Finite Group Databasebeta

← Group #10858085

Character table — Group #10858085

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1
χ71111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ911111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-1-1-1-11111-1-111-1
χ1011111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-111-1-11
χ1111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-11-1-111-1-1-1-1-11111-1-11
χ1211111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11111111-1-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-111-1-111-111-1-111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-11-1-111-1-1111
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-22222-200-2000000-2-2000000000000000022-2-2220000000-2000000000
χ18222222222-2-2-2-22222222220000-2-2-22222-200-2000000-2-20000000000000000-2-222-2-200000002000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200200000022000000000000000022-2-2-2-200000002000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000220000000000000000-2-222220000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-22222-2-2111111-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-2-2-2-2-222111111-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-222-2-22211-1-1-1-111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-2-2-222-2-211-1-1-1-11111-1-1-1-11111000000211-1-1000000000000
χ2922-222-2-2-2222-2-22-22-2-22-200000022-20000-22-200000000022-2-20000000000002-22-200000002-20000000000
χ3022-222-2-2-2222-2-22-22-2-22-200000022-20000-22-200000000022-2-2000000000000-22-220000000-220000000000
χ3122-222-2-2-2222-2-22-22-2-22-200000022-20000-2-22000000000-2-2220000000000002-22-20000000-220000000000
χ3222-222-2-2-2222-2-22-22-2-22-200000022-20000-2-22000000000-2-222000000000000-22-2200000002-20000000000
χ3322-222-2-2-22-2-2222-22-2-22-2002i2i−2i−2i-2-22000020000000000000002i2i−2i−2i000000002-2-220000000000002i−2i00000
χ3422-222-2-2-22-2-2222-22-2-22-2002i2i−2i−2i-2-22000020000000000000002i2i−2i−2i00000000-222-2000000000000−2i2i00000
χ3522-222-2-2-22-2-2222-22-2-22-200−2i−2i2i2i-2-2200002000000000000000−2i−2i2i2i000000002-2-22000000000000−2i2i00000
χ3622-222-2-2-22-2-2222-22-2-22-200−2i−2i2i2i-2-2200002000000000000000−2i−2i2i2i00000000-222-20000000000002i−2i00000
χ372-22-222-2-222-2-22-2-2222-2-2002i−2i2i−2i2-2-2000020002i−2i2-2000000002i−2i2i−2i22-2-2000000000002i−2i00000000000000
χ382-22-222-2-222-2-22-2-2222-2-2002i−2i2i−2i2-2-200002000−2i2i-22000000002i−2i2i−2i-2-22200000000000−2i2i00000000000000
χ392-22-222-2-222-2-22-2-2222-2-200−2i2i−2i2i2-2-2000020002i−2i-2200000000−2i2i−2i2i-2-222000000000002i−2i00000000000000
χ402-22-222-2-222-2-22-2-2222-2-200−2i2i−2i2i2-2-200002000−2i2i2-200000000−2i2i−2i2i22-2-200000000000−2i2i00000000000000
χ412-22-222-2-2-12-2-2211-1-1-111002i−2i2i−2i-111−i3−i3i3i3-10002i−2i2-200−i3i33−33−3−ii−ii-1-111−i3−i3i3i30000000−ii3−3000000000000
χ422-22-222-2-2-12-2-2211-1-1-111002i−2i2i−2i-111−i3−i3i3i3-1000−2i2i-2200−i3i33−33−3−ii−ii11-1-1i3i3−i3−i30000000i−i−33000000000000
χ432-22-222-2-2-12-2-2211-1-1-111002i−2i2i−2i-111i3i3−i3−i3-10002i−2i2-200i3−i3−33−33−ii−ii-1-111i3i3−i3−i30000000−ii−33000000000000
χ442-22-222-2-2-12-2-2211-1-1-111002i−2i2i−2i-111i3i3−i3−i3-1000−2i2i-2200i3−i3−33−33−ii−ii11-1-1−i3−i3i3i30000000i−i3−3000000000000
χ452-22-222-2-2-12-2-2211-1-1-11100−2i2i−2i2i-111−i3−i3i3i3-10002i−2i-2200−i3i3−33−33i−ii−i11-1-1i3i3−i3−i30000000−ii3−3000000000000
χ462-22-222-2-2-12-2-2211-1-1-11100−2i2i−2i2i-111−i3−i3i3i3-1000−2i2i2-200−i3i3−33−33i−ii−i-1-111−i3−i3i3i30000000i−i−33000000000000
χ472-22-222-2-2-12-2-2211-1-1-11100−2i2i−2i2i-111i3i3−i3−i3-10002i−2i-2200i3−i33−33−3i−ii−i11-1-1−i3−i3i3i30000000−ii−33000000000000
