Finite Group Databasebeta

← Group #10849336

Character table — Group #10849336

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666444444121212121212121222444666688881212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111
χ5111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-111-1-11111-1-1-111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1111-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1111-1-11111-1-1-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11-1-111-1-11111111-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-11-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-11111-1-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-111-1-1-1-1111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-111-1-1-1-111-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-1-1111111-1-11-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-200000000000022-2-2-2-200000000000200000
χ18222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-2000000000000-2-2222200000000000-200000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-20000200000000220000000000002222-2-200000000000-200000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000000022000000000000-2-2-2-22200000000000200000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-222-2111122-2-211-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-21111-2-22211-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-2-1-1-1-1-2-2221111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-2-2-1-1-1-122-2-2111111-1-1-1-11111000000211-1-1000000000000
χ2922-22-22-2-22-2-2222-2-22-22-22i2i−2i−2i002-200002-2002-2000002i−2i00002i2i−2i−2i2i2i−2i−2i000000000002-200000000000000
χ3022-22-22-2-22-2-2222-2-22-22-22i2i−2i−2i002-200002-200-2200000−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000-2200000000000000
χ3122-22-22-2-22-2-2222-2-22-22-2−2i−2i2i2i002-200002-2002-200000−2i2i0000−2i−2i2i2i−2i−2i2i2i000000000002-200000000000000
χ3222-22-22-2-22-2-2222-2-22-22-2−2i−2i2i2i002-200002-200-22000002i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000-2200000000000000
χ3322-22-22-2-2-1-2-222-111-11-112i2i−2i−2i00-1133−3−3-11002-20−i3−i3i3i32i−2i003−3−i−iii−i−iii−i3−i3i3i30000000-113−3000000000000
χ3422-22-22-2-2-1-2-222-111-11-112i2i−2i−2i00-1133−3−3-1100-220−i3−i3i3i3−2i2i003−3−i−iiiii−i−ii3i3−i3−i300000001-1−33000000000000
χ3522-22-22-2-2-1-2-222-111-11-112i2i−2i−2i00-11−3−333-11002-20i3i3−i3−i32i−2i00−33−i−iii−i−iiii3i3−i3−i30000000-11−33000000000000
χ3622-22-22-2-2-1-2-222-111-11-112i2i−2i−2i00-11−3−333-1100-220i3i3−i3−i3−2i2i00−33−i−iiiii−i−i−i3−i3i3i300000001-13−3000000000000
χ3722-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i00-1133−3−3-11002-20i3i3−i3−i3−2i2i003−3ii−i−iii−i−ii3i3−i3−i30000000-113−3000000000000
χ3822-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i00-1133−3−3-1100-220i3i3−i3−i32i−2i003−3ii−i−i−i−iii−i3−i3i3i300000001-1−33000000000000
χ3922-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i00-11−3−333-11002-20−i3−i3i3i3−2i2i00−33ii−i−iii−i−i−i3−i3i3i30000000-11−33000000000000
χ4022-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i00-11−3−333-1100-220−i3−i3i3i32i−2i00−33ii−i−i−i−iiii3i3−i3−i300000001-13−3000000000000
χ412-22-222-2-22-22-22-2222-2-2-22i−2i2i−2i00-2-20000220000000000000002i−2i2i−2i0000000000000000000002-20002i−2i000
χ422-22-222-2-22-22-22-2222-2-2-22i−2i2i−2i00-2-20000220000000000000002i−2i2i−2i000000000000000000000-22000−2i2i000
χ432-22-222-2-22-22-22-2222-2-2-2−2i2i−2i2i00-2-2000022000000000000000−2i2i−2i2i0000000000000000000002-2000−2i2i000
χ442-22-222-2-22-22-22-2222-2-2-2−2i2i−2i2i00-2-2000022000000000000000−2i2i−2i2i000000000000000000000-220002i−2i000
χ452-2-2-2-222222-2-22-2-2-222-222-2-2200-2200002-20000000000000002-2-22000000002-2002-2000002-20000000000
χ462-2-2-2-222222-2-22-2-2-222-222-2-2200-2200002-20000000000000002-2-2200000000-2200-2200000-220000000000
