Finite Group Databasebeta

← Group #10778185

Character table — Group #10778185

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order1222344444444666244888812121212121212121212688122424242424242424444424446612121212121224888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ51111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111111-11-111-1-111-1-111-1-1-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-11111-11-11-1-111-1-1111111-1-1-1-1-1-1-1-111
χ71111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1111111-1-1-1-111
χ81111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-111111111-1-1
χ911111-1-1-1-11111111-11-111-1-111-1-111-1-111-11-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1
χ1011111-1-1-1-11111111-11-111-1-111-1-111-1-111-11-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ1111111-1-1-1-11111111-11-111-1-111-1-111-1-111-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-11111
χ1211111-1-1-1-11111111-11-111-1-111-1-111-1-111-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1
χ1311111-1-1-1-11111111-11-1-1-11111-1-111-1-111-1-11-1-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-1-1-11111-1-111
χ1411111-1-1-1-11111111-11-1-1-11111-1-111-1-111-1-11-1-1-1-1-111111111-111-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1511111-1-1-1-11111111-11-1-1-11111-1-111-1-111-1-11-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111111111-1-1-1-111-1-1
χ1611111-1-1-1-11111111-11-1-1-11111-1-111-1-111-1-11-1-1-1-1-11111-1-1-1-1-111-1-1-11111-1-111-1-111-1-111-1-111
χ17222222222-222-2222-2-2-22222-2-222-2-22222-2-2-2-222-2-222-2-2000000000000000000000000000000
χ18222222222-222-2222-2-2-2-2-2-2-2-2-222-2-22222-222-2-2-222-2-222000000000000000000000000000000
χ192222222-2-22-2-22222-2-220000-2-22222-2-2-2-2-20020000000022-2-20000000000002-2000000000000
χ202222222-2-22-2-22222-2-220000-2-22222-2-2-2-2-200200000000-2-222000000000000-22000000000000
χ212222222-2-2-2-2-2-222222-200002222-2-2-2-2-2-2200-200000000000000000000000000002i−2i2i−2i000000
χ222222222-2-2-2-2-2-222222-200002222-2-2-2-2-2-2200-20000000000000000000000000000−2i2i−2i2i000000
χ2322222-2-2222-2-222222-2-20000-2-2-2-22222-2-2200-20000000022-2-2000000000000-22000000000000
χ2422222-2-2222-2-222222-2-20000-2-2-2-22222-2-2200-200000000-2-2220000000000002-2000000000000
χ2522222-2-222-2-2-2-2222-222000022-2-2-2-222-2-2-200200000000000000000000000000002i−2i−2i2i000000
χ2622222-2-222-2-2-2-2222-222000022-2-2-2-222-2-2-20020000000000000000000000000000−2i2i2i−2i000000
χ2722222-2-2-2-2-222-22222-2222-2-2-2-2-2-2-2-2-2-2222-22222-2-2-2-222000000000000000000000000000000
χ2822222-2-2-2-2-222-22222-22-2-222-2-2-2-2-2-2-2-22222-22-2-22222-2-2000000000000000000000000000000
χ292222-122222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000000000
χ302222-122222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-10000-2-2-2-21111111100000000000000
χ312222-122222222-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-11111111100002-22-2-1-111-1-11100000000000000
χ322222-122222222-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-1111111110000-22-2211-1-111-1-100000000000000
χ332222-12222-222-2-1-1-1-2-2-2222211-1-111-1-1-1-11-2-21-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i300000000000000
χ342222-12222-222-2-1-1-1-2-2-2222211-1-111-1-1-1-11-2-21-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i300000000000000
χ352222-12222-222-2-1-1-1-2-2-2-2-2-2-211-1-111-1-1-1-1122111-1-111-1-100000000−i3i3i3−i3−i3i3i3−i300000000000000
χ362222-12222-222-2-1-1-1-2-2-2-2-2-2-211-1-111-1-1-1-1122111-1-111-1-100000000i3−i3−i3i3i3−i3−i3i300000000000000
χ372222-1-2-2-2-22222-1-1-1-22-222-2-2-1-111-1-111-1-112-21-1-1-1-11111000022-2-2-1-1-1-1111100000000000000
χ382222-1-2-2-2-22222-1-1-1-22-222-2-2-1-111-1-111-1-112-21-1-1-1-111110000-2-2221111-1-1-1-100000000000000
