Finite Group Databasebeta

← Group #10845235

Character table — Group #10845235

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122244488881212121212121212121224242424242424244444444661212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-1-1111111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1111-1-1-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-111-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-111111-1-11111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-11111-1-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111-1-111111-1-111-1
χ17222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-200000000000000002222-2-20000000-2000000000
χ18222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-20000000000000000-2-2-2-22200000002000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200002000022000000000000000022-2-2-2-200000002000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000220000000000000000-2-222220000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-122-2-2-222-2-211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2-222111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-222-222-2-2111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-2-22-2-222-2-2222-2-2-22-2002i2i−2i−2i00002-22-22-20002i−2i00002i2i−2i−2i00002i2i−2i−2i000000000002-200000000000000
χ30222-2-22-2-222-2-2222-2-2-22-2002i2i−2i−2i00002-22-2-22000−2i2i00002i2i−2i−2i0000−2i−2i2i2i00000000000-2200000000000000
χ31222-2-22-2-222-2-2222-2-2-22-200−2i−2i2i2i00002-22-22-2000−2i2i0000−2i−2i2i2i0000−2i−2i2i2i000000000002-200000000000000
χ32222-2-22-2-222-2-2222-2-2-22-200−2i−2i2i2i00002-22-2-220002i−2i0000−2i−2i2i2i00002i2i−2i−2i00000000000-2200000000000000
χ33222-2-22-2-2-12-2-22-1-1111-11002i2i−2i−2i33−3−3-11-112-20002i−2i003−3−i−iii−i3−i3i3i3−i−iii−i3−i3i3i30000000-113−3000000000000
χ34222-2-22-2-2-12-2-22-1-1111-11002i2i−2i−2i33−3−3-11-11-22000−2i2i003−3−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ35222-2-22-2-2-12-2-22-1-1111-11002i2i−2i−2i−3−333-11-112-20002i−2i00−33−i−iiii3i3−i3−i3−i−iiii3i3−i3−i30000000-11−33000000000000
χ36222-2-22-2-2-12-2-22-1-1111-11002i2i−2i−2i−3−333-11-11-22000−2i2i00−33−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i300000001-13−3000000000000
χ37222-2-22-2-2-12-2-22-1-1111-1100−2i−2i2i2i33−3−3-11-112-2000−2i2i003−3ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ38222-2-22-2-2-12-2-22-1-1111-1100−2i−2i2i2i33−3−3-11-11-220002i−2i003−3ii−i−ii3i3−i3−i3−i−iii−i3−i3i3i300000001-1−33000000000000
χ39222-2-22-2-2-12-2-22-1-1111-1100−2i−2i2i2i−3−333-11-112-2000−2i2i00−33ii−i−i−i3−i3i3i3ii−i−i−i3−i3i3i30000000-11−33000000000000
χ40222-2-22-2-2-12-2-22-1-1111-1100−2i−2i2i2i−3−333-11-11-220002i−2i00−33ii−i−i−i3−i3i3i3−i−iiii3i3−i3−i300000001-13−3000000000000
χ412-222-2-2-22222-2-2-2-22-222-2002i−2i2i−2i000022-2-2000000000002i−2i2i−2i0000000000002-2002-2000000002i−2i0000000
χ422-222-2-2-22222-2-2-2-22-222-2002i−2i2i−2i000022-2-2000000000002i−2i2i−2i000000000000-2200-2200000000−2i2i0000000
χ432-222-2-2-22222-2-2-2-22-222-200−2i2i−2i2i000022-2-200000000000−2i2i−2i2i0000000000002-2002-200000000−2i2i0000000
χ442-222-2-2-22222-2-2-2-22-222-200−2i2i−2i2i000022-2-200000000000−2i2i−2i2i000000000000-2200-22000000002i−2i0000000
χ452-222-2-2-222-2-222-2-22-222-20000000000-2-222002-2000000000002-22-2000000002-200-22000002-20000000000
χ462-222-2-2-222-2-222-2-22-222-20000000000-2-222002-2000000000002-22-200000000-22002-200000-220000000000
χ472-222-2-2-222-2-222-2-22-222-20000000000-2-22200-2200000000000-22-22000000002-200-2200000-220000000000
χ482-222-2-2-222-2-222-2-22-222-20000000000-2-22200-2200000000000-22-2200000000-22002-2000002-20000000000
