Finite Group Databasebeta

← Group #10767971

Character table — Group #10767971

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222223444466644446612121212121212122244444466661212121212122222881212121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ4111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ51111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-111111-1-1-11-11111-11-1-1-1-111-1-11-11-11-111-1-11-11-11-111-1-11-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-111111-1-1-11-11111-11-1-1-1-1-1-1111-11-11-111-1-1-11-11-11-1-111-11
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-11-1-1-111111-11-1-1-1-111-1-1-11-11-11-1-111-111-1-1111-1-1-11
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-11-1-1-111111-11-1-1-1-1-1-111-11-11-11-1-1111-1-111-1-1-1111-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11-1111-1-1-1-1-1-11111111-1-1-111-11-1-1-1111-11-11-1-1-111-11
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11-1111-1-1-1-1-1-111111-1-111-111-11-1-1-111-11-11-1111-1-11-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1111-11-1-1-1-1-11111111-1-11-1-11-1111-1-1-111-1-11-1-1111-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1111-11-1-1-1-1-111111-1-1111-1-11-1111-1-11-1-111-111-1-1-11
χ1722222222222222-2-2-2-222-2-22222-2-2000000000000-2-2000022-2-2000000000000-2200000000
χ1822222222222222-2-2-2-222-2-22222-2-2000000000000-2-20000-2-2220000000000002-200000000
χ192222222-2-2-2-222222-2-22222-2-2-2-2-2-20000000000002-200002222000000000000-2-200000000
χ202222222-2-2-2-222222-2-22222-2-2-2-2-2-20000000000002-20000-2-2-2-20000000000002200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111-1-111110000-2-2-1-1-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-111110000221111-1-1-1-1000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1222-2-2-22-2-1-1-1-11-1111100002-2-11-11-1-111000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-22-2-2-22-1-1-1-11-111110000-221-11-111-1-1000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-22-2222-211111-1-1-1-1-10000-22-11-1111-1-1000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-2-2222-2211111-1-1-1-1-100002-21-11-1-1-111000000000000
χ292222-2-2222-2-22222-22-2-2-22222-2-222002-200-220000-2-200000000002-2-220000000000000000
χ302222-2-2222-2-22222-22-2-2-22222-2-22200-22002-20000-2-20000000000-222-20000000000000000
χ312222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-2000000000000220000000000000000002-200-22000000
χ322222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-200000000000022000000000000000000-22002-2000000
χ332222-2-22-2-2222222-2-22-2-222-2-222-2-2000000000000-220000000000000000002200-2-2000000
χ342222-2-22-2-2222222-2-22-2-222-2-222-2-2000000000000-22000000000000000000-2-20022000000
χ352222-2-22-2-222222-222-2-2-2-2-2-2-22222002200-2-200002-2000000000022-2-20000000000000000
χ362222-2-22-2-222222-222-2-2-2-2-2-2-2222200-2-2002200002-20000000000-2-2220000000000000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-1002-200-22−i3−i3i3i311−i3−i3i3i3000000-111-1−i3i3−i3i3000000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-1002-200-22i3i3−i3−i311i3i3−i3−i3000000-111-1i3−i3i3−i3000000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-100-22002-2−i3−i3i3i311−i3−i3i3i30000001-1-11i3−i3i3−i3000000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-1-1-111-1-100-22002-2i3i3−i3−i311i3i3−i3−i30000001-1-11−i3i3−i3i3000000000000
χ412222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-1002200-2-2−i3−i3i3i3-11i3i3−i3−i3000000-1-111−i3i3i3−i3000000000000
χ422222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-1002200-2-2i3i3−i3−i3-11−i3−i3i3i3000000-1-111i3−i3−i3i3000000000000
χ432222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-100-2-20022−i3−i3i3i3-11i3i3−i3−i300000011-1-1i3−i3−i3i3000000000000
χ442222-2-2-1-2-222-1-1-1-222-2111111-1-1-1-100-2-20022i3i3−i3−i3-11−i3−i3i3i300000011-1-1−i3i3i3−i3000000000000
χ45444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200000000000022000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-244-4-4-2-2-2-2222222000000000000-22000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-44-442222-2-22222000000000000-2-2000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-24-4-4422-2-222-2-2220000000000002-2000000000000000000000000000000
χ4944-4-44-4400004-4-400004-400000000000000000000000000004-40000000000000000000000
χ5044-4-44-4400004-4-400004-40000000000000000000000000000-440000000000000000000000
χ5144-4-4-44400004-4-40000-44000000000000000000000000004-4000000000000000000000000
χ5244-4-4-44400004-4-40000-4400000000000000000000000000-44000000000000000000000000
χ534-44-40044i−4i00-44-4000000004i−4i00002-2002i−2i002-22-2002i−2i2i−2i00000000000000000000000000
χ544-44-40044i−4i00-44-4000000004i−4i0000-2200−2i2i00-22-2200−2i2i−2i2i00000000000000000000000000
χ554-44-4004−4i4i00-44-400000000−4i4i00002-200−2i2i002-22-200−2i2i−2i2i00000000000000000000000000
χ564-44-4004−4i4i00-44-400000000−4i4i0000-22002i−2i00-22-22002i−2i2i−2i00000000000000000000000000
χ574-44-400-24i−4i002-2200000023−23−2i2i00−2i32i32-2002i−2i00−1−i31+i3−1+i31−i3002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ584-44-400-24i−4i002-2200000023−23−2i2i00−2i32i3-2200−2i2i001+i3−1−i31−i3−1+i300−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ594-44-400-24i−4i002-22000000−2323−2i2i002i3−2i32-2002i−2i00−1+i31−i3−1−i31+i3002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ604-44-400-24i−4i002-22000000−2323−2i2i002i3−2i3-2200−2i2i001−i3−1+i31+i3−1−i300−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ614-44-400-2−4i4i002-2200000023−232i−2i002i3−2i32-200−2i2i00−1+i31−i3−1−i31+i300−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ624-44-400-2−4i4i002-2200000023−232i−2i002i3−2i3-22002i−2i001−i3−1+i31+i3−1−i3002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ634-44-400-2−4i4i002-22000000−23232i−2i00−2i32i32-200−2i2i00−1−i31+i3−1+i31−i300−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ644-44-400-2−4i4i002-22000000−23232i−2i00−2i32i3-22002i−2i001+i3−1−i31−i3−1+i3002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ654-4-44004004-4-4-4400000000004-400000000000000000000000000000000000000002-22-200
χ664-4-44004004-4-4-4400000000004-40000000000000000000000000000000000000000-22-2200
χ674-4-4400400-44-4-440000000000-4400000000000000000000000000000000000000002-2-2200
χ684-4-4400400-44-4-440000000000-440000000000000000000000000000000000000000-222-200
χ6988-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000000000
χ718-8-8800-4008-844-40000000000-440000000000000000000000000000000000000000000000
χ728-8-8800-400-8844-400000000004-40000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.