2i2i−2i2i-220000002-20000−2i2i−2i2i0022-2-20000000000000000−2i2i0000
χ3222-2-2-222-22-22-20000−2i2i−2i2i-220000002-20000−2i2i−2i2i00-2-22200000000000000002i−2i0000
χ3322-2-2-222-22-2-2222-2-22i−2i−2i2i-2200002i−2i-2222-2-22i−2i−2i2i00000000002i−2i0000000000000000
χ3422-2-2-222-22-2-2222-2-2−2i2i2i−2i-220000−2i2i-2222-2-2−2i2i2i−2i0000000000−2i2i0000000000000000
χ3522-2-2-222-22-2-22-2-2222i−2i−2i2i-220000−2i2i-22-2-2222i−2i−2i2i0000000000−2i2i0000000000000000
χ3622-2-2-222-22-2-22-2-222−2i2i2i−2i-2200002i−2i-22-2-222−2i2i2i−2i00000000002i−2i0000000000000000
χ3722-2-2-22-11-11-2222-2-22i−2i−2i2i1-100002i−2i1-1-1-111−iii−i0000000000−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000
χ3822-2-2-22-11-11-2222-2-22i−2i−2i2i1-100002i−2i1-1-1-111−iii−i0000000000−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000
χ3922-2-2-22-11-11-2222-2-2−2i2i2i−2i1-10000−2i2i1-1-1-111i−i−ii0000000000i−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000
χ4022-2-2-22-11-11-2222-2-2−2i2i2i−2i1-10000−2i2i1-1-1-111i−i−ii0000000000i−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000
χ4122-2-2-22-11-11-22-2-2222i−2i−2i2i1-10000−2i2i1-111-1-1−iii−i0000000000i−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ4222-2-2-22-11-11-22-2-2222i−2i−2i2i1-10000−2i2i1-111-1-1−iii−i0000000000i−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ4322-2-2-22-11-11-22-2-222−2i2i2i−2i1-100002i−2i1-111-1-1i−i−ii0000000000−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ4422-2-2-22-11-11-22-2-222−2i2i2i−2i1-100002i−2i1-111-1-1i−i−ii0000000000−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ45444444-2-2-2-2-4-4000044-4-4-2-2000000220000-2-2220000000000000000000000000000
χ46444444-2-2-2-2-4-40000-4-444-2-200000022000022-2-20000000000000000000000000000
χ474444-4-444440000000000-4-444-4-40000000000000000000000000000000000000000
χ484444-4-444440000000000-4-4-4-4440000000000000000000000000000000000000000
χ4944-4-44-44-44-400000000004-400000000000000004-400000000000000000000000000
χ5044-4-44-44-44-400000000004-40000000000000000-4400000000000000000000000000
χ5144-4-4-44-22-224-400004i−4i4i−4i2-2000000-220000−2i2i−2i2i0000000000000000000000000000
χ5244-4-4-44-22-224-40000−4i4i−4i4i2-2000000-2200002i−2i2i−2i0000000000000000000000000000
χ534-44-4004-4-44002-22-2000000004i−4i00002-22-20000002i−2i2i−2i0000000000000000000000
χ544-44-4004-4-44002-22-200000000−4i4i00002-22-2000000−2i2i−2i2i0000000000000000000000
χ554-44-4004-4-4400-22-22000000004i−4i0000-22-22000000−2i2i−2i2i0000000000000000000000
χ564-44-4004-4-4400-22-2200000000−4i4i0000-22-220000002i−2i2i−2i0000000000000000000000
χ574-4-440044-4-4002-2-220000004i−4i0000002-2-220000002i−2i−2i2i0000000000000000000000
χ584-4-440044-4-4002-2-22000000−4i4i0000002-2-22000000−2i2i2i−2i0000000000000000000000
χ594-4-440044-4-400-222-20000004i−4i000000-222-2000000−2i2i2i−2i0000000000000000000000
χ604-4-440044-4-400-222-2000000−4i4i000000-222-20000002i−2i−2i2i0000000000000000000000
χ618888-8-8-4-4-4-400000000004400000000000000000000000000000000000000000000
χ6288-8-88-8-44-440000000000-4400000000000000000000000000000000000000000000
χ638-88-800-444-4004-44-400000000000000-22-2200000000000000000000000000000000
χ648-88-800-444-400-44-44000000000000002-22-200000000000000000000000000000000
χ658-8-8800-4-444004-4-4400000000000000-222-200000000000000000000000000000000
χ668-8-8800-4-44400-444-4000000000000002-2-2200000000000000000000000000000000

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