Finite Group Databasebeta

← Group #10853227

Character table — Group #10853227

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121244668888121212121212121224242424242424244444441212121244444444448888
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
χ5111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-11111
χ911111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-11-1-1-11111-1-111-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1111-1-1-1111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1111-1-1-111-1-111-1-111
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11-1-1-111111-1-1-1-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1111-1-1111-1-1-111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1111-1-1-1-1-1111-1-11111-1-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200220000000000000000000022-2-2000000-20020000000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2002200000000000000000000-2-222000000200-20000000000
χ19222222222-2-2-2-22222222-2-2220000-2-22222-2-200-2-2000000000000000000002222000000-200-20000000000
χ20222222222-2-2-2-22222222-2-2220000-2-22222-2-200-2-200000000000000000000-2-2-2-200000020020000000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1222211111111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-21122-2-2-1-1-1-11111-1-1-1-111110000-22-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-211-2-222-1-1-1-111111111-1-1-1-100002-211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1221122-2-21111-1-1-1-1-1-1-1-1111100002-211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-12211-2-2221111-1-1-1-11111-1-1-1-10000-22-1-11100000000000000
χ292222-2-2-2-2222-2-2-2-2222-2-22-22-222-2-22222-2-2-2-22-22-2000022-2-222-2-200000000000000000000000000000000
χ302222-2-2-2-2222-2-2-2-2222-2-22-22-2-2-2222222-2-2-2-2-222-20000-2-222-2-22200000000000000000000000000000000
χ312222-2-2-2-2222-2-2-2-2222-2-2-22-2222-2-222-2-222-2-2-22-22000022-2-2-2-22200000000000000000000000000000000
χ322222-2-2-2-2222-2-2-2-2222-2-2-22-22-2-22222-2-222-2-22-2-220000-2-22222-2-200000000000000000000000000000000
χ332222-2-2-2-22-2-222-2-2222-2-22-2-220000-2-2-2-22222002-200000000000000000000000000000002i−2i02i−2i00000000
χ342222-2-2-2-22-2-222-2-2222-2-22-2-220000-2-2-2-22222002-20000000000000000000000000000000−2i2i0−2i2i00000000
χ352222-2-2-2-22-2-222-2-2222-2-2-222-20000-2-222-2-22200-2200000000000000000000000000000002i−2i0−2i2i00000000
χ362222-2-2-2-22-2-222-2-2222-2-2-222-20000-2-222-2-22200-220000000000000000000000000000000−2i2i02i−2i00000000
χ372222-2-2-2-2-122-2-211-1-1-1112-22-222-2-2-1-1-1-111112-2-110000-1-111-1-11133−3−333−3−30000003−33−300000000000000
χ382222-2-2-2-2-122-2-211-1-1-1112-22-222-2-2-1-1-1-111112-2-110000-1-111-1-111−3−333−3−333000000−33−3300000000000000
χ392222-2-2-2-2-122-2-211-1-1-1112-22-2-2-222-1-1-1-11111-22-11000011-1-111-1-133−3−333−3−3000000−33−3300000000000000
χ402222-2-2-2-2-122-2-211-1-1-1112-22-2-2-222-1-1-1-11111-22-11000011-1-111-1-1−3−333−3−3330000003−33−300000000000000
χ412222-2-2-2-2-122-2-211-1-1-111-22-2222-2-2-1-111-1-111-221-10000-1-11111-1-133−3−3−3−3330000003−3−3300000000000000
χ422222-2-2-2-2-122-2-211-1-1-111-22-2222-2-2-1-111-1-111-221-10000-1-11111-1-1−3−33333−3−3000000−333−300000000000000
χ432222-2-2-2-2-122-2-211-1-1-111-22-22-2-222-1-111-1-1112-21-1000011-1-1-1-11133−3−3−3−333000000−333−300000000000000
χ442222-2-2-2-2-122-2-211-1-1-111-22-22-2-222-1-111-1-1112-21-1000011-1-1-1-111−3−33333−3−30000003−3−3300000000000000
χ4522-2-22-22-222-2-222-22-2-22-200002i−2i2i−2i2-200002-2000000002i−2i2i−2i0000000000000000000000000000002i−2i002-2
χ4622-2-22-22-222-2-222-22-2-22-200002i−2i2i−2i2-200002-2000000002i−2i2i−2i000000000000000000000000000000−2i2i00-22
χ4722-2-22-22-222-2-222-22-2-22-20000−2i2i−2i2i2-200002-200000000−2i2i−2i2i0000000000000000000000000000002i−2i00-22
