Finite Group Databasebeta

← Group #10827625

Character table — Group #10827625

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121244668888121212121212121224242424242424242244441212121244444444448888
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
χ51111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ71111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-11111
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
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111-1-1-1111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-111111-1-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-1-111111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111-111-1-1111-1-1-1-1-11111-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-200220000000000000000000022-2-2000000200-20000000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-2002200000000000000000000-2-222000000-20020000000000
χ19222222222-2-2-2-22222222-2-2000022-2-22222-2-200-2-2000000000000000000002222000000-200-20000000000
χ20222222222-2-2-2-22222222-2-2000022-2-22222-2-200-2-200000000000000000000-2-2-2-200000020020000000000
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
χ2922-22-2-2-22222-2-22-222-2-2-2002i2i−2i−2i002-200002-2000000002i2i−2i−2i0000000000000000000000000000002-2002i−2i
χ3022-22-2-2-22222-2-22-222-2-2-2002i2i−2i−2i002-200002-2000000002i2i−2i−2i000000000000000000000000000000-2200−2i2i
χ3122-22-2-2-22222-2-22-222-2-2-200−2i−2i2i2i002-200002-200000000−2i−2i2i2i0000000000000000000000000000002-200−2i2i
χ3222-22-2-2-22222-2-22-222-2-2-200−2i−2i2i2i002-200002-200000000−2i−2i2i2i000000000000000000000000000000-22002i−2i
χ332-22-22-2-2222-22-2-222-22-2-2002i−2i2i−2i002-20000-22000000002i−2i2i−2i00000000000000000000000000002-2002i−2i00
χ342-22-22-2-2222-22-2-222-22-2-2002i−2i2i−2i002-20000-22000000002i−2i2i−2i0000000000000000000000000000-2200−2i2i00
χ352-22-22-2-2222-22-2-222-22-2-200−2i2i−2i2i002-20000-2200000000−2i2i−2i2i00000000000000000000000000002-200−2i2i00
χ362-22-22-2-2222-22-2-222-22-2-200−2i2i−2i2i002-20000-2200000000−2i2i−2i2i0000000000000000000000000000-22002i−2i00
χ372-2-2-2-222222-2-22-2-22-2-2222-22-2-222-22222-2-2-2-22-22-200002-2-2222-2-200000000000000000000000000000000
χ382-2-2-2-222222-2-22-2-22-2-2222-2-222-22-22222-2-2-2-2-222-20000-222-2-2-22200000000000000000000000000000000
χ392-2-2-2-222222-2-22-2-22-2-222-222-2-22-2222-2-222-2-2-22-2200002-2-22-2-22200000000000000000000000000000000
χ402-2-2-2-222222-2-22-2-22-2-222-22-222-2-2222-2-222-2-22-2-220000-222-222-2-200000000000000000000000000000000
χ412-2-2-2-22222-222-2-2-22-2-2222-20000-22-2-2-2-22222002-200000000000000000000000000000002-202-200000000
χ422-2-2-2-22222-222-2-2-22-2-2222-20000-22-2-2-2-22222002-20000000000000000000000000000000-220-2200000000
χ432-2-2-2-22222-222-2-2-22-2-222-2200002-2-2-222-2-22200-2200000000000000000000000000000002-20-2200000000
χ442-2-2-2-22222-222-2-2-22-2-222-2200002-2-2-222-2-22200-220000000000000000000000000000000-2202-200000000
χ452-2-2-2-2222-12-2-2211-111-1-12-22-2-222-2-1-1-1-111112-2-110000-111-1-1-11133−3−333−3−30000003−33−300000000000000
χ462-2-2-2-2222-12-2-2211-111-1-12-22-2-222-2-1-1-1-111112-2-110000-111-1-1-111−3−333−3−333000000−33−3300000000000000
χ472-2-2-2-2222-12-2-2211-111-1-12-2-222-22-2-1-1-1-11111-22-1100001-1-1111-1-133−3−333−3−3000000−33−3300000000000000
χ482-2-2-2-2222-12-2-2211-111-1-12-2-222-22-2-1-1-1-11111-22-1100001-1-1111-1-1−3−333−3−3330000003−33−300000000000000
χ492-2-2-2-2222-12-2-2211-111-1-1-222-2-22-22-1-111-1-111-221-10000-111-111-1-133−3−3−3−3330000003−3−3300000000000000
