Finite Group Databasebeta

← Group #10778135

Character table — Group #10778135

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order1222344444444666121212122224444121212121212121244666888812121212121212242424242424242488884412121212888888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-111-1-111111111-1-11-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111-1-111-1-111111111-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-111-1-111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-111-1-111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ911111-1-1-1-11111111-1-1-1-1-1111-11111-1-1-1-111-1-1-11111-1-11-1-111-1-11111-1-1-1-111-1-11-111-1-11-111-1-111-1-11-1
χ1011111-1-1-1-11111111-1-1-1-1-1111-11111-1-1-1-111-1-1-11111-1-11-1-111-1-11111-1-1-1-1-1-1111-111-1-1-11-1-111-1-111-11
χ1111111-1-1-1-11111111-1-1-1-1-1111-11111-1-1-1-111-1-1-111-1-1111-1-111-1-1-1-1-1-1111111-1-1-11-1-1111-111-1-1-1-111-11
χ1211111-1-1-1-11111111-1-1-1-1-1111-11111-1-1-1-111-1-1-111-1-1111-1-111-1-1-1-1-1-11111-1-111-11-1-111-11-1-11111-1-11-1
χ1311111-1-1-1-11111111-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-111-1-1111-1-1111111-1-1-1-111-1-1-11-1-1111-1-1-11111-1-1-11
χ1411111-1-1-1-11111111-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-111-1-1111-1-1111111-1-1-1-1-1-111-11-1-111-1111-1-1-1-1111-1
χ1511111-1-1-1-11111111-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-111111-1-111-1-1-1-1111111-1-11-111-1-11-1-1-111-1-1111-1
χ1611111-1-1-1-11111111-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-111111-1-111-1-1-1-11111-1-1111-111-1-1-1111-1-111-1-1-11
χ17222222222-222-22222222-200-2-2002222-2-2-2-200-2000000-2000000000000002222000000-2-20000000000
χ18222222222-222-22222222-200-2-2002222-2-2-2-200-2000000-200000000000000-2-2-2-2000000220000000000
χ192222222-2-22-2-222222222-222-22-2-2-2-2-2-222222-2-2220000-222-2-2-2-2000000000000000000000000000000
χ202222222-2-22-2-222222222-2-2-2-2222-2-2-2-22222-22-2-2-20000-2-2-22222000000000000000000000000000000
χ212222222-2-2-2-2-2-222222222002-200-2-2-2-2-2-2-2-20020000002000000000000000000000000002i−2i2i−2i000000
χ222222222-2-2-2-2-2-222222222002-200-2-2-2-2-2-2-2-2002000000200000000000000000000000000−2i2i−2i2i000000
χ2322222-2-2222-2-22222-2-2-2-2222-2-2-2-2-2-222-2-222-222220000-2-2-2-2-222000000000000000000000000000000
χ2422222-2-2222-2-22222-2-2-2-22-2-2-2-222-2-222-2-2222-22-2-20000-22222-2-2000000000000000000000000000000
χ2522222-2-222-2-2-2-2222-2-2-2-2-2002200-2-22222-2-200-20000002000000000000000000000000002i−2i−2i2i000000
χ2622222-2-222-2-2-2-2222-2-2-2-2-2002200-2-22222-2-200-2000000200000000000000000000000000−2i2i2i−2i000000
χ2722222-2-2-2-2-222-2222-2-2-2-2200-220022-2-222-2-2002000000-20000000000000022-2-2000000-220000000000
χ2822222-2-2-2-2-222-2222-2-2-2-2200-220022-2-222-2-2002000000-200000000000000-2-2220000002-20000000000
χ292222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ302222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ312222-122222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2-1112222-1111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ322222-122222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2-111-2-2-2-2-111111111111111000022-1-1-1-1000000000000
χ332222-122-2-22-2-22-1-1-1-1-1-1-1-222-22-2-21111-1-1-1-12-21-1-100001-1-11111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ342222-122-2-22-2-22-1-1-1-1-1-1-1-222-22-2-21111-1-1-1-12-21-1-100001-1-11111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ352222-122-2-22-2-22-1-1-1-1-1-1-1-2-2-2-22221111-1-1-1-1-221110000111-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ362222-122-2-22-2-22-1-1-1-1-1-1-1-2-2-2-22221111-1-1-1-1-221110000111-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ372222-1-2-2222-2-22-1-1-11111222-2-2-2-211-1-111-1-1-22-1-1-1000011111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ382222-1-2-2222-2-22-1-1-11111222-2-2-2-211-1-111-1-1-22-1-1-1000011111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ392222-1-2-2222-2-22-1-1-111112-2-2-2-22211-1-111-1-12-2-11100001-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ402222-1-2-2222-2-22-1-1-111112-2-2-2-22211-1-111-1-12-2-11100001-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ412222-1-2-2-2-22222-1-1-11111-2222-222-1-11111-1-1-2-21-1-122-2-2-111-1-111-1-1-1-1111100002-2-1-111000000000000
