Finite Group Databasebeta

← Group #10767978

Character table — Group #10767978

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666444466121212121212121244444444121212121212121212122222881212121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ51111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-11-11-1-111111-1-1-1-111-1-11-11-11-111-1-11-11-11-111-1-11-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-11-11-1-111111-1-1-1-1-1-1111-11-11-111-1-1-11-11-11-1-111-11
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-11-11-111111-1-1-1-111-1-1-11-11-11-1-111-111-1-1111-1-1-11
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-11-11-111111-1-1-1-1-1-111-11-11-11-1-1111-1-111-1-1-1111-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1111-11-1-1-1-1-1-11111111-1-1-111-11-1-1-1111-11-11-1-1-111-11
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1111-11-1-1-1-1-1-111111-1-111-111-11-1-1-111-11-11-1111-1-11-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-11-11-1-1-1-1-11111111-1-11-1-11-1111-1-1-111-1-11-1-1111-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-11-11-1-1-1-1-111111-1-1111-1-11-1111-1-11-1-111-111-1-1-11
χ1722222222222222-2-2-2-2222222-2-2-2-200000000-20000-2000022-2-2000000000000-2200000000
χ1822222222222222-2-2-2-2222222-2-2-2-200000000-20000-20000-2-2220000000000002-200000000
χ192222222-2-2-2-222222-2-222-2-2-2-222-2-20000000020000-200002222000000000000-2-200000000
χ202222222-2-2-2-222222-2-222-2-2-2-222-2-20000000020000-20000-2-2-2-20000000000002200000000
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
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-11111-111110000-2-2-1-1-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-111110000221111-1-1-1-1000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-22-22-21-1-1-1-1-1111100002-2-11-11-1-111000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-2-22-221-1-1-1-1-111110000-221-11-111-1-1000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-2222-22-211111-1-1-1-1-10000-22-11-1111-1-1000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-222-22-2211111-1-1-1-1-100002-21-11-1-1-111000000000000
χ292222-2-2222-2-22222-22-2-2-222-2-2222200002-2-22-20000-20000000000-222-20000000000000000
χ302222-2-2222-2-22222-22-2-2-222-2-222220000-222-2-20000-200000000002-2-220000000000000000
χ312222-2-2222-2-2222-22-22-2-222-2-2-2-2-2-2000000002000020000000000000000002-200-22000000
χ322222-2-2222-2-2222-22-22-2-222-2-2-2-2-2-200000000200002000000000000000000-22002-2000000
χ332222-2-22-2-2222222-2-22-2-2-2-22222-2-200000000-2000020000000000000000002200-2-2000000
χ342222-2-22-2-2222222-2-22-2-2-2-22222-2-200000000-200002000000000000000000-2-20022000000
χ352222-2-22-2-222222-222-2-2-2-2-222-2-222000022-2-220000-20000000000-2-2220000000000000000
χ362222-2-22-2-222222-222-2-2-2-2-222-2-2220000-2-22220000-2000000000022-2-20000000000000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-100002-2-221−i3−i3i3i31−i3−i3i3i30000001-1-11−i3i3−i3i3000000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-100002-2-221i3i3−i3−i31i3i3−i3−i30000001-1-11i3−i3i3−i3000000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-10000-222-21−i3−i3i3i31−i3−i3i3i3000000-111-1i3−i3i3−i3000000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-111-1-1-1-10000-222-21i3i3−i3−i31i3i3−i3−i3000000-111-1−i3i3−i3i3000000000000
χ412222-2-2-1-2-222-1-1-1-222-21111-1-111-1-1000022-2-2-1−i3−i3i3i31i3i3−i3−i300000011-1-1−i3i3i3−i3000000000000
χ422222-2-2-1-2-222-1-1-1-222-21111-1-111-1-1000022-2-2-1i3i3−i3−i31−i3−i3i3i300000011-1-1i3−i3−i3i3000000000000
χ432222-2-2-1-2-222-1-1-1-222-21111-1-111-1-10000-2-222-1−i3−i3i3i31i3i3−i3−i3000000-1-111i3−i3−i3i3000000000000
χ442222-2-2-1-2-222-1-1-1-222-21111-1-111-1-10000-2-222-1i3i3−i3−i31−i3−i3i3i3000000-1-111−i3i3i3−i3000000000000
χ45444444-24444-2-2-2-4-4-4-4-2-2-2-2-2-2222200000000200002000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-244-4-4-2-22222-2-22200000000-200002000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-44-4422-2-222222200000000-20000-2000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-24-4-442222-2-2-2-2220000000020000-2000000000000000000000000000000
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−4i00-4-440000004i−4i0000002i−2i2-2000002i−2i2i−2i02-22-200000000000000000000000000
χ544-44-40044i−4i00-4-440000004i−4i000000−2i2i-2200000−2i2i−2i2i0-22-2200000000000000000000000000
χ554-44-4004−4i4i00-4-44000000−4i4i0000002i−2i-22000002i−2i2i−2i0-22-2200000000000000000000000000
χ564-44-4004−4i4i00-4-44000000−4i4i000000−2i2i2-200000−2i2i−2i2i02-22-200000000000000000000000000
χ574-44-400-24i−4i0022-2000000−2i2i0023−23−2i32i32i−2i2-2000002ζ7−2ζ72ζ11−2ζ110−1+i31−i3−1−i31+i300000000000000000000000000
χ584-44-400-24i−4i0022-2000000−2i2i0023−23−2i32i3−2i2i-2200000−2ζ72ζ7−2ζ112ζ1101−i3−1+i31+i3−1−i300000000000000000000000000
χ594-44-400-24i−4i0022-2000000−2i2i00−23232i3−2i32i−2i2-2000002ζ11−2ζ112ζ7−2ζ70−1−i31+i3−1+i31−i300000000000000000000000000
χ604-44-400-24i−4i0022-2000000−2i2i00−23232i3−2i3−2i2i-2200000−2ζ112ζ11−2ζ72ζ701+i3−1−i31−i3−1+i300000000000000000000000000
χ614-44-400-2−4i4i0022-20000002i−2i0023−232i3−2i32i−2i-22000002ζ11−2ζ112ζ7−2ζ701+i3−1−i31−i3−1+i300000000000000000000000000
χ624-44-400-2−4i4i0022-20000002i−2i0023−232i3−2i3−2i2i2-200000−2ζ112ζ11−2ζ72ζ70−1−i31+i3−1+i31−i300000000000000000000000000
χ634-44-400-2−4i4i0022-20000002i−2i00−2323−2i32i32i−2i-22000002ζ7−2ζ72ζ11−2ζ1101−i3−1+i31+i3−1−i300000000000000000000000000
χ644-44-400-2−4i4i0022-20000002i−2i00−2323−2i32i3−2i2i2-200000−2ζ72ζ7−2ζ112ζ110−1+i31−i3−1−i31+i300000000000000000000000000
χ654-4-44004004-4-44-4000000004-40000000000000000000000000000000000000000002i−2i2i−2i00
χ664-4-44004004-4-44-4000000004-4000000000000000000000000000000000000000000−2i2i−2i2i00
χ674-4-4400400-44-44-400000000-440000000000000000000000000000000000000000002i−2i−2i2i00
χ684-4-4400400-44-44-400000000-44000000000000000000000000000000000000000000−2i2i2i−2i00
χ6988-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000000000
χ718-8-8800-4008-84-4400000000-44000000000000000000000000000000000000000000000000
χ728-8-8800-400-884-44000000004-4000000000000000000000000000000000000000000000000

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