Finite Group Databasebeta

← Group #10849295

Character table — Group #10849295

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111
χ5111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-111-1-11111-1-1-111-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1111-1-1111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-11111111-1-1-1
χ911111111111111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-111-1-11-1-1-1-11
χ1011111111111111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-111-1-1-1-1111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111-1-1-1-111-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111111-1-11-1-111-1
χ17222222222-2-2-2-222222220000222222-2-2-2-20000-2000000000000-2-20000000022-2-22200000000000-200000
χ18222222222-2-2-2-222222220000222222-2-2-2-20000-2000000000000-2-200000000-2-222-2-200000000000200000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200002000000000000220000000022-2-2-2-200000000000200000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000000000002200000000-2-2222200000000000-200000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-122-2-2-222-2-21111-1-1-1-111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-2-2-2221111-1-1-1-1111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-122-2-22-2-2-2-211111111-1-1111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-22222211111111-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2-222-1-1-1-11111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-222-222-2-2-1-1-1-1111111-1-1-1-11111000000211-1-1000000000000
χ2922-22-22-2-22-2-2222-2-2-222-22i2i−2i−2i0000002-22-22-20002i−2i0000002i2i−2i−2i002i2i−2i−2i000000000002-200000000000000
χ3022-22-22-2-22-2-2222-2-2-222-22i2i−2i−2i0000002-22-2-22000−2i2i0000002i2i−2i−2i00−2i−2i2i2i00000000000-2200000000000000
χ3122-22-22-2-22-2-2222-2-2-222-2−2i−2i2i2i0000002-22-22-2000−2i2i000000−2i−2i2i2i00−2i−2i2i2i000000000002-200000000000000
χ3222-22-22-2-22-2-2222-2-2-222-2−2i−2i2i2i0000002-22-2-220002i−2i000000−2i−2i2i2i002i2i−2i−2i00000000000-2200000000000000
χ3322-22-22-2-2-1-2-222-1111-1-112i2i−2i−2i0033−3−3-11-112-20002i−2i00−i3−i3i3i3−i−iii3−3−i−iii−i3−i3i3i30000000-113−3000000000000
χ3422-22-22-2-2-1-2-222-1111-1-112i2i−2i−2i0033−3−3-11-11-22000−2i2i00−i3−i3i3i3−i−iii3−3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ3522-22-22-2-2-1-2-222-1111-1-112i2i−2i−2i00−3−333-11-112-20002i−2i00i3i3−i3−i3−i−iii−33−i−iiii3i3−i3−i30000000-11−33000000000000
χ3622-22-22-2-2-1-2-222-1111-1-112i2i−2i−2i00−3−333-11-11-22000−2i2i00i3i3−i3−i3−i−iii−33ii−i−i−i3−i3i3i300000001-13−3000000000000
χ3722-22-22-2-2-1-2-222-1111-1-11−2i−2i2i2i0033−3−3-11-112-2000−2i2i00i3i3−i3−i3ii−i−i3−3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ3822-22-22-2-2-1-2-222-1111-1-11−2i−2i2i2i0033−3−3-11-11-220002i−2i00i3i3−i3−i3ii−i−i3−3−i−iii−i3−i3i3i300000001-1−33000000000000
χ3922-22-22-2-2-1-2-222-1111-1-11−2i−2i2i2i00−3−333-11-112-2000−2i2i00−i3−i3i3i3ii−i−i−33ii−i−i−i3−i3i3i30000000-11−33000000000000
χ4022-22-22-2-2-1-2-222-1111-1-11−2i−2i2i2i00−3−333-11-11-220002i−2i00−i3−i3i3i3ii−i−i−33−i−iiii3i3−i3−i300000001-13−3000000000000
χ412-22-222-2-22-22-22-222-2-22-22i−2i2i−2i000000-2-22200000000000002i−2i2i−2i000000000000000000000002-20002i−2i000
χ422-22-222-2-22-22-22-222-2-22-22i−2i2i−2i000000-2-22200000000000002i−2i2i−2i00000000000000000000000-22000−2i2i000
χ432-22-222-2-22-22-22-222-2-22-2−2i2i−2i2i000000-2-2220000000000000−2i2i−2i2i000000000000000000000002-2000−2i2i000
χ442-22-222-2-22-22-22-222-2-22-2−2i2i−2i2i000000-2-2220000000000000−2i2i−2i2i00000000000000000000000-220002i−2i000
χ452-2-2-2-222222-2-22-2-2-22-2222-2-22000000-222-200000000000002-2-2200000000002-22-200000002-20000000000
χ462-2-2-2-222222-2-22-2-2-22-2222-2-22000000-222-200000000000002-2-220000000000-22-220000000-220000000000
