Finite Group Databasebeta

← Group #10858374

Character table — Group #10858374

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666222244121212121212121244444666688881212121212122424242424242424444444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ5111111111111111111111111-1-1111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-111-1-111-1-1-11111-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-1-1-1111
χ7111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-1-1-111-1-1111
χ8111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-11111111-1-111-1-1-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-111-111-1-111-111-1-1-1-111-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-111-1-1-1-11-1-11111-1-11
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111111-1-111-1-111-1
χ17222222222-2-2-2-22222222000022-2-2-22222-2-2000000000000-2-200000000000022-2-2-2-200000002000000000
χ18222222222-2-2-2-22222222000022-2-2-22222-2-2000000000000-2-2000000000000-2-222220000000-2000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-22000000000000220000000000002222-2-20000000-2000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000000022000000000000-2-2-2-22200000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-222-1-1-1-122-2-2111111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-2-2-2-1-1-1-1-2-2221111111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-222221111-2-22211-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-222-2-2111122-2-211-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-22-2-2-222-22-222-2-22-2-222-2-20022-20000-20000022-2-2000000000000000000000000000002-2000002-2000
χ30222-22-2-2-222-22-222-2-22-2-222-2-20022-20000-20000022-2-200000000000000000000000000000-2200000-22000
χ31222-22-2-2-222-22-222-2-22-2-2-2-2220022-20000-200000-2-222000000000000000000000000000002-200000-22000
χ32222-22-2-2-222-22-222-2-22-2-2-2-2220022-20000-200000-2-22200000000000000000000000000000-22000002-2000
χ332-2-222-2-222-222-2-2-2-2-22222-22-2002-2-2000020002-22-22-22-20000000022-2-2000000000002-200000000000000
χ342-2-222-2-222-222-2-2-2-2-22222-22-2002-2-200002000-222-22-2-2200000000-2-22200000000000-2200000000000000
χ352-2-222-2-222-222-2-2-2-2-2222-22-22002-2-2000020002-2-22-22-2200000000-2-222000000000002-200000000000000
χ362-2-222-2-222-222-2-2-2-2-2222-22-22002-2-200002000-22-22-222-20000000022-2-200000000000-2200000000000000
χ372-2-222-2-22-1-222-21111-1-1-12-22-200-111−i3−i3i3i3-10002-2-11-112-200−i3i3−i3−i3i3i3-1-111−i3−i3i3i30000000-11−i3i3000000000000
χ382-2-222-2-22-1-222-21111-1-1-12-22-200-111−i3−i3i3i3-1000-22-11-11-2200−i3i3−i3−i3i3i311-1-1i3i3−i3−i300000001-1i3−i3000000000000
χ392-2-222-2-22-1-222-21111-1-1-12-22-200-111i3i3−i3−i3-10002-2-11-112-200i3−i3i3i3−i3−i3-1-111i3i3−i3−i30000000-11i3−i3000000000000
χ402-2-222-2-22-1-222-21111-1-1-12-22-200-111i3i3−i3−i3-1000-22-11-11-2200i3−i3i3i3−i3−i311-1-1−i3−i3i3i300000001-1−i3i3000000000000
χ412-2-222-2-22-1-222-21111-1-1-1-22-2200-111−i3−i3i3i3-10002-21-11-1-2200−i3i3i3i3−i3−i311-1-1i3i3−i3−i30000000-11−i3i3000000000000
χ422-2-222-2-22-1-222-21111-1-1-1-22-2200-111−i3−i3i3i3-1000-221-11-12-200−i3i3i3i3−i3−i3-1-111−i3−i3i3i300000001-1i3−i3000000000000
χ432-2-222-2-22-1-222-21111-1-1-1-22-2200-111i3i3−i3−i3-10002-21-11-1-2200i3−i3−i3−i3i3i311-1-1−i3−i3i3i30000000-11i3−i3000000000000
χ442-2-222-2-22-1-222-21111-1-1-1-22-2200-111i3i3−i3−i3-1000-221-11-12-200i3−i3−i3−i3i3i3-1-111i3i3−i3−i300000001-1−i3i3000000000000
χ452-2-2-2222-2222-2-2-2-2222-2-2000000-22-20000202i−2i0000000000002i−2i2i−2i000000002i−2i002i−2i000000002-20000000
χ462-2-2-2222-2222-2-2-2-2222-2-2000000-22-20000202i−2i0000000000002i−2i2i−2i00000000−2i2i00−2i2i00000000-220000000
χ472-2-2-2222-2222-2-2-2-2222-2-2000000-22-2000020−2i2i000000000000−2i2i−2i2i000000002i−2i002i−2i00000000-220000000