χ502-2-2-2-2222-12-2-2211-111-1-1-222-2-22-22-1-111-1-111-221-10000-111-111-1-1−3−33333−3−3000000−333−300000000000000
χ512-2-2-2-2222-12-2-2211-111-1-1-22-222-2-22-1-111-1-1112-21-100001-1-11-1-11133−3−3−3−333000000−333−300000000000000
χ522-2-2-2-2222-12-2-2211-111-1-1-22-222-2-22-1-111-1-1112-21-100001-1-11-1-111−3−33333−3−30000003−3−3300000000000000
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
χ55444-4-4-44-44000044-4-4-44-400000000000000000000000000000000000000004-40000000000000000000000
χ56444-4-4-44-44000044-4-4-44-40000000000000000000000000000000000000000-440000000000000000000000
χ5744-44-4-4-444-4-4444-444-4-4-400000000-440000-44000000000000000000000000000000000000000000000000
χ5844-44-4-4-44-244-4-4-22-2-2222004i4i−4i−4i00-220000-2200000000−2i−2i2i2i000000000000000000000000000000000000
χ5944-44-4-4-44-244-4-4-22-2-222200−4i−4i4i4i00-220000-22000000002i2i−2i−2i000000000000000000000000000000000000
χ6044-44-4-4-44-2-4-444-22-2-2222000000002-200002-200000000000023−2323−2300000000000000000000000000000000
χ6144-44-4-4-44-2-4-444-22-2-2222000000002-200002-2000000000000−2323−232300000000000000000000000000000000
χ6244-4-444-4-4400004-4-4-44-44000000000000000000000022−2200000000000022−2222−22000000000000000000000000
χ6344-4-444-4-4400004-4-4-44-440000000000000000000000−2222000000000000−2222−2222000000000000000000000000
χ6444-4-444-4-4-20000-2222-22-2000000000023−2323−230000000022−22000000006−66−6−22−22000000000000000000000000
χ6544-4-444-4-4-20000-2222-22-2000000000023−2323−2300000000−222200000000−66−662−22−2000000000000000000000000
χ6644-4-444-4-4-20000-2222-22-20000000000−2323−23230000000022−2200000000−66−66−22−22000000000000000000000000
χ6744-4-444-4-4-20000-2222-22-20000000000−2323−232300000000−2222000000006−66−62−22−2000000000000000000000000
χ684-444-44-4-440000-44-44-4-440000000000000000000022−22000000000022−22−22220000000000000000000000000000
χ694-444-44-4-440000-44-44-4-4400000000000000000000−22220000000000−222222−220000000000000000000000000000
χ704-444-44-4-4-200002-22-222-2000000000023−23−232300000022−220000000000−222−2−666−6000000000000000000000000
χ714-444-44-4-4-200002-22-222-2000000000023−23−2323000000−222200000000002−2−226−6−66000000000000000000000000
χ724-444-44-4-4-200002-22-222-20000000000−232323−2300000022−220000000000−222−26−6−66000000000000000000000000
χ734-444-44-4-4-200002-22-222-20000000000−232323−23000000−222200000000002−2−22−666−6000000000000000000000000
χ744-44-44-4-444-44-44-444-44-4-400000000-4400004-4000000000000000000000000000000000000000000000000
χ754-44-44-4-44-24-44-42-2-22-222004i−4i4i−4i00-2200002-200000000−2i2i−2i2i000000000000000000000000000000000000
χ764-44-44-4-44-24-44-42-2-22-22200−4i4i−4i4i00-2200002-2000000002i−2i2i−2i000000000000000000000000000000000000
χ774-44-44-4-44-2-44-442-2-22-222000000002-20000-2200000000000023−23−232300000000000000000000000000000000
χ784-44-44-4-44-2-44-442-2-22-222000000002-20000-22000000000000−232323−2300000000000000000000000000000000
χ794-4-444-44-440000-4-4-4444-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ804-4-444-44-440000-4-4-4444-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ814-4-4-4-4444-2-444-422-222-2-24-40000-442222-2-2-2-200-2200000000000000000000000000000000000000000000
χ824-4-4-4-4444-2-444-422-222-2-2-4400004-422-2-222-2-2002-200000000000000000000000000000000000000000000
χ83888-8-8-88-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000

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