χ472-2-2-2-222222-2-22-2-2-22-222-222-2000000-222-20000000000000-222-200000000002-22-20000000-220000000000
χ482-2-2-2-222222-2-22-2-2-22-222-222-2000000-222-20000000000000-222-20000000000-22-2200000002-20000000000
χ492-2-2-2-22222-222-2-2-2-22-22200000000002-2-22002-2000002-22-2000000000000002-2-22000000000002-2000000
χ502-2-2-2-22222-222-2-2-2-22-22200000000002-2-22002-2000002-22-200000000000000-222-200000000000-22000000
χ512-2-2-2-22222-222-2-2-2-22-22200000000002-2-2200-2200000-22-22000000000000002-2-2200000000000-22000000
χ522-2-2-2-22222-222-2-2-2-22-22200000000002-2-2200-2200000-22-2200000000000000-222-2000000000002-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-222220000-4000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222200004000000000000-2-20000000000000000000000000000000
χ55444-4-4-4-444000044-44-4-4-400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ56444-4-4-4-444000044-44-4-4-4000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ57444-4-4-4-44-20000-2-22-2222000000−2i32i3−2i32i30000000000022−220000000000i6−i6i6−i6−22−2200000000000000000000000
χ58444-4-4-4-44-20000-2-22-2222000000−2i32i3−2i32i300000000000−22220000000000−i6i6−i6i62−22−200000000000000000000000
χ59444-4-4-4-44-20000-2-22-22220000002i3−2i32i3−2i30000000000022−220000000000−i6i6−i6i6−22−2200000000000000000000000
χ60444-4-4-4-44-20000-2-22-22220000002i3−2i32i3−2i300000000000−22220000000000i6−i6i6−i62−22−200000000000000000000000
χ6144-44-44-4-4444-4-44-4-4-444-40000000000-44-4400000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-244-4-4-2222-2-220000002323−23−232-22-200000000000000000−23230000000000000000000000000000000
χ6344-44-44-4-4-244-4-4-2222-2-22000000−23−2323232-22-20000000000000000023−230000000000000000000000000000000
χ6444-4-44-44-4400004-44-4-4-4400004i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ6544-4-44-44-4400004-44-4-4-440000−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ6644-4-44-44-4-20000-22-2222-200004i−4i−2i2i2i−2i000000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ6744-4-44-44-4-20000-22-2222-200004i−4i−2i2i2i−2i00000000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ6844-4-44-44-4-20000-22-2222-20000−4i4i2i−2i−2i2i000000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ6944-4-44-44-4-20000-22-2222-20000−4i4i2i−2i−2i2i00000000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ704-444-4-44-440000-44-4-44-440000000000000000000000000000000000000000000004i−4i00000000000000000
χ714-444-4-44-440000-44-4-44-44000000000000000000000000000000000000000000000−4i4i00000000000000000
χ724-44-444-4-444-44-4-444-4-44-4000000000044-4-400000000000000000000000000000000000000000000000000
χ734-44-444-4-4-24-44-42-2-222-220000000000-2-222000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ744-44-444-4-4-24-44-42-2-222-220000000000-2-2220000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ754-44-444-4-4-2-44-442-2-222-224i−4i4i−4i00000022-2-20000000000000−2i2i−2i2i000000000000000000000000000000000
χ764-44-444-4-4-2-44-442-2-222-22−4i4i−4i4i00000022-2-200000000000002i−2i2i−2i000000000000000000000000000000000
χ774-4-444-4-4440000-4-4444-4-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ784-4-444-4-4440000-4-4444-4-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ794-4-4-4-4444-24-4-44222-22-2-24-4-440000002-2-220000000000000-222-2000000000000000000000000000000000
χ804-4-4-4-4444-24-4-44222-22-2-2-444-40000002-2-2200000000000002-2-22000000000000000000000000000000000
χ814-4-4-4-4444-2-444-4222-22-2-20000000000-222-2004-400000-22-220000000000000000000000000000000000000
χ824-4-4-4-4444-2-444-4222-22-2-20000000000-222-200-44000002-22-20000000000000000000000000000000000000
χ838-888-8-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000000000

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