Finite Group Databasebeta

← Group #10784399

Character table — Group #10784399

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212121212121616161616161616161616162424242448484848
order12223444444666244488881212121212121212121268812242424242424242488888888224466661212121288882444
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
χ5111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-1-111
χ7111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-111-1-111
χ8111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-111-1-11111-1-1
χ911111111111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-11-11-1
χ1011111111111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-111-1-1-11111-1-1-1-1-1-1-11-11
χ1111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111-11-11
χ1211111111111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111111-11-1
χ1311111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-111-111-1
χ1511111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-1-111-1
χ1611111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-11-1-11
χ172222222-2-2-2-22222-2-2222-2-2-2-2-2-222-2-22222-2-222-2-222-2-20000000000000000000000000000
χ182222222-2-2-2-22222-2-22-2-222-2-2-2-222-2-2222-22-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-222-222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-222-2-2-222-2-2-2-2-2-22222-22-22-2-22222-2-20000000000000000000000000000
χ2122222-2-222-2-222222-2-20000-2-222-2-222-2-2200-20000000022-2-200000000000000002-2000000
χ2222222-2-222-2-222222-2-20000-2-222-2-222-2-2200-200000000-2-2220000000000000000-22000000
χ2322222-2-222-2-2222-2-2220000-2-22222-2-2-2-2-20020000000022-2-20000000000000000-22000000
χ2422222-2-222-2-2222-2-2220000-2-22222-2-2-2-2-200200000000-2-22200000000000000002-2000000
χ2522222-2-2-2-2222222-22-2000022-2-2-2-2-2-2-2-2200200000000000022-2-2000000000000002-20000
χ2622222-2-2-2-2222222-22-2000022-2-2-2-2-2-2-2-22002000000000000-2-22200000000000000-220000
χ2722222-2-2-2-222222-22-22000022-2-22222-2-2-200-200000000000022-2-200000000000000-220000
χ2822222-2-2-2-222222-22-22000022-2-22222-2-2-200-2000000000000-2-222000000000000002-20000
χ292222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ302222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ312222-1222222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-111111111000000002-22-2-1-111-1-11100000000
χ322222-1222222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-11111111100000000-22-2211-1-111-1-100000000
χ332222-1222222-1-1-1-2-2-2-22222-1-1-1-11111-1-11-2-21-1-1-1-11111000000002-2-22-1-11111-1-100000000
χ342222-1222222-1-1-1-2-2-2-22222-1-1-1-11111-1-11-2-21-1-1-1-1111100000000-222-211-1-1-1-11100000000
χ352222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111-1-112211111-1-1-1-10000000022-2-2-1-1-1-1111100000000
χ362222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111-1-112211111-1-1-1-100000000-2-2221111-1-1-1-100000000
χ372222-122-2-2-2-2-1-1-12-2-2222-2-21111-1-111-1-1-12-21-1-111-1-111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ382222-122-2-2-2-2-1-1-12-2-2222-2-21111-1-111-1-1-12-21-1-111-1-111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ392222-122-2-2-2-2-1-1-12-2-22-2-2221111-1-111-1-1-1-22111-1-111-1-1000000000000−i3i3i3−i3−i3i3i3−i300000000
