Finite Group Databasebeta

← Group #10845213

Character table — Group #10845213

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666444444121212121212121222444666688881212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-1-11
χ6111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-111-1
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1111-1-1111-1-111-1-111-1
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111111-1-1-1-1-111-1-111-1-11
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1111-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-11111-1-1-11111-1-1-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111-1-1-1-11111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1111
χ17222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-200000000000022-2-2220000000-2000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-2000000000000-2-222-2-200000002000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-20000200000000220000000000002222-2-20000000-2000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000000022000000000000-2-2-2-22200000002000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-222-2111122-2-211-1-1-1-1-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-21111-2-22211-1-1-1-11111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-2-1-1-1-1-2-2221111111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-2-2-1-1-1-122-2-2111111-1-1-1-111110000002-1-111000000000000
χ29222-22-2-2-222-2-2222-2-2-22-22i2i−2i−2i002-200002-2002-2000002i−2i00002i2i−2i−2i2i2i−2i−2i00000000000002-2000000000000
χ30222-22-2-2-222-2-2222-2-2-22-22i2i−2i−2i002-200002-200-2200000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000-22000000000000
χ31222-22-2-2-222-2-2222-2-2-22-2−2i−2i2i2i002-200002-2002-200000−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000000002-2000000000000
χ32222-22-2-2-222-2-2222-2-2-22-2−2i−2i2i2i002-200002-200-22000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000-22000000000000
χ33222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i00-1133−3−3-11002-20−i3−i3i3i32i−2i003−3−i−iii−i−iii−i3−i3i3i300000003−3-11000000000000
χ34222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i00-1133−3−3-1100-220−i3−i3i3i3−2i2i003−3−i−iiiii−i−ii3i3−i3−i30000000−331-1000000000000
χ35222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i00-11−3−333-11002-20i3i3−i3−i32i−2i00−33−i−iii−i−iiii3i3−i3−i30000000−33-11000000000000
χ36222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i00-11−3−333-1100-220i3i3−i3−i3−2i2i00−33−i−iiiii−i−i−i3−i3i3i300000003−31-1000000000000
χ37222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i00-1133−3−3-11002-20i3i3−i3−i3−2i2i003−3ii−i−iii−i−ii3i3−i3−i300000003−3-11000000000000
χ38222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i00-1133−3−3-1100-220i3i3−i3−i32i−2i003−3ii−i−i−i−iii−i3−i3i3i30000000−331-1000000000000
χ39222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i00-11−3−333-11002-20−i3−i3i3i3−2i2i00−33ii−i−iii−i−i−i3−i3i3i30000000−33-11000000000000
χ40222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i00-11−3−333-1100-220−i3−i3i3i32i−2i00−33ii−i−i−i−iiii3i3−i3−i300000003−31-1000000000000
χ412-222-22-2-222-22-2-2-2-22-2222-22-2002-20000-220000000000000002-22-20000000000000000000000002i−2i002i−2i0
χ422-222-22-2-222-22-2-2-2-22-2222-22-2002-20000-220000000000000002-22-2000000000000000000000000−2i2i00−2i2i0
χ432-222-22-2-222-22-2-2-2-22-222-22-22002-20000-22000000000000000-22-220000000000000000000000002i−2i00−2i2i0
χ442-222-22-2-222-22-2-2-2-22-222-22-22002-20000-22000000000000000-22-22000000000000000000000000−2i2i002i−2i0
χ452-22-2-2-222222-2-2-2-22-222-22i−2i−2i2i00220000-2-20000000000000002i−2i−2i2i00000000002-22-2000000002i−2i0000000
χ462-22-2-2-222222-2-2-2-22-222-22i−2i−2i2i00220000-2-20000000000000002i−2i−2i2i0000000000-22-2200000000−2i2i0000000
