Finite Group Databasebeta

← Group #10853209

Character table — Group #10853209

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-111-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-111-1-11111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-11-1-111-1-1-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-111-1-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-1111-1-1111111-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-1-11111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1111-1-1-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111111-1-111-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-20000-20000-2-200000000000000002222-2-200000-200000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-20000-20000-2-20000000000000000-2-2-2-22200000200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200002000022000000000000000022-2-2-2-200000200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000220000000000000000-2-2222200000-200000000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-222-2-2-22211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-222-2-2111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-2-2-2-222111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ2922-22-22-2-2222-2-22-22-22-2-222-2-200220000-2-20000000000022-2-20000000000002-2002-20000002-2000000000
χ3022-22-22-2-2222-2-22-22-22-2-222-2-200220000-2-20000000000022-2-2000000000000-2200-22000000-22000000000
χ3122-22-22-2-2222-2-22-22-22-2-2-2-22200220000-2-200000000000-2-2220000000000002-2002-2000000-22000000000
χ3222-22-22-2-2222-2-22-22-22-2-2-2-22200220000-2-200000000000-2-222000000000000-2200-220000002-2000000000
χ3322-22-22-2-22-2-2222-22-22-2-2000000-2-20000222i−2i00000000000002i2i−2i−2i000000002-200-22000000002i−2i0000000
χ3422-22-22-2-22-2-2222-22-22-2-2000000-2-20000222i−2i00000000000002i2i−2i−2i00000000-22002-200000000−2i2i0000000
χ3522-22-22-2-22-2-2222-22-22-2-2000000-2-2000022−2i2i0000000000000−2i−2i2i2i000000002-200-2200000000−2i2i0000000
χ3622-22-22-2-22-2-2222-22-22-2-2000000-2-2000022−2i2i0000000000000−2i−2i2i2i00000000-22002-2000000002i−2i0000000
χ372-2222-2-2-222-2-22-222-2-2-222i−2i2i−2i002-200002-2002i−2i0002-2002i−2i2i−2i000022-2-2000000000002i−2i00000000000000
χ382-2222-2-2-222-2-22-222-2-2-222i−2i2i−2i002-200002-200−2i2i000-22002i−2i2i−2i0000-2-22200000000000−2i2i00000000000000
χ392-2222-2-2-222-2-22-222-2-2-22−2i2i−2i2i002-200002-2002i−2i000-2200−2i2i−2i2i0000-2-222000000000002i−2i00000000000000
χ402-2222-2-2-222-2-22-222-2-2-22−2i2i−2i2i002-200002-200−2i2i0002-200−2i2i−2i2i000022-2-200000000000−2i2i00000000000000
χ412-2222-2-2-2-12-2-221-1-1111-12i−2i2i−2i00-1133−3−3-11002i−2i0002-23−3−ii−ii−i3i3−i3i3-1-11133−3−30000000−ii−i3i3000000000000
χ422-2222-2-2-2-12-2-221-1-1111-12i−2i2i−2i00-1133−3−3-1100−2i2i000-223−3−ii−ii−i3i3−i3i311-1-1−3−3330000000i−ii3−i3000000000000
χ432-2222-2-2-2-12-2-221-1-1111-12i−2i2i−2i00-11−3−333-11002i−2i0002-2−33−ii−iii3−i3i3−i3-1-111−3−3330000000−iii3−i3000000000000
χ442-2222-2-2-2-12-2-221-1-1111-12i−2i2i−2i00-11−3−333-1100−2i2i000-22−33−ii−iii3−i3i3−i311-1-133−3−30000000i−i−i3i3000000000000
χ452-2222-2-2-2-12-2-221-1-1111-1−2i2i−2i2i00-1133−3−3-11002i−2i000-223−3i−ii−ii3−i3i3−i311-1-1−3−3330000000−ii−i3i3000000000000
χ462-2222-2-2-2-12-2-221-1-1111-1−2i2i−2i2i00-1133−3−3-1100−2i2i0002-23−3i−ii−ii3−i3i3−i3-1-11133−3−30000000i−ii3−i3000000000000
χ472-2222-2-2-2-12-2-221-1-1111-1−2i2i−2i2i00-11−3−333-11002i−2i000-22−33i−ii−i−i3i3−i3i311-1-133−3−30000000−iii3−i3000000000000
χ482-2222-2-2-2-12-2-221-1-1111-1−2i2i−2i2i00-11−3−333-1100−2i2i0002-2−33i−ii−i−i3i3−i3i3-1-111−3−3330000000i−i−i3i3000000000000