χ402222-122-2-2-2-2-1-1-12-2-22-2-2221111-1-111-1-1-1-22111-1-111-1-1000000000000i3−i3−i3i3i3−i3−i3i300000000
χ412222-122-2-2-2-2-1-1-1-222-222-2-2111111-1-1-1-11-22-1-1-11111-1-1000000000000−i3i3i3−i3i3−i3−i3i300000000
χ422222-122-2-2-2-2-1-1-1-222-222-2-2111111-1-1-1-11-22-1-1-11111-1-1000000000000i3−i3−i3i3−i3i3i3−i300000000
χ432222-122-2-2-2-2-1-1-1-222-2-2-222111111-1-1-1-112-2-111-1-1-1-111000000000000−i3i3−i3i3i3−i3i3−i300000000
χ442222-122-2-2-2-2-1-1-1-222-2-2-222111111-1-1-1-112-2-111-1-1-1-111000000000000i3−i3i3−i3−i3i3−i3i300000000
χ454444-2-4-444-4-4-2-2-244-4-4000022-2-222-2-222-2002000000000000000000000000000000000000
χ464444-2-4-444-4-4-2-2-2-4-444000022-2-2-2-22222200-2000000000000000000000000000000000000
χ474444-2-4-4-4-444-2-2-24-44-40000-2-222222222-200-2000000000000000000000000000000000000
χ484444-2-4-4-4-444-2-2-2-44-440000-2-222-2-2-2-2222002000000000000000000000000000000000000
χ4944-4-44004-400-44-400000000004-40000000000000000000000−2i22i2−2i22i200000000000000000000
χ5044-4-44004-400-44-400000000004-400000000000000000000002i2−2i22i2−2i200000000000000000000
χ5144-4-4400-4400-44-40000000000-440000000000000000000000−2i22i22i2−2i200000000000000000000
χ5244-4-4400-4400-44-40000000000-4400000000000000000000002i2−2i2−2i22i200000000000000000000
χ534-44-4400004-44-4-40000−2i22i2−2i22i24-4000000000000−2i22i2−2i22i200000000000000000000000000000000
χ544-44-4400004-44-4-400002i2−2i22i2−2i24-40000000000002i2−2i22i2−2i200000000000000000000000000000000
χ554-44-440000-444-4-40000−2i22i22i2−2i2-44000000000000−2i22i22i2−2i200000000000000000000000000000000
χ564-44-440000-444-4-400002i2−2i2−2i22i2-440000000000002i2−2i2−2i22i200000000000000000000000000000000
χ574-44-4-200004-4-2220000−2i22i2−2i22i2-220023−2323−23000000i2−i2i2−i2i6−i6i6−i60000000000000000000000000000
χ584-44-4-200004-4-2220000−2i22i2−2i22i2-2200−2323−2323000000i2−i2i2−i2−i6i6−i6i60000000000000000000000000000
χ594-44-4-200004-4-22200002i2−2i22i2−2i2-220023−2323−23000000−i2i2−i2i2−i6i6−i6i60000000000000000000000000000
χ604-44-4-200004-4-22200002i2−2i22i2−2i2-2200−2323−2323000000−i2i2−i2i2i6−i6i6−i60000000000000000000000000000
χ614-44-4-20000-44-2220000−2i22i22i2−2i22-20023−23−2323000000i2−i2−i2i2i6−i6−i6i60000000000000000000000000000
χ624-44-4-20000-44-2220000−2i22i22i2−2i22-200−232323−23000000i2−i2−i2i2−i6i6i6−i60000000000000000000000000000
χ634-44-4-20000-44-22200002i2−2i2−2i22i22-20023−23−2323000000−i2i2i2−i2−i6i6i6−i60000000000000000000000000000
χ644-44-4-20000-44-22200002i2−2i2−2i22i22-200−232323−23000000−i2i2i2−i2i6−i6−i6i60000000000000000000000000000
χ654-4-4444-40000-4-4400000000000000004-400000000000022−2222−22000000000000000000000000
χ664-4-4444-40000-4-4400000000000000004-4000000000000−2222−2222000000000000000000000000
χ674-4-444-440000-4-440000000000000000-4400000000000022−22−2222000000000000000000000000
χ684-4-444-440000-4-440000000000000000-44000000000000−222222−22000000000000000000000000
χ6988-8-8-4008-8004-440000000000-440000000000000000000000000000000000000000000000
χ7088-8-8-400-88004-4400000000004-40000000000000000000000000000000000000000000000
χ718-8-88-48-8000044-40000000000000000-440000000000000000000000000000000000000000
χ728-8-88-4-88000044-400000000000000004-40000000000000000000000000000000000000000

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