Finite Group Databasebeta

← Group #10830069

Character table — Group #10830069

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212222246666888812121212121224242424242424244444444661212222244488884
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
χ5111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-111-1-111-1-1-11111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-1-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1111-1-11111-1-1-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11-1-111-1-11111111-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-111-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-111-1-11-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-1-11111-1-1111-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-20000000000002222-2-2000000000-20000000
χ18222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-2000000000000-2-2-2-22200000000020000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200002000000002200000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000000022000000000000-2-22222000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-222-2111122-2-211-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-21111-2-22211-1-1-1-11111-1-1-1-1000000211-1-1000000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-2-1-1-1-1-2-2221111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-2-2-1-1-1-122-2-2111111-1-1-1-11111000000211-1-1000000000000
χ292222-2-2-2-22-2-22222-22-2-2-22i2i−2i−2i002-200002-2002-2000002i−2i00002i2i−2i−2i2i2i−2i−2i000000000002-200000000000000
χ302222-2-2-2-22-2-22222-22-2-2-22i2i−2i−2i002-200002-200-2200000−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000-2200000000000000
χ312222-2-2-2-22-2-22222-22-2-2-2−2i−2i2i2i002-200002-2002-200000−2i2i0000−2i−2i2i2i−2i−2i2i2i000000000002-200000000000000
χ322222-2-2-2-22-2-22222-22-2-2-2−2i−2i2i2i002-200002-200-22000002i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000-2200000000000000
χ332222-2-2-2-2-1-2-222-1-11-11112i2i−2i−2i00-1133−3−3-11002-20−i3−i3i3i32i−2i003−3−i−iii−i−iii−i3−i3i3i30000000-113−3000000000000
χ342222-2-2-2-2-1-2-222-1-11-11112i2i−2i−2i00-1133−3−3-1100-220−i3−i3i3i3−2i2i003−3−i−iiiii−i−ii3i3−i3−i300000001-1−33000000000000
χ352222-2-2-2-2-1-2-222-1-11-11112i2i−2i−2i00-11−3−333-11002-20i3i3−i3−i32i−2i00−33−i−iii−i−iiii3i3−i3−i30000000-11−33000000000000
χ362222-2-2-2-2-1-2-222-1-11-11112i2i−2i−2i00-11−3−333-1100-220i3i3−i3−i3−2i2i00−33−i−iiiii−i−i−i3−i3i3i300000001-13−3000000000000
χ372222-2-2-2-2-1-2-222-1-11-1111−2i−2i2i2i00-1133−3−3-11002-20i3i3−i3−i3−2i2i003−3ii−i−iii−i−ii3i3−i3−i30000000-113−3000000000000
χ382222-2-2-2-2-1-2-222-1-11-1111−2i−2i2i2i00-1133−3−3-1100-220i3i3−i3−i32i−2i003−3ii−i−i−i−iii−i3−i3i3i300000001-1−33000000000000
χ392222-2-2-2-2-1-2-222-1-11-1111−2i−2i2i2i00-11−3−333-11002-20−i3−i3i3i3−2i2i00−33ii−i−iii−i−i−i3−i3i3i30000000-11−33000000000000
χ402222-2-2-2-2-1-2-222-1-11-1111−2i−2i2i2i00-11−3−333-1100-220−i3−i3i3i32i−2i00−33ii−i−i−i−iiii3i3−i3−i300000001-13−3000000000000
χ412-2-2222-2-222-22-2-2-222-22-22i−2i2i−2i00220000-2-20000000000000002i−2i2i−2i0000000000000000000000002i−2i2-2000
χ422-2-2222-2-222-22-2-2-222-22-22i−2i2i−2i00220000-2-20000000000000002i−2i2i−2i000000000000000000000000−2i2i-22000
χ432-2-2222-2-222-22-2-2-222-22-2−2i2i−2i2i00220000-2-2000000000000000−2i2i−2i2i0000000000000000000000002i−2i-22000
χ442-2-2222-2-222-22-2-2-222-22-2−2i2i−2i2i00220000-2-2000000000000000−2i2i−2i2i000000000000000000000000−2i2i2-2000
χ452-2-22-2-22222-2-22-2-2-222-22000000-2200002-22-20002-22-20000000000000000002-2002-200000002-200000000
χ462-2-22-2-22222-2-22-2-2-222-22000000-2200002-22-20002-22-2000000000000000000-2200-220000000-2200000000