χ492-22-22-22-222-22-2-2-2-22-222002-2-2200002-2-22000000000002-2-2200000000000000000000000000002i−2i2i−2i000
χ502-22-22-22-222-22-2-2-2-22-222002-2-2200002-2-22000000000002-2-220000000000000000000000000000−2i2i−2i2i000
χ512-22-22-22-222-22-2-2-2-22-22200-222-200002-2-2200000000000-222-200000000000000000000000000002i−2i−2i2i000
χ522-22-22-22-222-22-2-2-2-22-22200-222-200002-2-2200000000000-222-20000000000000000000000000000−2i2i2i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-222220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222000040000-2-2000000000000000000000000000000000000000
χ55444-4-44-4-44-444-444-4-4-44-40000000000-44-4400000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-2-444-4-2-2222-220000002323−23−232-22-2000000000−2323000000000000000000000000000000000000000
χ57444-4-44-4-4-2-444-4-2-2222-22000000−23−2323232-22-200000000023−23000000000000000000000000000000000000000
χ5844-444-4-4-4400004-444-4-4-4000000000000000000000000000000000000000000000000000000000000022−220
χ5944-444-4-4-4400004-444-4-4-40000000000000000000000000000000000000000000000000000000000000−22220
χ6044-4-4-4-444400004-4-4-44-4400000000000000000000000000000000000000000004-40000000000000000000
χ6144-4-4-4-444400004-4-4-44-440000000000000000000000000000000000000000000-440000000000000000000
χ624-444-4-4-44-244-4-422-22-2-22004i−4i4i−4i0000-2-22200000000000−2i2i−2i2i00000000000000000000000000000000000
χ634-444-4-4-44-244-4-422-22-2-2200−4i4i−4i4i0000-2-222000000000002i−2i2i−2i00000000000000000000000000000000000
χ644-444-4-4-44-2-4-44422-22-2-22000000000022-2-2004-400000000000-22-220000000000000000000000000000000
χ654-444-4-4-44-2-4-44422-22-2-22000000000022-2-200-44000000000002-22-20000000000000000000000000000000
χ664-44-44-44-44-44-44-4-4-44-4440000000000-444-400000000000000000000000000000000000000000000000000
χ674-44-44-44-4-24-44-4222-22-2-2004-4-440000-222-200000000000-222-200000000000000000000000000000000000
χ684-44-44-44-4-24-44-4222-22-2-200-444-40000-222-2000000000002-2-2200000000000000000000000000000000000
χ694-44-44-44-4-2-44-44222-22-2-200000000002-2-22000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ704-44-44-44-4-2-44-44222-22-2-200000000002-2-220000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ714-4-44-444-440000-444-4-4-44000000000000000000000−2i22i200000000000000−2i22i2−2i22i200000000000000000000000
χ724-4-44-444-440000-444-4-4-440000000000000000000002i2−2i2000000000000002i2−2i22i2−2i200000000000000000000000
χ734-4-44-444-4-200002-2-2222-200000023−2323−2300000000000−2i22i20000000000i6−i6i6−i6i2−i2i2−i200000000000000000000000
χ744-4-44-444-4-200002-2-2222-200000023−2323−23000000000002i2−2i20000000000−i6i6−i6i6−i2i2−i2i200000000000000000000000
χ754-4-44-444-4-200002-2-2222-2000000−2323−232300000000000−2i22i20000000000−i6i6−i6i6i2−i2i2−i200000000000000000000000
χ764-4-44-444-4-200002-2-2222-2000000−2323−2323000000000002i2−2i20000000000i6−i6i6−i6−i2i2−i2i200000000000000000000000
χ774-4-4-444-4440000-44-444-4-44-400004-4-44000000000000000000000000000000000000000000000000000000
χ784-4-4-444-4440000-44-444-4-4-440000-444-4000000000000000000000000000000000000000000000000000000
χ794-4-4-444-44-200002-22-2-2224-40000-222-2000000000000000000000006−6−66−666−600000000000000000000000
χ804-4-4-444-44-200002-22-2-2224-40000-222-200000000000000000000000−666−66−6−6600000000000000000000000
χ814-4-4-444-44-200002-22-2-222-4400002-2-22000000000000000000000006−6−666−6−6600000000000000000000000
χ824-4-4-444-44-200002-22-2-222-4400002-2-2200000000000000000000000−666−6−666−600000000000000000000000
χ8388-888-8-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-888-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000

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