Finite Group Databasebeta

← Group #10844635

Character table — Group #10844635

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212124444488881212121212121212121224242424242424244444442661212224444488882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ4111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ5111111111111111111111111-1-111-1-1-1-111-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-11111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1111-1-1-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111111-1-111-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11111-111-1-1-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111-1-11-1-11111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-111-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-20000-20000-2-2000000000000000022-2-2-2-200000002000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-20000-20000-2-20000000000000000-2-222220000000-2000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200002000022000000000000000022-2-2220000000-2000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000220000000000000000-2-222-2-200000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-222-222-2-211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-2-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-2-222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ292222-2-2-2-222-2-222-22-2-22-222-2-2002-200002-2002i−2i02i−2i000022-2-200002i2i−2i−2i00000000000002i−2i000000000000
χ302222-2-2-2-222-2-222-22-2-22-222-2-2002-200002-200−2i2i0−2i2i000022-2-20000−2i−2i2i2i0000000000000−2i2i000000000000
χ312222-2-2-2-222-2-222-22-2-22-2-2-222002-200002-2002i−2i0−2i2i0000-2-2220000−2i−2i2i2i00000000000002i−2i000000000000
χ322222-2-2-2-222-2-222-22-2-22-2-2-222002-200002-200−2i2i02i−2i0000-2-22200002i2i−2i−2i0000000000000−2i2i000000000000
χ332222-2-2-2-2-12-2-22-11-111-1122-2-200-1133−3−3-11002i−2i02i−2i003−3-1-11133−3−3−i−iii−i3−i3i3i30000000−i3i3−ii000000000000
χ342222-2-2-2-2-12-2-22-11-111-1122-2-200-1133−3−3-1100−2i2i0−2i2i003−3-1-11133−3−3ii−i−ii3i3−i3−i30000000i3−i3i−i000000000000
χ352222-2-2-2-2-12-2-22-11-111-1122-2-200-11−3−333-11002i−2i02i−2i00−33-1-111−3−333−i−iiii3i3−i3−i30000000i3−i3−ii000000000000
χ362222-2-2-2-2-12-2-22-11-111-1122-2-200-11−3−333-1100−2i2i0−2i2i00−33-1-111−3−333ii−i−i−i3−i3i3i30000000−i3i3i−i000000000000
χ372222-2-2-2-2-12-2-22-11-111-11-2-22200-1133−3−3-11002i−2i0−2i2i003−311-1-1−3−333ii−i−ii3i3−i3−i30000000−i3i3−ii000000000000
χ382222-2-2-2-2-12-2-22-11-111-11-2-22200-1133−3−3-1100−2i2i02i−2i003−311-1-1−3−333−i−iii−i3−i3i3i30000000i3−i3i−i000000000000
χ392222-2-2-2-2-12-2-22-11-111-11-2-22200-11−3−333-11002i−2i0−2i2i00−3311-1-133−3−3ii−i−i−i3−i3i3i30000000i3−i3−ii000000000000
χ402222-2-2-2-2-12-2-22-11-111-11-2-22200-11−3−333-1100−2i2i02i−2i00−3311-1-133−3−3−i−iiii3i3−i3−i30000000−i3i3i−i000000000000
χ412-22-22-2-2222-22-2-2-2222-2-22i−2i2i−2i002-20000-22000000000002i−2i2i−2i000000000000000000000002-2000002i−2i000
χ422-22-22-2-2222-22-2-2-2222-2-22i−2i2i−2i002-20000-22000000000002i−2i2i−2i00000000000000000000000-2200000−2i2i000
χ432-22-22-2-2222-22-2-2-2222-2-2−2i2i−2i2i002-20000-2200000000000−2i2i−2i2i000000000000000000000002-200000−2i2i000
χ442-22-22-2-2222-22-2-2-2222-2-2−2i2i−2i2i002-20000-2200000000000−2i2i−2i2i00000000000000000000000-22000002i−2i000
χ452-22-2-222-2222-2-2-222-2-2-222i−2i−2i2i00220000-2-2000000000002i−2i−2i2i0000000000002-22-20000000000002i−2i00000
χ462-22-2-222-2222-2-2-222-2-2-222i−2i−2i2i00220000-2-2000000000002i−2i−2i2i000000000000-22-22000000000000−2i2i00000
χ472-22-2-222-2222-2-2-222-2-2-22−2i2i2i−2i00220000-2-200000000000−2i2i2i−2i0000000000002-22-2000000000000−2i2i00000