χ4822-2-22-22-222-2-222-22-2-22-20000−2i2i−2i2i2-200002-200000000−2i2i−2i2i000000000000000000000000000000−2i2i002-2
χ4922-2-2-22-2222-22-2-222-2-2-2200002i−2i−2i2i2-20000-22000000002i−2i−2i2i00000000000000000000000000002-2002i−2i00
χ5022-2-2-22-2222-22-2-222-2-2-2200002i−2i−2i2i2-20000-22000000002i−2i−2i2i0000000000000000000000000000-2200−2i2i00
χ5122-2-2-22-2222-22-2-222-2-2-220000−2i2i2i−2i2-20000-2200000000−2i2i2i−2i00000000000000000000000000002-200−2i2i00
χ5222-2-2-22-2222-22-2-222-2-2-220000−2i2i2i−2i2-20000-2200000000−2i2i2i−2i0000000000000000000000000000-22002i−2i00
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-400002222222200-2-200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022-2-2-2-222002200000000000000000000000000000000000000000000
χ554444-4-4-4-4-2-4-44422-2-2-2224-4-4400002222-2-2-2-200-2200000000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-44422-2-2-222-444-4000022-2-222-2-2002-200000000000000000000000000000000000000000000
χ5744-4-44-44-44-444-44-44-4-44-400000000-440000-44000000000000000000000000000000000000000000000000
χ5844-4-44-44-4-24-4-44-22-222-2200004i−4i4i−4i-220000-2200000000−2i2i−2i2i000000000000000000000000000000000000
χ5944-4-44-44-4-24-4-44-22-222-220000−4i4i−4i4i-220000-22000000002i−2i2i−2i000000000000000000000000000000000000
χ6044-4-44-44-4-2-444-4-22-222-22000000002-200002-200000000000023−2323−2300000000000000000000000000000000
χ6144-4-44-44-4-2-444-4-22-222-22000000002-200002-2000000000000−2323−232300000000000000000000000000000000
χ6244-4-4-44-444-44-44-444-4-4-4400000000-4400004-4000000000000000000000000000000000000000000000000
χ6344-4-4-44-44-24-44-42-2-2222-200004i−4i−4i4i-2200002-200000000−2i2i2i−2i000000000000000000000000000000000000
χ6444-4-4-44-44-24-44-42-2-2222-20000−4i4i4i−4i-2200002-2000000002i−2i−2i2i000000000000000000000000000000000000
χ6544-4-4-44-44-2-44-442-2-2222-2000000002-20000-2200000000000023−23−232300000000000000000000000000000000
χ6644-4-4-44-44-2-44-442-2-2222-2000000002-20000-22000000000000−232323−2300000000000000000000000000000000
χ674-44-444-4-4400004-4-44-4-440000000000000000000022−22000000000022−2222−220000000000000000000000000000
χ684-44-444-4-4400004-4-44-4-4400000000000000000000−22220000000000−2222−22220000000000000000000000000000
χ694-44-444-4-4-20000-222-222-2000000000023−2323−2300000022−220000000000−22−226−66−6000000000000000000000000
χ704-44-444-4-4-20000-222-222-2000000000023−2323−23000000−222200000000002−22−2−66−66000000000000000000000000
χ714-44-444-4-4-20000-222-222-20000000000−2323−232300000022−220000000000−22−22−66−66000000000000000000000000
χ724-44-444-4-4-20000-222-222-20000000000−2323−2323000000−222200000000002−22−26−66−6000000000000000000000000
χ734-44-4-4-44440000-44-44-44-4000000000000000000000022−2200000000000022−22−2222000000000000000000000000
χ744-44-4-4-44440000-44-44-44-40000000000000000000000−2222000000000000−222222−22000000000000000000000000
χ754-44-4-4-444-200002-22-22-22000000000023−23−23230000000022−2200000000−666−6−222−2000000000000000000000000
χ764-44-4-4-444-200002-22-22-22000000000023−23−232300000000−2222000000006−6−662−2−22000000000000000000000000
χ774-44-4-4-444-200002-22-22-220000000000−232323−230000000022−22000000006−6−66−222−2000000000000000000000000
χ784-44-4-4-444-200002-22-22-220000000000−232323−2300000000−222200000000−666−62−2−22000000000000000000000000
χ794-4-444-4-444000044-4-44-4-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ804-4-444-4-444000044-4-44-4-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ814-4-44-444-440000-4-4-4-444400000000000000000000000000000000000000004i−4i0000000000000000000000
χ824-4-44-444-440000-4-4-4-44440000000000000000000000000000000000000000−4i4i0000000000000000000000
χ838-8-888-8-88-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400004444-4-4-40000000000000000000000000000000000000000000000000000000000000000

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