Finite Group Databasebeta

← Group #10855061

Character table — Group #10855061

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121244668888121212121212121224242424242424244444441212121224444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111
χ911111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-1-1111-1-111-1-111-1-1
χ1011111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-11-1-1-111-1-111-1-111
χ1111111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1111-1-1-1-111-1-111
χ1211111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-11-1-1111-1-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111-11-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-1111-111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-11-1-11111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111-111-1-11-111-1-1-1-11111-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-200220000000000000000000022-2-20000002-2000000000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-2002200000000000000000000-2-222000000-22000000000000
χ19222222222-2-2-2-22222222-2-2000022-2-22222-2-200-2-2000000000000000000002222000000-2-2000000000000
χ20222222222-2-2-2-22222222-2-2000022-2-22222-2-200-2-200000000000000000000-2-2-2-200000022000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-2-2-1-1222211111111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-11111-1-1-2-21122-2-2-1-1-1-11111-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-11111-1-1-2-211-2-222-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1221122-2-21111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-12211-2-2221111-1-1-1-11111-1-1-1-100002-2-1-11100000000000000
χ2922-2-2-222-22-22-2222-2-2-2-22002i2i−2i−2i002-200002-2000000002i2i−2i−2i0000000000000000000000000000002i−2i002-2
χ3022-2-2-222-22-22-2222-2-2-2-22002i2i−2i−2i002-200002-2000000002i2i−2i−2i000000000000000000000000000000−2i2i00-22
χ3122-2-2-222-22-22-2222-2-2-2-2200−2i−2i2i2i002-200002-200000000−2i−2i2i2i0000000000000000000000000000002i−2i00-22
χ3222-2-2-222-22-22-2222-2-2-2-2200−2i−2i2i2i002-200002-200000000−2i−2i2i2i000000000000000000000000000000−2i2i002-2
χ332-22-2-2-2222-2-222-2-2-222-22002-22-2002-20000-22000000002-22-200000000000000000000000000002-2002-200
χ342-22-2-2-2222-2-222-2-2-222-22002-22-2002-20000-22000000002-22-20000000000000000000000000000-2200-2200
χ352-22-2-2-2222-2-222-2-2-222-2200-22-22002-20000-2200000000-22-2200000000000000000000000000002-200-2200
χ362-22-2-2-2222-2-222-2-2-222-2200-22-22002-20000-2200000000-22-220000000000000000000000000000-22002-200
χ372-2-222-22-222-2-22-2-22-2-2222-22i−2i−2i2i2-22222-2-2-2-22i−2i2-200002i−2i−2i2i2i2i−2i−2i00000000000000000000000000000000
χ382-2-222-22-222-2-22-2-22-2-2222-2−2i2i2i−2i2-22222-2-2-2-2−2i2i2-20000−2i2i2i−2i−2i−2i2i2i00000000000000000000000000000000
χ392-2-222-22-222-2-22-2-22-2-222-222i−2i−2i2i-2222-2-222-2-2−2i2i-2200002i−2i−2i2i−2i−2i2i2i00000000000000000000000000000000
χ402-2-222-22-222-2-22-2-22-2-222-22−2i2i2i−2i-2222-2-222-2-22i−2i-220000−2i2i2i−2i2i2i−2i−2i00000000000000000000000000000000
χ412-2-222-22-22-222-2-2-22-2-2222-20000-22-2-2-2-22222002-2000000000000000000000000000000002i−2i2i−2i00000000
χ422-2-222-22-22-222-2-2-22-2-2222-20000-22-2-2-2-22222002-200000000000000000000000000000000−2i2i−2i2i00000000
χ432-2-222-22-22-222-2-2-22-2-222-2200002-2-2-222-2-22200-22000000000000000000000000000000002i−2i−2i2i00000000
χ442-2-222-22-22-222-2-2-22-2-222-2200002-2-2-222-2-22200-2200000000000000000000000000000000−2i2i2i−2i00000000
χ452-2-222-22-2-12-2-2211-111-1-12-22i−2i−2i2i2-2-1-1-1-111112i−2i-110000−iii−i−i−iii33−3−333−3−3000000−i3i3−i3i300000000000000
χ462-2-222-22-2-12-2-2211-111-1-12-22i−2i−2i2i2-2-1-1-1-111112i−2i-110000−iii−i−i−iii−3−333−3−333000000i3−i3i3−i300000000000000
χ472-2-222-22-2-12-2-2211-111-1-12-2−2i2i2i−2i2-2-1-1-1-11111−2i2i-110000i−i−iiii−i−i33−3−333−3−3000000i3−i3i3−i300000000000000