χ482-2-2-2222-2222-2-2-2-2222-2-2000000-22-2000020−2i2i000000000000−2i2i−2i2i00000000−2i2i00−2i2i000000002-20000000
χ492-2-2-2222-22-2-222-2-2222-2-22-2-22002-220000-2000002-2-220000000000000000002i−2i00−2i2i00000000002i−2i00000
χ502-2-2-2222-22-2-222-2-2222-2-22-2-22002-220000-2000002-2-22000000000000000000−2i2i002i−2i0000000000−2i2i00000
χ512-2-2-2222-22-2-222-2-2222-2-2-222-2002-220000-200000-222-20000000000000000002i−2i00−2i2i0000000000−2i2i00000
χ522-2-2-2222-22-2-222-2-2222-2-2-222-2002-220000-200000-222-2000000000000000000−2i2i002i−2i00000000002i−2i00000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044222-2-2-2-22-40000000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222224000000000000-2-200000000000000000000000000000000000
χ55444-44-4-4-44-44-4444-4-44-4-4000000-4-440000400000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-24-44-4-2-222-22244-4-400-2-220000200000-2-22200000000000000000000000000000000000000000
χ57444-44-4-4-4-24-44-4-2-222-222-4-44400-2-22000020000022-2-200000000000000000000000000000000000000000
χ58444-44-4-4-4-2-44-44-2-222-22200000022-20000-200000000000000023−23−23230000000000000000000000000000000
χ59444-44-4-4-4-2-44-44-2-222-22200000022-20000-2000000000000000−232323−230000000000000000000000000000000
χ6044-44-44-4-4400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000022−220
χ6144-44-44-4-4400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000−22220
χ6244-4-4-4-444400004-4-44-4-4400004-40004-44-4000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444400004-4-44-4-440000-44000-44-44000000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-20000-222-222-200004-4000-22-2200000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ6544-4-4-4-444-20000-222-222-200004-4000-22-2200000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ6644-4-4-4-444-20000-222-222-20000-440002-22-200000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ6744-4-4-4-444-20000-222-222-20000-440002-22-200000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ684-444-4-44-440000-44-44-44-400000000000000000000000000000000000000000004-40000000000000000000
χ694-444-4-44-440000-44-44-44-40000000000000000000000000000000000000000000-440000000000000000000
χ704-44-4-44-4440000-444-4-4-44000000000000000000000000022−22000000000022−22−222200000000000000000000000
χ714-44-4-44-4440000-444-4-4-440000000000000000000000000−22220000000000−222222−2200000000000000000000000
χ724-44-4-44-44-200002-2-2222-2000000000−2i32i32i3−2i300000000000022−22000000−i6i6i6−i6−222−200000000000000000000000
χ734-44-4-44-44-200002-2-2222-2000000000−2i32i32i3−2i3000000000000−2222000000i6−i6−i6i62−2−2200000000000000000000000
χ744-44-4-44-44-200002-2-2222-20000000002i3−2i3−2i32i300000000000022−22000000i6−i6−i6i6−222−200000000000000000000000
χ754-44-4-44-44-200002-2-2222-20000000002i3−2i3−2i32i3000000000000−2222000000−i6i6i6−i62−2−2200000000000000000000000
χ764-4-444-4-4444-4-44-4-4-4-4444000000-4440000-400000000000000000000000000000000000000000000000000
χ774-4-444-4-44-24-4-442222-2-2-20000002-2-2−2i3−2i32i32i3200000000000002i3−2i300000000000000000000000000000000000
χ784-4-444-4-44-24-4-442222-2-2-20000002-2-22i32i3−2i3−2i320000000000000−2i32i300000000000000000000000000000000000
χ794-4-4-4444-4-244-4-422-2-2-2220000002-220000-204i−4i000000000000−2i2i−2i2i0000000000000000000000000000000
χ804-4-4-4444-4-244-4-422-2-2-2220000002-220000-20−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000
χ814-4-4-4444-4-2-4-44422-2-2-2224-4-4400-22-20000200000-222-200000000000000000000000000000000000000000
χ824-4-4-4444-4-2-4-44422-2-2-222-444-400-22-200002000002-2-2200000000000000000000000000000000000000000
χ8388-88-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-88-8-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000

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