χ472-2-2-2-222222-2-22-2-2-222-22-222-200-2200002-2000000000000000-222-2000000002-2002-200000-220000000000
χ482-2-2-2-222222-2-22-2-2-222-22-222-200-2200002-2000000000000000-222-200000000-2200-22000002-20000000000
χ492-2-2-2-22222-222-2-2-2-222-220000002-20000-222-20002-22-20000000000000000002-200-220000000002-2000000
χ502-2-2-2-22222-222-2-2-2-222-220000002-20000-222-20002-22-2000000000000000000-22002-2000000000-22000000
χ512-2-2-2-22222-222-2-2-2-222-220000002-20000-22-22000-22-220000000000000000002-200-22000000000-22000000
χ522-2-2-2-22222-222-2-2-2-222-220000002-20000-22-22000-22-22000000000000000000-22002-20000000002-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-2220000-4000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222220000400000000-2-200000000000000000000000000000000000
χ55444-4-4-44-44000044-4-44-4-400000000000000000000000000000000000000000004-40000000000000000000
χ56444-4-4-44-44000044-4-44-4-40000000000000000000000000000000000000000000-440000000000000000000
χ5744-44-44-4-4444-4-44-4-44-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ5844-44-44-4-4-244-4-4-222-22-220000002-22323−23−232-20000000000000−232300000000000000000000000000000000000
χ5944-44-44-4-4-244-4-4-222-22-220000002-2−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ6044-4-44-4-44400004-44-4-4-44000000000000000000000000000000000000000000000000000000000000022−220
χ6144-4-44-4-44400004-44-4-4-440000000000000000000000000000000000000000000000000000000000000−22220
χ624-444-4-4-4440000-44-4-4-444000000000000000000000000022−22000000000022−2222−2200000000000000000000000
χ634-444-4-4-4440000-44-4-4-4440000000000000000000000000−22220000000000−2222−222200000000000000000000000
χ644-444-4-4-44-200002-2222-2-200000000−2i32i3−2i32i3000000000000022−22000000i6−i6i6−i6−22−2200000000000000000000000
χ654-444-4-4-44-200002-2222-2-200000000−2i32i3−2i32i30000000000000−2222000000−i6i6−i6i62−22−200000000000000000000000
χ664-444-4-4-44-200002-2222-2-2000000002i3−2i32i3−2i3000000000000022−22000000−i6i6−i6i6−22−2200000000000000000000000
χ674-444-4-4-44-200002-2222-2-2000000002i3−2i32i3−2i30000000000000−2222000000i6−i6i6−i62−22−200000000000000000000000
χ684-44-444-4-444-44-4-4444-4-4-4000000440000-4-400000000000000000000000000000000000000000000000000
χ694-44-444-4-4-24-44-42-2-2-2222000000-2-200002200000−2i32i32i3−2i300000000000000000000000000000000000000000
χ704-44-444-4-4-24-44-42-2-2-2222000000-2-2000022000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ714-44-444-4-4-2-44-442-2-2-22224i−4i4i−4i00220000-2-2000000000000000−2i2i−2i2i0000000000000000000000000000000
χ724-44-444-4-4-2-44-442-2-2-2222−4i4i−4i4i00220000-2-20000000000000002i−2i2i−2i0000000000000000000000000000000
χ734-4-444-44-440000-4-44-444-400004i−4i004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ744-4-444-44-440000-4-44-444-40000−4i4i00−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ754-4-444-44-4-2000022-22-2-2200004i−4i00−2i2i2i−2i0000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ764-4-444-44-4-2000022-22-2-2200004i−4i00−2i2i2i−2i000000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ774-4-444-44-4-2000022-22-2-220000−4i4i002i−2i−2i2i0000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ784-4-444-44-4-2000022-22-2-220000−4i4i002i−2i−2i2i000000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ794-4-4-4-4444-24-4-44222-2-22-24-4-44002-20000-22000000000000000-222-20000000000000000000000000000000
χ804-4-4-4-4444-24-4-44222-2-22-2-444-4002-20000-220000000000000002-2-220000000000000000000000000000000
χ814-4-4-4-4444-2-444-4222-2-22-2000000-2200002-24-4000-22-2200000000000000000000000000000000000000000
χ824-4-4-4-4444-2-444-4222-2-22-2000000-2200002-2-440002-22-200000000000000000000000000000000000000000
χ83888-8-8-88-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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