χ482-22-222-2-2-12-2-2211-1-1-11100−2i2i−2i2i-111i3i3−i3−i3-1000−2i2i2-200i3−i33−33−3i−ii−i-1-111i3i3−i3−i30000000i−i3−3000000000000
χ492-2-2-22-2222-22-22-222-2-2-22002-2-22-22-2000020000000000000002-2-2200000000000000000000002-200002-20
χ502-2-2-22-2222-22-22-222-2-2-22002-2-22-22-2000020000000000000002-2-220000000000000000000000-220000-220
χ512-2-2-22-2222-22-22-222-2-2-2200-222-2-22-200002000000000000000-222-200000000000000000000002-20000-220
χ522-2-2-22-2222-22-22-222-2-2-2200-222-2-22-200002000000000000000-222-20000000000000000000000-2200002-20
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222-2-2-2-2200-400000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222004000000-2-2000000000000000000000000000000000000000
χ55444-4-4-44-44000044-44-4-4-400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ56444-4-4-44-44000044-44-4-4-4000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ57444-4-4-44-4-20000-2-22-2222000000000−2i32i3−2i32i30000000022−220000000000i6−i6i6−i6−22−2200000000000000000000000
χ58444-4-4-44-4-20000-2-22-2222000000000−2i32i3−2i32i300000000−22220000000000−i6i6−i6i62−22−200000000000000000000000
χ59444-4-4-44-4-20000-2-22-22220000000002i3−2i32i3−2i30000000022−220000000000−i6i6−i6i6−22−2200000000000000000000000
χ60444-4-4-44-4-20000-2-22-22220000000002i3−2i32i3−2i300000000−22220000000000i6−i6i6−i62−22−200000000000000000000000
χ6144-444-4-4-4-244-4-4-22-222-22000000-2-22000024-4000000000-2-22200000000000000000000000000000000000
χ6244-444-4-4-4-244-4-4-22-222-22000000-2-2200002-4400000000022-2-200000000000000000000000000000000000
χ6344-444-4-4-4-2-4-444-22-222-22004i4i−4i−4i22-20000-2000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6444-444-4-4-4-2-4-444-22-222-2200−4i−4i4i4i22-20000-20000000000000002i2i−2i−2i0000000000000000000000000000000
χ6544-4-4-44-44400004-4-4-44-440000000000000000000000000000000000000000000000000000000000022−22000
χ6644-4-4-44-44400004-4-4-44-4400000000000000000000000000000000000000000000000000000000000−2222000
χ674-444-4-4-4440000-4-4-44-4444-400000004-4-44000000000000000000000000000000000000000000000000000
χ684-444-4-4-4440000-4-4-44-444-440000000-444-4000000000000000000000000000000000000000000000000000
χ694-444-4-4-44-20000222-22-2-24-40000000-222-200000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ704-444-4-4-44-20000222-22-2-24-40000000-222-200000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ714-444-4-4-44-20000222-22-2-2-4400000002-2-2200000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ724-444-4-4-44-20000222-22-2-2-4400000002-2-2200000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ734-44-444-4-44-444-4-4-4444-4-4000000-4440000-400000000000000000000000000000000000000000000000000
χ744-44-444-4-4-2-444-422-2-2-2220000002-2-2−2i3−2i32i32i320000000002i3−2i3000000000000000000000000000000000000000
χ754-44-444-4-4-2-444-422-2-2-2220000002-2-22i32i3−2i3−2i32000000000−2i32i3000000000000000000000000000000000000000
χ764-4-44-444-440000-44-4-444-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ774-4-44-444-440000-44-4-444-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ784-4-4-44-44444-44-4-444-4-4-440000004-440000-400000000000000000000000000000000000000000000000000
χ794-4-4-44-444-24-44-42-2-2222-2000000-22-2000020000000000023−23−232300000000000000000000000000000000000
χ804-4-4-44-444-24-44-42-2-2222-2000000-22-20000200000000000−232323−2300000000000000000000000000000000000
χ814-4-4-44-444-2-44-442-2-2222-2004-4-442-220000-2000000000000000-222-20000000000000000000000000000000
χ824-4-4-44-444-2-44-442-2-2222-200-444-42-220000-20000000000000002-2-220000000000000000000000000000000
χ8388-8-8-88-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

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