χ422222-1-2-2-2-22222-1-1-11111-2222-222-1-11111-1-1-2-21-1-1-2-222-111-1-1111111-1-1-1-10000-2211-1-1000000000000
χ432222-1-2-2-2-22222-1-1-11111-2-2-22-2-2-2-1-11111-1-12211122-2-2-1-1-111-1-1-1-1-1-111110000-2211-1-1000000000000
χ442222-1-2-2-2-22222-1-1-11111-2-2-22-2-2-2-1-11111-1-122111-2-222-1-1-111-1-11111-1-1-1-100002-2-1-111000000000000
χ452-22-222i−2i2i−2i02-20-22-22i2i−2i−2i00000002-22i−2i0000000002−2−i2i200000002−22−2−i2i2−i2i22-22i−2i0000000000002−2−i2i200
χ462-22-222i−2i2i−2i02-20-22-22i2i−2i−2i00000002-22i−2i0000000002−2−i2i200000002−22−2−i2i2−i2i2-22−2i2i000000000000−22i2−i200
χ472-22-222i−2i2i−2i02-20-22-22i2i−2i−2i00000002-22i−2i000000000−22i2−i20000000−22−22i2−i2i2−i22-22i−2i000000000000−22i2−i200
χ482-22-222i−2i2i−2i02-20-22-22i2i−2i−2i00000002-22i−2i000000000−22i2−i20000000−22−22i2−i2i2−i2-22−2i2i0000000000002−2−i2i200
χ492-22-22−2i2i−2i2i02-20-22-2−2i−2i2i2i00000002-2−2i2i0000000002−2i2−i200000002−22−2i2−i2i2−i22-2−2i2i0000000000002−2i2−i200
χ502-22-22−2i2i−2i2i02-20-22-2−2i−2i2i2i00000002-2−2i2i0000000002−2i2−i200000002−22−2i2−i2i2−i2-222i−2i000000000000−22−i2i200
χ512-22-22−2i2i−2i2i02-20-22-2−2i−2i2i2i00000002-2−2i2i000000000−22−i2i20000000−22−22−i2i2−i2i22-2−2i2i000000000000−22−i2i200
χ522-22-22−2i2i−2i2i02-20-22-2−2i−2i2i2i00000002-2−2i2i000000000−22−i2i20000000−22−22−i2i2−i2i2-222i−2i0000000000002−2i2−i200
χ534444-24444-444-4-2-2-2-2-2-2-2-400-4-400-2-2-2-222220020000002000000000000000000000000000000000000
χ544444-244-4-4-4-4-4-4-2-2-2-2-2-2-24004-4002222222200-2000000-2000000000000000000000000000000000000
χ554444-2-4-444-4-4-4-4-2-2-22222-400440022-2-2-2-222002000000-2000000000000000000000000000000000000
χ564444-2-4-4-4-4-444-4-2-2-22222400-4400-2-222-2-22200-20000002000000000000000000000000000000000000
χ574-44-444i−4i−4i4i0-440-44-44i4i−4i−4i0000000-44−4i4i00000000000000000000000000000000000000000000000000
χ584-44-44−4i4i4i−4i0-440-44-4−4i−4i4i4i0000000-444i−4i00000000000000000000000000000000000000000000000000
χ594-44-4-24i−4i4i−4i04-402-22−2i−2i2i2i0000000-22−2i2i00000000022−22−2i22i20000000−22−22i2−i2i2−i20000000000000000000000
χ604-44-4-24i−4i4i−4i04-402-22−2i−2i2i2i0000000-22−2i2i000000000−22222i2−2i200000002−22−2−i2i2−i2i20000000000000000000000
χ614-44-4-24i−4i−4i4i0-4402-22−2i−2i2i2i00000002-22i−2i00000000000000000000i6−i6−i6i66−6−660000000000000000000000
χ624-44-4-24i−4i−4i4i0-4402-22−2i−2i2i2i00000002-22i−2i00000000000000000000−i6i6i6−i6−666−60000000000000000000000
χ634-44-4-2−4i4i4i−4i0-4402-222i2i−2i−2i00000002-2−2i2i00000000000000000000i6−i6−i6i6−666−60000000000000000000000
χ644-44-4-2−4i4i4i−4i0-4402-222i2i−2i−2i00000002-2−2i2i00000000000000000000−i6i6i6−i66−6−660000000000000000000000
χ654-44-4-2−4i4i−4i4i04-402-222i2i−2i−2i0000000-222i−2i00000000022−222i2−2i20000000−22−22−i2i2−i2i20000000000000000000000
χ664-44-4-2−4i4i−4i4i04-402-222i2i−2i−2i0000000-222i−2i000000000−2222−2i22i200000002−22−2i2−i2i2−i20000000000000000000000
χ674-4-4440000400-4-4-440000000004i−4i0000004-40000000000004i−4i00000000000000000000000000000000
χ684-4-4440000400-4-4-44000000000−4i4i0000004-4000000000000−4i4i00000000000000000000000000000000
χ694-4-4440000-4004-4-44000004-40000000000-440004-400000000000000000000000000000000000000000
χ704-4-4440000-4004-4-4400000-440000000000-44000-4400000000000000000000000000000000000000000
χ714-4-44-20000400-422-223−2323−23000004i−4i000023−23-22000000000000−2i2i−2i32i3000000000000000000000000000000
χ724-4-44-20000400-422-223−2323−2300000−4i4i000023−23-220000000000002i−2i2i3−2i3000000000000000000000000000000
χ734-4-44-20000400-422-2−2323−2323000004i−4i0000−2323-22000000000000−2i2i2i3−2i3000000000000000000000000000000
χ744-4-44-20000400-422-2−2323−232300000−4i4i0000−2323-220000000000002i−2i−2i32i3000000000000000000000000000000
χ754-4-44-20000-400422-223−2323−2304-400000000−23232-2000-220000023−230000000000000000000000000000000000
χ764-4-44-20000-400422-223−2323−230-4400000000−23232-20002-200000−23230000000000000000000000000000000000
χ774-4-44-20000-400422-2−2323−232304-40000000023−232-2000-2200000−23230000000000000000000000000000000000
χ784-4-44-20000-400422-2−2323−23230-440000000023−232-20002-20000023−230000000000000000000000000000000000
χ7988-8-88000000008-8-800000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-400000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000
χ8188-8-8-400000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000

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