Finite Group Databasebeta

← Group #10784415

Character table — Group #10784415

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212121212121616161616161616161616162424242448484848
order12223444444666244466888812121212121212128812122424242424242424888888884444121212121212121288882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ611111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-11-11
χ711111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-11-11
χ811111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111-11-1
χ911111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1111111111-11-111-1-111-1-1-1-1-1-111-1-1
χ1011111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111111111-11-11-1-111-1-111-1-1-1-1-1-111
χ1111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-111
χ1211111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111111111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-1-111-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11111-1-1-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-111-1-11-1-11
χ172222222-2-2-2-222222-2-22222-2-2-2-2-2-2-2-2222-22-222-2-222-2-20000000000000000000000000000
χ182222222-2-2-2-222222-2-222-2-222-2-2-2-2-2-222-222-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-222-2-222-2-2-2-222-2-222-22-2222-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-222-2-2-2-222-2-222-2-2222-2-22-2-22222-2-20000000000000000000000000000
χ2122222-2-222-2-22222-22-22200002222-2-2-2-200-2-200000000000022-2-2000000000000002-20000
χ2222222-2-222-2-22222-22-22200002222-2-2-2-200-2-2000000000000-2-22200000000000000-220000
χ2322222-2-222-2-2222-22-22-2-2000022-2-2-2-2-2-2002200000000000022-2-200000000000000-220000
χ2422222-2-222-2-2222-22-22-2-2000022-2-2-2-2-2-20022000000000000-2-222000000000000002-20000
χ2522222-2-2-2-2222222-2-22220000-2-2-2-222-2-200-220000000022-2-200000000000000002-2000000
χ2622222-2-2-2-2222222-2-22220000-2-2-2-222-2-200-2200000000-2-2220000000000000000-22000000
χ2722222-2-2-2-222222-222-2-2-20000-2-22222-2-2002-20000000022-2-20000000000000000-22000000
χ2822222-2-2-2-222222-222-2-2-20000-2-22222-2-2002-200000000-2-22200000000000000002-2000000
χ292222-1222222-1-1-12222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ302222-1222222-1-1-12222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ312222-1222222-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ322222-1222222-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ332222-1222222-1-1-1-2-2-2-2112222-1-111-1-1-1-1-2-211-1-1-1-11111000000002-22-2-1-111-1-11100000000
χ342222-1222222-1-1-1-2-2-2-2112222-1-111-1-1-1-1-2-211-1-1-1-1111100000000-22-2211-1-111-1-100000000
χ352222-1222222-1-1-1-2-2-2-211-2-2-2-2-1-111-1-1-1-122111111-1-1-1-1000000002-2-22-1-11111-1-100000000
χ362222-1222222-1-1-1-2-2-2-211-2-2-2-2-1-111-1-1-1-122111111-1-1-1-100000000-222-211-1-1-1-11100000000
χ372222-122-2-2-2-2-1-1-122-2-2-1-122-2-2111111-1-12-2-11-1-111-1-111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ382222-122-2-2-2-2-1-1-122-2-2-1-122-2-2111111-1-12-2-11-1-111-1-111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ392222-122-2-2-2-2-1-1-122-2-2-1-1-2-222111111-1-1-22-1111-1-111-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ402222-122-2-2-2-2-1-1-122-2-2-1-1-2-222111111-1-1-22-1111-1-111-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ412222-122-2-2-2-2-1-1-1-2-2221122-2-211-1-111-1-1-221-1-1-11111-1-1000000000000−i3i3i3−i3−i3i3i3−i300000000
χ422222-122-2-2-2-2-1-1-1-2-2221122-2-211-1-111-1-1-221-1-1-11111-1-1000000000000i3−i3−i3i3i3−i3−i3i300000000
χ432222-122-2-2-2-2-1-1-1-2-22211-2-22211-1-111-1-12-21-111-1-1-1-111000000000000−i3i3i3−i3i3−i3−i3i300000000
χ442222-122-2-2-2-2-1-1-1-2-22211-2-22211-1-111-1-12-21-111-1-1-1-111000000000000i3−i3−i3i3−i3i3i3−i300000000
χ454444-2-4-444-4-4-2-2-24-44-4-2-20000-2-2-2-222220022000000000000000000000000000000000000
χ464444-2-4-444-4-4-2-2-2-44-44220000-2-222222200-2-2000000000000000000000000000000000000
χ474444-2-4-4-4-444-2-2-24-4-44-2-200002222-2-222002-2000000000000000000000000000000000000
χ484444-2-4-4-4-444-2-2-2-444-422000022-2-2-2-22200-22000000000000000000000000000000000000
χ4944-4-444-40000-44-400000000000000004-400000000000022−2222−22000000000000000000000000
χ5044-4-444-40000-44-400000000000000004-4000000000000−2222−2222000000000000000000000000
χ5144-4-44-440000-44-40000000000000000-4400000000000022−22−2222000000000000000000000000
χ5244-4-44-440000-44-40000000000000000-44000000000000−222222−22000000000000000000000000
χ534-44-44004-4004-4-400000022−2222−224-4000000000022−2222−2200000000000000000000000000000000
χ544-44-44004-4004-4-4000000−2222−22224-40000000000−2222−222200000000000000000000000000000000
χ554-44-4400-44004-4-400000022−22−2222-44000000000022−22−222200000000000000000000000000000000
χ564-44-4400-44004-4-4000000−222222−22-440000000000−222222−2200000000000000000000000000000000
χ574-44-4-2004-400-2220000−2i32i322−2222−22-22−2i32i300000000−22−22i6−i6i6−i60000000000000000000000000000
χ584-44-4-2004-400-2220000−2i32i3−2222−2222-22−2i32i3000000002−22−2−i6i6−i6i60000000000000000000000000000
χ594-44-4-2004-400-22200002i3−2i322−2222−22-222i3−2i300000000−22−22−i6i6−i6i60000000000000000000000000000
χ604-44-4-2004-400-22200002i3−2i3−2222−2222-222i3−2i3000000002−22−2i6−i6i6−i60000000000000000000000000000
χ614-44-4-200-4400-2220000−2i32i322−22−22222-22i3−2i300000000−222−2i6−i6−i6i60000000000000000000000000000
χ624-44-4-200-4400-2220000−2i32i3−222222−222-22i3−2i3000000002−2−22−i6i6i6−i60000000000000000000000000000
χ634-44-4-200-4400-22200002i3−2i322−22−22222-2−2i32i300000000−222−2−i6i6i6−i60000000000000000000000000000
χ644-44-4-200-4400-22200002i3−2i3−222222−222-2−2i32i3000000002−2−22i6−i6−i6i60000000000000000000000000000
χ654-4-44400004-4-4-44000000000000004-400000000000000000022−2222−2200000000000000000000
χ664-4-44400004-4-4-44000000000000004-4000000000000000000−2222−222200000000000000000000
χ674-4-4440000-44-4-4400000000000000-4400000000000000000022−22−222200000000000000000000
χ684-4-4440000-44-4-4400000000000000-44000000000000000000−222222−2200000000000000000000
χ6988-8-8-48-800004-440000000000000000-440000000000000000000000000000000000000000
χ7088-8-8-4-8800004-4400000000000000004-40000000000000000000000000000000000000000
χ718-8-88-400008-844-400000000000000-44000000000000000000000000000000000000000000
χ728-8-88-40000-8844-4000000000000004-4000000000000000000000000000000000000000000

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