χ472-2-22-2-22222-2-22-2-2-222-22000000-2200002-2-22000-22-220000000000000000002-2002-20000000-2200000000
χ482-2-22-2-22222-2-22-2-2-222-22000000-2200002-2-22000-22-22000000000000000000-2200-2200000002-200000000
χ492-2-22-2-2222-222-2-2-2-222-222-2-22002-20000-220000000000000002-2-22000000002-200-22000002-20000000000
χ502-2-22-2-2222-222-2-2-2-222-222-2-22002-20000-220000000000000002-2-2200000000-22002-200000-220000000000
χ512-2-22-2-2222-222-2-2-2-222-22-222-2002-20000-22000000000000000-222-2000000002-200-2200000-220000000000
χ522-2-22-2-2222-222-2-2-2-222-22-222-2002-20000-22000000000000000-222-200000000-22002-2000002-20000000000
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
χ554444-4-4-4-4444-4-444-44-4-4-4000000-440000-4400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-244-4-4-2-22-22220000002-22323−23−232-20000000000000−232300000000000000000000000000000000000
χ574444-4-4-4-4-244-4-4-2-22-22220000002-2−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ5844-4-44-44-4400004-4-4-4-44400004-4004-44-40000000000000000000000000000000000000000000000000000
χ5944-4-44-44-4400004-4-4-4-4440000-4400-44-440000000000000000000000000000000000000000000000000000
χ6044-4-44-44-4-20000-22222-2-200004-400-22-22000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ6144-4-44-44-4-20000-22222-2-200004-400-22-22000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ6244-4-44-44-4-20000-22222-2-20000-44002-22-2000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ6344-4-44-44-4-20000-22222-2-20000-44002-22-2000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ6444-4-4-44-44400004-44-44-4-4000000000000000000000000022−22000000000022−22−222200000000000000000000000
χ6544-4-4-44-44400004-44-44-4-40000000000000000000000000−22220000000000−222222−2200000000000000000000000
χ6644-4-4-44-44-20000-22-22-2220000000023−23−2323000000000000022−220000006−6−66−222−200000000000000000000000
χ6744-4-4-44-44-20000-22-22-2220000000023−23−23230000000000000−2222000000−666−62−2−2200000000000000000000000
χ6844-4-4-44-44-20000-22-22-22200000000−232323−23000000000000022−22000000−666−6−222−200000000000000000000000
χ6944-4-4-44-44-20000-22-22-22200000000−232323−230000000000000−22220000006−6−662−2−2200000000000000000000000
χ704-44-44-4-4440000-44-4-444-4000000000000000000000000000000000000000000000000000000000000022−220
χ714-44-44-4-4440000-44-4-444-40000000000000000000000000000000000000000000000000000000000000−22220
χ724-44-4-444-440000-444-4-4-4400000000000000000000000000000000000000000004-40000000000000000000
χ734-44-4-444-440000-444-4-4-440000000000000000000000000000000000000000000-440000000000000000000
χ744-4-4444-4-44-44-44-4-444-44-4000000-4-400004400000000000000000000000000000000000000000000000000
χ754-4-4444-4-4-24-44-422-2-22-224i−4i4i−4i00-2-2000022000000000000000−2i2i−2i2i0000000000000000000000000000000
χ764-4-4444-4-4-24-44-422-2-22-22−4i4i−4i4i00-2-20000220000000000000002i−2i2i−2i0000000000000000000000000000000
χ774-4-4444-4-4-2-44-4422-2-22-22000000220000-2-200000−2i32i32i3−2i300000000000000000000000000000000000000000
χ784-4-4444-4-4-2-44-4422-2-22-22000000220000-2-2000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ794-4-44-4-444-24-4-44222-2-22-20000002-20000-224-4000-22-2200000000000000000000000000000000000000000
χ804-4-44-4-444-24-4-44222-2-22-20000002-20000-22-440002-22-200000000000000000000000000000000000000000
χ814-4-44-4-444-2-444-4222-2-22-24-4-4400-2200002-2000000000000000-222-20000000000000000000000000000000
χ824-4-44-4-444-2-444-4222-2-22-2-444-400-2200002-20000000000000002-2-220000000000000000000000000000000
χ838-88-88-8-88-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-888-8-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000

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