χ392222-1-2-2-2-22222-1-1-1-22-2-2-222-1-111-1-111-1-11-2211111-1-1-1-100002-2-22-1-11111-1-100000000000000
χ402222-1-2-2-2-22222-1-1-1-22-2-2-222-1-111-1-111-1-11-2211111-1-1-1-10000-222-211-1-1-1-11100000000000000
χ412222-1-2-2-2-2-222-2-1-1-12-2222-2-211111111-1-1-1-22-1-1-11111-1-100000000−i3i3−i3i3i3−i3i3−i300000000000000
χ422222-1-2-2-2-2-222-2-1-1-12-2222-2-211111111-1-1-1-22-1-1-11111-1-100000000i3−i3i3−i3−i3i3−i3i300000000000000
χ432222-1-2-2-2-2-222-2-1-1-12-22-2-22211111111-1-1-12-2-111-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i300000000000000
χ442222-1-2-2-2-2-222-2-1-1-12-22-2-22211111111-1-1-12-2-111-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i300000000000000
χ452-22-222i−2i2i−2i02-20-22-20002-22i−2i002i−2i002i−2i2-200002-2002i−2i00000000000000000000−i2i20000−i2i22−22−2
χ462-22-222i−2i2i−2i02-20-22-20002-22i−2i002i−2i002i−2i2-200002-2002i−2i00000000000000000000i2−i20000i2−i2−22−22
χ472-22-222i−2i2i−2i02-20-22-2000-22−2i2i002i−2i002i−2i2-20000-2200−2i2i00000000000000000000−i2i20000i2−i2−222−2
χ482-22-222i−2i2i−2i02-20-22-2000-22−2i2i002i−2i002i−2i2-20000-2200−2i2i00000000000000000000i2−i20000−i2i22−2−22
χ492-22-22−2i2i−2i2i02-20-22-20002-2−2i2i00−2i2i00−2i2i2-200002-200−2i2i00000000000000000000−i2i20000−i2i2−22−22
χ502-22-22−2i2i−2i2i02-20-22-20002-2−2i2i00−2i2i00−2i2i2-200002-200−2i2i00000000000000000000i2−i20000i2−i22−22−2
χ512-22-22−2i2i−2i2i02-20-22-2000-222i−2i00−2i2i00−2i2i2-20000-22002i−2i00000000000000000000−i2i20000i2−i22−2−22
χ522-22-22−2i2i−2i2i02-20-22-2000-222i−2i00−2i2i00−2i2i2-20000-22002i−2i00000000000000000000i2−i20000−i2i2−222−2
χ534444-244-4-44-4-44-2-2-2-4-44000022-2-2-2-22222200-200000000000000000000000000000000000000
χ544444-244-4-4-4-4-4-4-2-2-244-40000-2-2-2-2222222-200200000000000000000000000000000000000000
χ554444-2-4-4444-4-44-2-2-24-4-400002222-2-2-2-222-200200000000000000000000000000000000000000
χ564444-2-4-444-4-4-4-4-2-2-2-4440000-2-22222-2-222200-200000000000000000000000000000000000000
χ574-44-444i−4i−4i4i0-440-44-40000000004i−4i00−4i4i-44000000000000000000000000000000000000000000
χ584-44-44−4i4i4i−4i0-440-44-4000000000−4i4i004i−4i-44000000000000000000000000000000000000000000
χ594-44-4-24i−4i4i−4i04-402-220004-44i−4i00−2i2i00−2i2i-220000-2200−2i2i00000000000000000000000000000000
χ604-44-4-24i−4i4i−4i04-402-22000-44−4i4i00−2i2i00−2i2i-2200002-2002i−2i00000000000000000000000000000000
χ614-44-4-24i−4i−4i4i0-4402-22000000000−2i2i002i−2i2-2000000−2i32i30023−23000000000000000000000000000000
χ624-44-4-24i−4i−4i4i0-4402-22000000000−2i2i002i−2i2-20000002i3−2i300−2323000000000000000000000000000000
χ634-44-4-2−4i4i4i−4i0-4402-220000000002i−2i00−2i2i2-2000000−2i32i300−2323000000000000000000000000000000
χ644-44-4-2−4i4i4i−4i0-4402-220000000002i−2i00−2i2i2-20000002i3−2i30023−23000000000000000000000000000000
χ654-44-4-2−4i4i−4i4i04-402-220004-4−4i4i002i−2i002i−2i-220000-22002i−2i00000000000000000000000000000000
χ664-44-4-2−4i4i−4i4i04-402-22000-444i−4i002i−2i002i−2i-2200002-200−2i2i00000000000000000000000000000000
χ674-4-4440000400-4-4-44000000000004-400000000000000004i−4i0000000000000000000000000000
χ684-4-4440000400-4-4-44000000000004-40000000000000000−4i4i0000000000000000000000000000
χ694-4-4440000-4004-4-4400000000000-440000000000000000004-400000000000000000000000000
χ704-4-4440000-4004-4-4400000000000-44000000000000000000-4400000000000000000000000000
χ7188-8-88000000008-8-800000000000000000000000000000000000000000000000000000000000
χ7288-8-8-400000000-4440000000−4i34i300000000000000000000000000000000000000000000000000
χ7388-8-8-400000000-44400000004i3−4i300000000000000000000000000000000000000000000000000
χ748-8-88-40000800-844-400000000000-440000000000000000000000000000000000000000000000
χ758-8-88-40000-800844-4000000000004-40000000000000000000000000000000000000000000000

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