χ492-2-22-2-22222-22-2-2-222-22-22i−2i−2i2i002-20000-22000000000002i−2i−2i2i00000000000000000000000000002-22i−2i000
χ502-2-22-2-22222-22-2-2-222-22-22i−2i−2i2i002-20000-22000000000002i−2i−2i2i0000000000000000000000000000-22−2i2i000
χ512-2-22-2-22222-22-2-2-222-22-2−2i2i2i−2i002-20000-2200000000000−2i2i2i−2i00000000000000000000000000002-2−2i2i000
χ522-2-22-2-22222-22-2-2-222-22-2−2i2i2i−2i002-20000-2200000000000−2i2i2i−2i0000000000000000000000000000-222i−2i000
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
χ55444-4-4-44-44000044-4-4-44-400000000000000000000000000000000000000000004-40000000000000000000
χ56444-4-4-44-44000044-4-4-44-40000000000000000000000000000000000000000000-440000000000000000000
χ5744-44-44-4-4-244-4-4-22-22-22244-4-400-2-200002200000000000-2-22200000000000000000000000000000000000
χ5844-44-44-4-4-244-4-4-22-22-222-4-44400-2-20000220000000000022-2-200000000000000000000000000000000000
χ5944-44-44-4-4-2-4-444-22-22-222000000220000-2-24i−4i0000000000000−2i−2i2i2i0000000000000000000000000000000
χ6044-44-44-4-4-2-4-444-22-22-222000000220000-2-2−4i4i00000000000002i2i−2i−2i0000000000000000000000000000000
χ6144-4-44-4-44400004-4-44-4-4400004i−4i004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ6244-4-44-4-44400004-4-44-4-440000−4i4i00−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6344-4-44-4-44-20000-222-222-200004i−4i00−2i2i−2i2i000000000000000000000i6−i6i6−i66−66−600000000000000000000000
χ6444-4-44-4-44-20000-222-222-200004i−4i00−2i2i−2i2i000000000000000000000−i6i6−i6i6−66−6600000000000000000000000
χ6544-4-44-4-44-20000-222-222-20000−4i4i002i−2i2i−2i000000000000000000000i6−i6i6−i6−66−6600000000000000000000000
χ6644-4-44-4-44-20000-222-222-20000−4i4i002i−2i2i−2i000000000000000000000−i6i6−i6i66−66−600000000000000000000000
χ674-4444-4-4-44-444-4-444-4-4-44000000-440000-4400000000000000000000000000000000000000000000000000
χ684-4444-4-4-4-2-444-42-2-2222-20000002-22323−23−232-2000000000−2323000000000000000000000000000000000000000
χ694-4444-4-4-4-2-444-42-2-2222-20000002-2−23−2323232-200000000023−23000000000000000000000000000000000000000
χ704-44-4-44-4440000-44-444-4-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ714-44-4-44-4440000-44-444-4-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ724-4-44-4-4444-44-44-4-444-44-4000000-4400004-400000000000000000000000000000000000000000000000000
χ734-4-44-4-444-24-44-422-2-22-224i−4i−4i4i00-2200002-200000000000−2i2i2i−2i00000000000000000000000000000000000
χ744-4-44-4-444-24-44-422-2-22-22−4i4i4i−4i00-2200002-2000000000002i−2i−2i2i00000000000000000000000000000000000
χ754-4-44-4-444-2-44-4422-2-22-220000002-20000-2200000000000000023−23−23230000000000000000000000000000000
χ764-4-44-4-444-2-44-4422-2-22-220000002-20000-22000000000000000−232323−230000000000000000000000000000000
χ774-4-4-4444-440000-4-4-4-4444000000000000000000022−22000000000000000022−22−222200000000000000000000000
χ784-4-4-4444-440000-4-4-4-44440000000000000000000−22220000000000000000−222222−2200000000000000000000000
χ794-4-4-4444-4-200002222-2-2-200000000−2i32i32i3−2i3000000022−22000000000000i6−i6−i6i6−222−200000000000000000000000
χ804-4-4-4444-4-200002222-2-2-200000000−2i32i32i3−2i30000000−2222000000000000−i6i6i6−i62−2−2200000000000000000000000
χ814-4-4-4444-4-200002222-2-2-2000000002i3−2i3−2i32i3000000022−22000000000000−i6i6i6−i6−222−200000000000000000000000
χ824-4-4-4444-4-200002222-2-2-2000000002i3−2i3−2i32i30000000−2222000000000000i6−i6−i6i62−2−2200000000000000000000000
χ83888-8-8-88-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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