χ482-2-222-22-2-12-2-2211-111-1-12-2−2i2i2i−2i2-2-1-1-1-11111−2i2i-110000i−i−iiii−i−i−3−333−3−333000000−i3i3−i3i300000000000000
χ492-2-222-22-2-12-2-2211-111-1-1-222i−2i−2i2i-22-1-111-1-111−2i2i1-10000−iii−iii−i−i33−3−3−3−333000000−i3i3i3−i300000000000000
χ502-2-222-22-2-12-2-2211-111-1-1-222i−2i−2i2i-22-1-111-1-111−2i2i1-10000−iii−iii−i−i−3−33333−3−3000000i3−i3−i3i300000000000000
χ512-2-222-22-2-12-2-2211-111-1-1-22−2i2i2i−2i-22-1-111-1-1112i−2i1-10000i−i−ii−i−iii33−3−3−3−333000000i3−i3−i3i300000000000000
χ522-2-222-22-2-12-2-2211-111-1-1-22−2i2i2i−2i-22-1-111-1-1112i−2i1-10000i−i−ii−i−iii−3−33333−3−3000000−i3i3i3−i300000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-4-42222222200-2-200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400004422-2-2-2-222002200000000000000000000000000000000000000000000
χ55444-44-4-4-4400004-4-44-44-40000000000000000000022−22000000000022−2222−220000000000000000000000000000
χ56444-44-4-4-4400004-4-44-44-400000000000000000000−22220000000000−2222−22220000000000000000000000000000
χ57444-44-4-4-4-20000-222-22-22000000000023−2323−2300000022−220000000000−22−226−66−6000000000000000000000000
χ58444-44-4-4-4-20000-222-22-22000000000023−2323−23000000−222200000000002−22−2−66−66000000000000000000000000
χ59444-44-4-4-4-20000-222-22-220000000000−2323−232300000022−220000000000−22−22−66−66000000000000000000000000
χ60444-44-4-4-4-20000-222-22-220000000000−2323−2323000000−222200000000002−22−26−66−6000000000000000000000000
χ6144-44-4-4-44400004-44-44-4-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ6244-44-4-4-44400004-44-44-4-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ6344-4-4-444-444-44-444-4-4-4-4400000000-440000-44000000000000000000000000000000000000000000000000
χ6444-4-4-444-4-24-44-4-2-22222-2000000002-200002-200000000000023−2323−2300000000000000000000000000000000
χ6544-4-4-444-4-24-44-4-2-22222-2000000002-200002-2000000000000−2323−232300000000000000000000000000000000
χ6644-4-4-444-4-2-44-44-2-22222-2004i4i−4i−4i00-220000-2200000000−2i−2i2i2i000000000000000000000000000000000000
χ6744-4-4-444-4-2-44-44-2-22222-200−4i−4i4i4i00-220000-22000000002i2i−2i−2i000000000000000000000000000000000000
χ684-444-44-4-440000-4444-4-4-400000000000000000000000000000000000000004-40000000000000000000000
χ694-444-44-4-440000-4444-4-4-40000000000000000000000000000000000000000-440000000000000000000000
χ704-44-4-4-444444-4-4-4-4-444-4400000000-4400004-4000000000000000000000000000000000000000000000000
χ714-44-4-4-444-244-4-4222-2-22-2000000002-20000-22000000000000−2i32i32i3−2i300000000000000000000000000000000
χ724-44-4-4-444-244-4-4222-2-22-2000000002-20000-220000000000002i3−2i3−2i32i300000000000000000000000000000000
χ734-44-4-4-444-2-4-444222-2-22-2004-44-400-2200002-200000000-22-22000000000000000000000000000000000000
χ744-44-4-4-444-2-4-444222-2-22-200-44-4400-2200002-2000000002-22-2000000000000000000000000000000000000
χ754-4-444-44-4-2-444-422-222-2-24-40000-442222-2-2-2-200-2200000000000000000000000000000000000000000000
χ764-4-444-44-4-2-444-422-222-2-2-4400004-422-2-222-2-2002-200000000000000000000000000000000000000000000
χ774-4-4-444-4440000-44-4-444-4000000000000000000000022−2200000000000022−22−2222000000000000000000000000
χ784-4-4-444-4440000-44-4-444-40000000000000000000000−2222000000000000−222222−22000000000000000000000000
χ794-4-4-444-44-200002-222-2-22000000000023−23−23230000000022−2200000000−666−6−222−2000000000000000000000000
χ804-4-4-444-44-200002-222-2-22000000000023−23−232300000000−2222000000006−6−662−2−22000000000000000000000000
χ814-4-4-444-44-200002-222-2-220000000000−232323−230000000022−22000000006−6−66−222−2000000000000000000000000
χ824-4-4-444-44-200002-222-2-220000000000−232323−2300000000−222200000000−666−62−2−22000000000000000000000000
χ8388-88-8-8-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000

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