Finite Group Databasebeta

← Group #10829236

Character table — Group #10829236

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666444444121212121212121222244668888121212121212121224242424242424244444444661212222444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-111-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-111-1-1-11111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-1-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1111-1-11111-1-1-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11-1-111-1-11111111-1-1-1
χ911111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-1-11111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1111-1-1-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111111-1-111-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-20000-2-2000000000000000000002222-2-20000000-2000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-20000-2-200000000000000000000-2-2-2-22200000002000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000220000000000000000000022-2-2-2-200000002000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200002200000000000000000000-2-222220000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-2-222-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-222-2-21122-2-2-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-211-2-222-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1222-2-2-1-1-2-2-2-211111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2222211-2-2221111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2-2-2221122-2-21111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-22-2-2-22-2-22222-22-2-2-22i2i−2i−2i002-200002-2000000000002i2i−2i−2i00000000000000000000000000002i−2i2-2000
χ30222-22-2-2-22-2-22222-22-2-2-22i2i−2i−2i002-200002-2000000000002i2i−2i−2i0000000000000000000000000000−2i2i-22000
χ31222-22-2-2-22-2-22222-22-2-2-2−2i−2i2i2i002-200002-200000000000−2i−2i2i2i00000000000000000000000000002i−2i-22000
χ32222-22-2-2-22-2-22222-22-2-2-2−2i−2i2i2i002-200002-200000000000−2i−2i2i2i0000000000000000000000000000−2i2i2-2000
χ332-2-222-22-222-22-2-2-2222-2-22i−2i2i−2i00220000-2-202-200002i−2i002i−2i2i−2i00002i2i−2i−2i000000000002-200000000000000
χ342-2-222-22-222-22-2-2-2222-2-22i−2i2i−2i00220000-2-20-220000−2i2i002i−2i2i−2i0000−2i−2i2i2i00000000000-2200000000000000
χ352-2-222-22-222-22-2-2-2222-2-2−2i2i−2i2i00220000-2-202-20000−2i2i00−2i2i−2i2i0000−2i−2i2i2i000000000002-200000000000000
χ362-2-222-22-222-22-2-2-2222-2-2−2i2i−2i2i00220000-2-20-2200002i−2i00−2i2i−2i2i00002i2i−2i−2i00000000000-2200000000000000
χ372-2-222-22-2-12-22-211-1-1-1112i−2i2i−2i00-1-1−i3−i3i3i31102-200−i3i32i−2i00−ii−ii33−3−3−i−iii33−3−30000000-11−i3i3000000000000
χ382-2-222-22-2-12-22-211-1-1-1112i−2i2i−2i00-1-1−i3−i3i3i3110-2200−i3i3−2i2i00−ii−ii33−3−3ii−i−i−3−33300000001-1i3−i3000000000000
χ392-2-222-22-2-12-22-211-1-1-1112i−2i2i−2i00-1-1i3i3−i3−i31102-200i3−i32i−2i00−ii−ii−3−333−i−iii−3−3330000000-11i3−i3000000000000
χ402-2-222-22-2-12-22-211-1-1-1112i−2i2i−2i00-1-1i3i3−i3−i3110-2200i3−i3−2i2i00−ii−ii−3−333ii−i−i33−3−300000001-1−i3i3000000000000
χ412-2-222-22-2-12-22-211-1-1-111−2i2i−2i2i00-1-1−i3−i3i3i31102-200−i3i3−2i2i00i−ii−i−3−333ii−i−i−3−3330000000-11−i3i3000000000000
χ422-2-222-22-2-12-22-211-1-1-111−2i2i−2i2i00-1-1−i3−i3i3i3110-2200−i3i32i−2i00i−ii−i−3−333−i−iii33−3−300000001-1i3−i3000000000000
χ432-2-222-22-2-12-22-211-1-1-111−2i2i−2i2i00-1-1i3i3−i3−i31102-200i3−i3−2i2i00i−ii−i33−3−3ii−i−i33−3−30000000-11i3−i3000000000000
χ442-2-222-22-2-12-22-211-1-1-111−2i2i−2i2i00-1-1i3i3−i3−i3110-2200i3−i32i−2i00i−ii−i33−3−3−i−iii−3−33300000001-1−i3i3000000000000
χ452-2-2-222-2222-2-22-2-2-22-222000000-2200002-20002-200000000002-22-2000000002-2002-2000000002-20000000
χ462-2-2-222-2222-2-22-2-2-22-222000000-2200002-20002-200000000002-22-200000000-2200-2200000000-220000000
