Finite Group Databasebeta

← Group #10840235

Character table — Group #10840235

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666662244446666121212122244488881212121212121212121224242424242424244444444661212244444488884
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
χ51111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-111-1-11111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-11-1-111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-111-1-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-1111-1-1111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-1-11111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1111-1-1-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111111-1-111-1-111-1
χ17222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-200000000000000002222-2-200000-200000000000
χ18222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-20000000000000000-2-2-2-22200000200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200002000022000000000000000022-2-2-2-200000200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000220000000000000000-2-2222200000-200000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
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
χ2922-22-2-2-2222-2-2222-2-22-2-2002i2i−2i−2i00002-22-2000000000002i2i−2i−2i0000000000002-2002-20000002i−2i000000000
χ3022-22-2-2-2222-2-2222-2-22-2-2002i2i−2i−2i00002-22-2000000000002i2i−2i−2i000000000000-2200-22000000−2i2i000000000
χ3122-22-2-2-2222-2-2222-2-22-2-200−2i−2i2i2i00002-22-200000000000−2i−2i2i2i0000000000002-2002-2000000−2i2i000000000
χ3222-22-2-2-2222-2-2222-2-22-2-200−2i−2i2i2i00002-22-200000000000−2i−2i2i2i000000000000-2200-220000002i−2i000000000
χ3322-22-2-2-222-222-222-2-22-2-20000000000-22-22002i−2i000000000002i2i−2i−2i000000002-200-22000000002i−2i0000000
χ3422-22-2-2-222-222-222-2-22-2-20000000000-22-22002i−2i000000000002i2i−2i−2i00000000-22002-200000000−2i2i0000000
χ3522-22-2-2-222-222-222-2-22-2-20000000000-22-2200−2i2i00000000000−2i−2i2i2i000000002-200-2200000000−2i2i0000000
χ3622-22-2-2-222-222-222-2-22-2-20000000000-22-2200−2i2i00000000000−2i−2i2i2i00000000-22002-2000000002i−2i0000000
χ372-2222-2-2-2222-2-2-2-22-22-22002-22-200002-2-22000000000002-22-200000000000000000000000000002i−2i2i−2i000
χ382-2222-2-2-2222-2-2-2-22-22-22002-22-200002-2-22000000000002-22-20000000000000000000000000000−2i2i−2i2i000
χ392-2222-2-2-2222-2-2-2-22-22-2200-22-2200002-2-2200000000000-22-2200000000000000000000000000002i−2i−2i2i000
χ402-2222-2-2-2222-2-2-2-22-22-2200-22-2200002-2-2200000000000-22-220000000000000000000000000000−2i2i2i−2i000
χ412-2-22-222-222-22-2-2-2-2222-2002i−2i−2i2i000022-2-22-20002i−2i00002i−2i−2i2i00002i2i−2i−2i000000000002-200000000000000
χ422-2-22-222-222-22-2-2-2-2222-2002i−2i−2i2i000022-2-2-22000−2i2i00002i−2i−2i2i0000−2i−2i2i2i00000000000-2200000000000000
χ432-2-22-222-222-22-2-2-2-2222-200−2i2i2i−2i000022-2-22-2000−2i2i0000−2i2i2i−2i0000−2i−2i2i2i000000000002-200000000000000
χ442-2-22-222-222-22-2-2-2-2222-200−2i2i2i−2i000022-2-2-220002i−2i0000−2i2i2i−2i00002i2i−2i−2i00000000000-2200000000000000
χ452-2-22-222-2-12-22-2111-1-1-11002i−2i−2i2i−i3−i3i3i3-1-1112-20002i−2i00−i3i3−iii−i3−33−3−i−iii33−3−30000000-11−i3i3000000000000
χ462-2-22-222-2-12-22-2111-1-1-11002i−2i−2i2i−i3−i3i3i3-1-111-22000−2i2i00−i3i3−iii−i3−33−3ii−i−i−3−33300000001-1i3−i3000000000000
χ472-2-22-222-2-12-22-2111-1-1-11002i−2i−2i2ii3i3−i3−i3-1-1112-20002i−2i00i3−i3−iii−i−33−33−i−iii−3−3330000000-11i3−i3000000000000
χ482-2-22-222-2-12-22-2111-1-1-11002i−2i−2i2ii3i3−i3−i3-1-111-22000−2i2i00i3−i3−iii−i−33−33ii−i−i33−3−300000001-1−i3i3000000000000
