Finite Group Databasebeta

← Group #10826917

Character table — Group #10826917

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222223444466622446612121212121212122224444466666612121212444468812121224242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1
χ4111111111111111111111111111111-1-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111
χ51111111111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-111-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111-1-111111-1-1
χ911111111111111-1-1-1-11111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1111-1-11-1-1-1-1111-1-11-1
χ1011111111111111-1-1-1-11111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-11111-1-1-111-11
χ1111111111111111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-1-1-11111-1-1111-1-1-111-111-1-1-111-1-1-11
χ1211111111111111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1111-1-1111-1
χ1311111111111111-1-1-1-11111-1-1-1-111-1-11-1-1111-1-1-1-1-1-1111111111-11-1-11-1-1111-1-1-1-11-1-111-11
χ1411111111111111-1-1-1-11111-1-1-1-111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-11-11-1-11-1-111-11111-111-1-11-1
χ1511111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-111111111-11-111-111-1-1-111-1-1-1-1-1111-1
χ1611111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-11-111-111-1-11-1-111111-1-1-11
χ172222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-200000000220000000022-2-200000000000002-20000000
χ182222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2000000002200000000-2-2220000000000000-220000000
χ192222222-2-2-2-2222-2-22222-2-22222-2-200000000-2-20000000022-2-20000000000000-220000000
χ202222222-2-2-2-2222-2-22222-2-22222-2-200000000-2-200000000-2-22200000000000002-20000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-122-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122-2-2-222-2-1-1-1-1-1-1-1-1-1-100001-2-21111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2222-2-22-1-1111111110000-1-2-2-1-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000122111-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-11111-1-1222-2-2-2-2211-1-1-1-111110000-12-211-1-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-11111-1-122-222-2-2-211-1-1-1-1111100001-22-1-1111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-11111-1-1-2-22-2-2222111111-1-1-1-10000-1-2211-111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-11111-1-1-2-2-22222-2111111-1-1-1-1000012-2-1-11-1-111000000000000
χ292222-2-2222-2-22222-22-2-2-2-2-222-2-2220022-200-22-20000000000002002-2-20000000000000000
χ302222-2-2222-2-22222-22-2-2-2-2-222-2-22200-2-220022-2000000000000-200-2220000000000000000
χ312222-2-2222-2-2222-22-22-2-2-2-2-2-22222002-2200-2-22000000000000200-22-20000000000000000
χ322222-2-2222-2-2222-22-22-2-2-2-2-2-2222200-22-2002-22000000000000-2002-220000000000000000
χ332222-2-22-2-2222222-2-22-2-222-2-222-2-2000000002-2000000000000000000000022-200-2000000
χ342222-2-22-2-2222222-2-22-2-222-2-222-2-2000000002-20000000000000000000000-2-22002000000
χ352222-2-22-2-222222-222-2-2-22222-2-2-2-200000000-2200000000000000000000002-2200-2000000
χ362222-2-22-2-222222-222-2-2-22222-2-2-2-200000000-220000000000000000000000-22-2002000000
χ372222-2-2-122-2-2-1-1-12-22-21111-1-111-1-10022-200-2-11−i3−i3i3i3−i3−i3i3i30000-100-111−i3i3−i3i3000000000000
χ382222-2-2-122-2-2-1-1-12-22-21111-1-111-1-10022-200-2-11i3i3−i3−i3i3i3−i3−i30000-100-111i3−i3i3−i3000000000000
χ392222-2-2-122-2-2-1-1-12-22-21111-1-111-1-100-2-22002-11−i3−i3i3i3−i3−i3i3i300001001-1-1i3−i3i3−i3000000000000
χ402222-2-2-122-2-2-1-1-12-22-21111-1-111-1-100-2-22002-11i3i3−i3−i3i3i3−i3−i300001001-1-1−i3i3−i3i3000000000000
χ412222-2-2-122-2-2-1-1-1-22-22111111-1-1-1-1002-2200-21-1−i3−i3i3i3i3i3−i3−i30000-1001-11−i3i3i3−i3000000000000
χ422222-2-2-122-2-2-1-1-1-22-22111111-1-1-1-1002-2200-21-1i3i3−i3−i3−i3−i3i3i30000-1001-11i3−i3−i3i3000000000000
χ432222-2-2-122-2-2-1-1-1-22-22111111-1-1-1-100-22-20021-1−i3−i3i3i3i3i3−i3−i30000100-11-1i3−i3−i3i3000000000000
χ442222-2-2-122-2-2-1-1-1-22-22111111-1-1-1-100-22-20021-1i3i3−i3−i3−i3−i3i3i30000100-11-1−i3i3i3−i3000000000000
χ452-2-22-2222-22-2-2-2200002-22-200002-2000002-200000002-22-22-22-20000000000000000002-200
χ462-2-22-2222-22-2-2-2200002-22-200002-2000002-200000002-22-2-22-22000000000000000000-2200
χ472-2-22-2222-22-2-2-2200002-22-200002-200000-220000000-22-222-22-2000000000000000000-2200
χ482-2-22-2222-22-2-2-2200002-22-200002-200000-220000000-22-22-22-220000000000000000002-200
χ492-2-22-222-22-22-2-2200002-2-220000-222-2000000002-22-200002-2-2200000000000000002-20000
χ502-2-22-222-22-22-2-2200002-2-220000-222-2000000002-22-20000-222-20000000000000000-220000
χ512-2-22-222-22-22-2-2200002-2-220000-22-2200000000-22-2200002-2-220000000000000000-220000
χ522-2-22-222-22-22-2-2200002-2-220000-22-2200000000-22-220000-222-200000000000000002-20000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-22222222200000000-2-20000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-222-2-2-2-22200000000220000000000000000000000000000000000
χ554444-4-4-2-4-444-2-2-24-4-4422-2-222-2-22200000000-220000000000000000000000000000000000
χ564444-4-4-2-4-444-2-2-2-444-422-2-2-2-22222000000002-20000000000000000000000000000000000
χ574-4-444-444-4-44-4-440000-44-4400004-400000000000000000000000000000000000000000000
χ584-4-444-44-444-4-4-440000-444-40000-4400000000000000000000000000000000000000000000
χ594-4-444-4-24-4-4422-200002-22-20000-2200000000000000−2i32i32i3−2i300000000000000000000000000
χ604-4-444-4-24-4-4422-200002-22-20000-22000000000000002i3−2i3−2i32i300000000000000000000000000
χ614-4-444-4-2-444-422-200002-2-2200002-20000000000−2i32i32i3−2i3000000000000000000000000000000
χ624-4-444-4-2-444-422-200002-2-2200002-200000000002i3−2i3−2i32i3000000000000000000000000000000
χ634-4-44-44-24-44-422-20000-22-220000-22000004-40000000-22-2200000000000000000000000000
χ644-4-44-44-24-44-422-20000-22-220000-2200000-4400000002-22-200000000000000000000000000
χ654-4-44-44-2-44-4422-20000-222-200002-24-400000000-22-22000000000000000000000000000000
χ664-4-44-44-2-44-4422-20000-222-200002-2-44000000002-22-2000000000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-444000000000043−430000000000000000000000000000000000000000000000
χ6988-8-800-40000-4440000000000−43430000000000000000000000000000000000000000000000
χ708-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-88-800-400004-440000000043−43000000000000000000000000000000000000000000000000
χ728-88-800-400004-4400000000−4343000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).