χ472-2-2-222-2222-2-22-2-2-22-222000000-2200002-2000-220000000000-22-22000000002-2002-200000000-220000000
χ482-2-2-222-2222-2-22-2-2-22-222000000-2200002-2000-220000000000-22-2200000000-2200-22000000002-20000000
χ492-2-2-222-222-222-2-2-2-22-2222-2-22002-20000-22000000000002-2-220000000000002-200-22000002-20000000000
χ502-2-2-222-222-222-2-2-2-22-2222-2-22002-20000-22000000000002-2-22000000000000-22002-200000-220000000000
χ512-2-2-222-222-222-2-2-2-22-222-222-2002-20000-2200000000000-222-20000000000002-200-2200000-220000000000
χ522-2-2-222-222-222-2-2-2-22-222-222-2002-20000-2200000000000-222-2000000000000-22002-2000002-20000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-222-40000220000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222240000-2-20000000000000000000000000000000000000000000
χ55444-44-4-4-4444-4-444-44-4-4-4000000-440000-4400000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-244-4-4-2-22-22220000002-200002-200000000000000023−23−23230000000000000000000000000000000
χ57444-44-4-4-4-244-4-4-2-22-22220000002-200002-2000000000000000−232323−230000000000000000000000000000000
χ58444-44-4-4-4-2-4-444-2-22-22224i4i−4i−4i00-220000-2200000000000−2i−2i2i2i00000000000000000000000000000000000
χ59444-44-4-4-4-2-4-444-2-22-2222−4i−4i4i4i00-220000-22000000000002i2i−2i−2i00000000000000000000000000000000000
χ6044-44-44-4-4400004-4-4-444-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ6144-44-44-4-4400004-4-4-444-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ6244-4-4-4-444400004-44-4-4-440000000000000000000000022−2200000000000022−2222−2200000000000000000000000
χ6344-4-4-4-444400004-44-4-4-4400000000000000000000000−2222000000000000−2222−222200000000000000000000000
χ6444-4-4-4-444-20000-22-2222-20000000023−2323−230000000000022−22000000006−66−6−22−2200000000000000000000000
χ6544-4-4-4-444-20000-22-2222-20000000023−2323−2300000000000−222200000000−66−662−22−200000000000000000000000
χ6644-4-4-4-444-20000-22-2222-200000000−2323−23230000000000022−2200000000−66−66−22−2200000000000000000000000
χ6744-4-4-4-444-20000-22-2222-200000000−2323−232300000000000−2222000000006−66−62−22−200000000000000000000000
χ684-444-4-4-4440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000022−220
χ694-444-4-4-4440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000−22220
χ704-44-4-444-440000-444-4-44-400004i−4i004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ714-44-4-444-440000-444-4-44-40000−4i4i00−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ724-44-4-444-4-200002-2-222-2200004i−4i00−2i2i2i−2i000000000000000000000i6−i6−i6i66−6−6600000000000000000000000
χ734-44-4-444-4-200002-2-222-2200004i−4i00−2i2i2i−2i000000000000000000000−i6i6i6−i6−666−600000000000000000000000
χ744-44-4-444-4-200002-2-222-220000−4i4i002i−2i−2i2i000000000000000000000i6−i6−i6i6−666−600000000000000000000000
χ754-44-4-444-4-200002-2-222-220000−4i4i002i−2i−2i2i000000000000000000000−i6i6i6−i66−6−6600000000000000000000000
χ764-4-444-44-44-44-44-4-4444-4-4000000-4-400004400000000000000000000000000000000000000000000000000
χ774-4-444-44-4-2-44-4422-2-2-22200000022−2i3−2i32i32i3-2-2000002i3−2i30000000000000000000000000000000000000000000
χ784-4-444-44-4-2-44-4422-2-2-222000000222i32i3−2i3−2i3-2-200000−2i32i30000000000000000000000000000000000000000000
χ794-4-4-444-44-24-4-44222-22-2-20000002-20000-220004-40000000000-22-220000000000000000000000000000000
χ804-4-4-444-44-24-4-44222-22-2-20000002-20000-22000-4400000000002-22-20000000000000000000000000000000
χ814-4-4-444-44-2-444-4222-22-2-24-4-4400-2200002-200000000000-222-200000000000000000000000000000000000
χ824-4-4-444-44-2-444-4222-22-2-2-444-400-2200002-2000000000002-2-2200000000000000000000000000000000000
χ8388-88-88-8-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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