χ472-22-2-2-222222-2-2-2-22-222-2−2i2i2i−2i00220000-2-2000000000000000−2i2i2i−2i00000000002-22-200000000−2i2i0000000
χ482-22-2-2-222222-2-2-2-22-222-2−2i2i2i−2i00220000-2-2000000000000000−2i2i2i−2i0000000000-22-22000000002i−2i0000000
χ492-22-2-2-2222-2-222-2-22-222-2000000-2-20000222-20002-22-2000000000000000000002-2-22000002-20000000000
χ502-22-2-2-2222-2-222-2-22-222-2000000-2-20000222-20002-22-200000000000000000000-222-200000-220000000000
χ512-22-2-2-2222-2-222-2-22-222-2000000-2-2000022-22000-22-22000000000000000000002-2-2200000-220000000000
χ522-22-2-2-2222-2-222-2-22-222-2000000-2-2000022-22000-22-2200000000000000000000-222-2000002-20000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-2220000-4000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222220000400000000-2-200000000000000000000000000000000000
χ55444-44-4-4-44-444-444-4-4-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-2-444-4-2-2222-220000002-22323−23−232-20000000000000−232300000000000000000000000000000000000
χ57444-44-4-4-4-2-444-4-2-2222-220000002-2−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ5844-44-4-4-44400004-4-444-4-400004i−4i004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ5944-44-4-4-44400004-4-444-4-40000−4i4i00−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6044-44-4-4-44-20000-222-2-22200004i−4i00−2i2i−2i2i000000000000000000000i6−i6i6−i66−66−600000000000000000000000
χ6144-44-4-4-44-20000-222-2-22200004i−4i00−2i2i−2i2i000000000000000000000−i6i6−i6i6−66−6600000000000000000000000
χ6244-44-4-4-44-20000-222-2-2220000−4i4i002i−2i2i−2i000000000000000000000i6−i6i6−i6−66−6600000000000000000000000
χ6344-44-4-4-44-20000-222-2-2220000−4i4i002i−2i2i−2i000000000000000000000−i6i6−i6i66−66−600000000000000000000000
χ6444-4-4-444-4400004-44-4-4-440000000000000000000000000−2i22i20000000000−2i22i22i2−2i200000000000000000000000
χ6544-4-4-444-4400004-44-4-4-4400000000000000000000000002i2−2i200000000002i2−2i2−2i22i200000000000000000000000
χ6644-4-4-444-4-20000-22-2222-200000000−2i32i32i3−2i30000000000000−2i22i2000000−666−6i2−i2−i2i200000000000000000000000
χ6744-4-4-444-4-20000-22-2222-200000000−2i32i32i3−2i300000000000002i2−2i20000006−6−66−i2i2i2−i200000000000000000000000
χ6844-4-4-444-4-20000-22-2222-2000000002i3−2i3−2i32i30000000000000−2i22i20000006−6−66i2−i2−i2i200000000000000000000000
χ6944-4-4-444-4-20000-22-2222-2000000002i3−2i3−2i32i300000000000002i2−2i2000000−666−6−i2i2i2−i200000000000000000000000
χ704-444-44-4-44-44-44-4-4-44-444000000-4400004-400000000000000000000000000000000000000000000000000
χ714-444-44-4-4-24-44-4222-22-2-24-44-400-2200002-2000000000000000-22-220000000000000000000000000000000
χ724-444-44-4-4-24-44-4222-22-2-2-44-4400-2200002-20000000000000002-22-20000000000000000000000000000000
χ734-444-44-4-4-2-44-44222-22-2-20000002-20000-2200000−2i32i32i3−2i300000000000000000000000000000000000000000
χ744-444-44-4-4-2-44-44222-22-2-20000002-20000-22000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ754-44-4-4-444-244-4-422-22-2-224i−4i−4i4i00-2-2000022000000000000000−2i2i2i−2i0000000000000000000000000000000
χ764-44-4-4-444-244-4-422-22-2-22−4i4i4i−4i00-2-20000220000000000000002i−2i−2i2i0000000000000000000000000000000
χ774-44-4-4-444-2-4-44422-22-2-22000000220000-2-24-4000-22-2200000000000000000000000000000000000000000
χ784-44-4-4-444-2-4-44422-22-2-22000000220000-2-2-440002-22-200000000000000000000000000000000000000000
χ794-4-444-44-440000-4444-4-4-400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ804-4-444-44-440000-4444-4-4-4000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ814-4-4-444-4440000-44-4-44-44000000000000000000000000000000000000000004-4000000000000000000000
χ824-4-4-444-4440000-44-4-44-4400000000000000000000000000000000000000000-44000000000000000000000
χ838-8-888-88-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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