χ482-22-2-222-2222-2-2-222-2-2-22−2i2i2i−2i00220000-2-200000000000−2i2i2i−2i000000000000-22-220000000000002i−2i00000
χ492-22-2-222-22-2-222-222-2-2-22000000-2-20000222-200000000000002-22-2000000002-2-2200000000002-20000000
χ502-22-2-222-22-2-222-222-2-2-22000000-2-20000222-200000000000002-22-200000000-222-20000000000-220000000
χ512-22-2-222-22-2-222-222-2-2-22000000-2-2000022-220000000000000-22-22000000002-2-220000000000-220000000
χ522-22-2-222-22-2-222-222-2-2-22000000-2-2000022-220000000000000-22-2200000000-222-200000000002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-2220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-422222222000040000-2-2000000000000000000000000000000000000000
χ554444-4-4-4-44-444-44-44-4-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-2-444-4-22-222-220000002-22323−23−232-2000000000−2323000000000000000000000000000000000000000
χ574444-4-4-4-4-2-444-4-22-222-220000002-2−23−2323232-200000000023−23000000000000000000000000000000000000000
χ5844-4-44-44-44000044-44-4-4-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ5944-4-44-44-44000044-44-4-4-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ6044-4-4-44-44400004-4-4-44-440000000000000000000000000000000000000000000004-400000000000000000
χ6144-4-4-44-44400004-4-4-44-44000000000000000000000000000000000000000000000-4400000000000000000
χ624-44-44-4-444-44-44-4-4444-4-4000000-4400004-400000000000000000000000000000000000000000000000000
χ634-44-44-4-44-24-44-422-2-2-2224i−4i4i−4i00-2200002-200000000000−2i2i−2i2i00000000000000000000000000000000000
χ644-44-44-4-44-24-44-422-2-2-222−4i4i−4i4i00-2200002-2000000000002i−2i2i−2i00000000000000000000000000000000000
χ654-44-44-4-44-2-44-4422-2-2-2220000002-20000-2200000000000000023−23−23230000000000000000000000000000000
χ664-44-44-4-44-2-44-4422-2-2-2220000002-20000-22000000000000000−232323−230000000000000000000000000000000
χ674-44-4-444-4-244-4-42-2-2222-24i−4i−4i4i00-2-200002200000000000−2i2i2i−2i00000000000000000000000000000000000
χ684-44-4-444-4-244-4-42-2-2222-2−4i4i4i−4i00-2-2000022000000000002i−2i−2i2i00000000000000000000000000000000000
χ694-44-4-444-4-2-4-4442-2-2222-2000000220000-2-24-40000000000000-22-220000000000000000000000000000000
χ704-44-4-444-4-2-4-4442-2-2222-2000000220000-2-2-4400000000000002-22-20000000000000000000000000000000
χ714-4-4444-4-440000-4-4-44-44400004-4004-44-40000000000000000000000000000000000000000000000000000
χ724-4-4444-4-440000-4-4-44-4440000-4400-44-440000000000000000000000000000000000000000000000000000
χ734-4-4444-4-4-20000222-22-2-200004-400-22-22000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ744-4-4444-4-4-20000222-22-2-200004-400-22-22000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ754-4-4444-4-4-20000222-22-2-20000-44002-22-2000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ764-4-4444-4-4-20000222-22-2-20000-44002-22-2000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ774-4-44-4-44440000-44-4-444-400000000000000000000022−220000000000000022−22−222200000000000000000000000
χ784-4-44-4-44440000-44-4-444-4000000000000000000000−222200000000000000−222222−2200000000000000000000000
χ794-4-44-4-444-200002-222-2-220000000023−23−232300000000022−2200000000006−6−66−222−200000000000000000000000
χ804-4-44-4-444-200002-222-2-220000000023−23−2323000000000−22220000000000−666−62−2−2200000000000000000000000
χ814-4-44-4-444-200002-222-2-2200000000−232323−2300000000022−220000000000−666−6−222−200000000000000000000000
χ824-4-44-4-444-200002-222-2-2200000000−232323−23000000000−222200000000006−6−662−2−2200000000000000000000000
χ8388-8-88-88-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000

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