χ492-2-22-222-2-12-22-2111-1-1-1100−2i2i2i−2i−i3−i3i3i3-1-1112-2000−2i2i00−i3i3i−i−ii−33−33ii−i−i−3−3330000000-11−i3i3000000000000
χ502-2-22-222-2-12-22-2111-1-1-1100−2i2i2i−2i−i3−i3i3i3-1-111-220002i−2i00−i3i3i−i−ii−33−33−i−iii33−3−300000001-1i3−i3000000000000
χ512-2-22-222-2-12-22-2111-1-1-1100−2i2i2i−2ii3i3−i3−i3-1-1112-2000−2i2i00i3−i3i−i−ii3−33−3ii−i−i33−3−30000000-11i3−i3000000000000
χ522-2-22-222-2-12-22-2111-1-1-1100−2i2i2i−2ii3i3−i3−i3-1-111-220002i−2i00i3−i3i−i−ii3−33−3−i−iii−3−33300000001-1−i3i3000000000000
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
χ55444-4-44-4-4400004-4-44-4-440000000000000000000000000000000000000000000000000000000000000−2i22i20
χ56444-4-44-4-4400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ5744-44-4-4-44-24-4-44-2-222-222004i4i−4i−4i0000-22-2200000000000−2i−2i2i2i00000000000000000000000000000000000
χ5844-44-4-4-44-24-4-44-2-222-22200−4i−4i4i4i0000-22-22000000000002i2i−2i−2i00000000000000000000000000000000000
χ5944-44-4-4-44-2-444-4-2-222-22200000000002-22-2004i−4i00000000000−2i−2i2i2i0000000000000000000000000000000
χ6044-44-4-4-44-2-444-4-2-222-22200000000002-22-200−4i4i000000000002i2i−2i−2i0000000000000000000000000000000
χ6144-4-44-44-4400004-44-4-44-4000000000000000000000−2i22i200000000000000−2i22i2−2i22i200000000000000000000000
χ6244-4-44-44-4400004-44-4-44-40000000000000000000002i2−2i2000000000000002i2−2i22i2−2i200000000000000000000000
χ6344-4-44-44-4-20000-22-222-22000000−2i32i3−2i32i300000000000−2i22i200000000006−66−6i2−i2i2−i200000000000000000000000
χ6444-4-44-44-4-20000-22-222-22000000−2i32i3−2i32i3000000000002i2−2i20000000000−66−66−i2i2−i2i200000000000000000000000
χ6544-4-44-44-4-20000-22-222-220000002i3−2i32i3−2i300000000000−2i22i20000000000−66−66i2−i2i2−i200000000000000000000000
χ6644-4-44-44-4-20000-22-222-220000002i3−2i32i3−2i3000000000002i2−2i200000000006−66−6−i2i2−i2i200000000000000000000000
χ674-4444-4-4-44-4-444-4-44-44-440000000000-444-400000000000000000000000000000000000000000000000000
χ684-4444-4-4-4-244-4-422-22-22-2004-44-40000-222-200000000000-22-2200000000000000000000000000000000000
χ694-4444-4-4-4-244-4-422-22-22-200-44-440000-222-2000000000002-22-200000000000000000000000000000000000
χ704-4444-4-4-4-2-4-44422-22-22-200000000002-2-22000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ714-4444-4-4-4-2-4-44422-22-22-200000000002-2-220000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ724-44-4-4-44440000-44-4-4-4444-400004-4-44000000000000000000000000000000000000000000000000000000
χ734-44-4-4-44440000-44-4-4-444-440000-444-4000000000000000000000000000000000000000000000000000000
χ744-44-4-4-444-200002-2222-2-24-40000-222-200000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ754-44-4-4-444-200002-2222-2-24-40000-222-200000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ764-44-4-4-444-200002-2222-2-2-4400002-2-2200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ774-44-4-4-444-200002-2222-2-2-4400002-2-2200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ784-4-44-444-44-44-44-4-4-4444-40000000000-4-44400000000000000000000000000000000000000000000000000
χ794-4-44-444-4-2-44-44222-2-2-22000000−2i3−2i32i32i322-2-20000000002i3−2i3000000000000000000000000000000000000000
χ804-4-44-444-4-2-44-44222-2-2-220000002i32i3−2i3−2i322-2-2000000000−2i32i3000000000000000000000000000000000000000
χ814-4-4-444-4440000-4444-4-4-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ824-4-4-444-4440000-4444-4-4-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ83888-8-88-8-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000

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