Finite Group Databasebeta

← Group #10829251

Character table — Group #10829251

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order122222223444466666664444444412121212121212124488881212121212121212121224242424242424242222441212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111
χ911111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-1111-111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-1-1-1-11-1-11111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-11-111-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1-11111-11-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111-1-11-1-1-1111111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-11111-1111-1-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-1111-1-1-111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-1-1-1-1111-1-11111-1-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-20000000000000000222200000000-2-20000000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-20000000000000000-2-2-2-200000000220000000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-200000022000000000000000022-2-200000000-220000000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-2000000220000000000000000-2-222000000002-20000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2-222-2-211-1-1-1-11111-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2-2-2-22211-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-12222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-122-2-222111111-1-1-1-11111-1-1-1-100002-2-1-11100000000000000
χ29222-2-2-22-22-222-222-2-2-22-200002i2i−2i−2i00002-2-22000000002i2i−2i−2i0000000000000000000000000000002i−2i002-2
χ30222-2-2-22-22-222-222-2-2-22-200002i2i−2i−2i00002-2-22000000002i2i−2i−2i000000000000000000000000000000−2i2i00-22
χ31222-2-2-22-22-222-222-2-2-22-20000−2i−2i2i2i00002-2-2200000000−2i−2i2i2i0000000000000000000000000000002i−2i00-22
χ32222-2-2-22-22-222-222-2-2-22-20000−2i−2i2i2i00002-2-2200000000−2i−2i2i2i000000000000000000000000000000−2i2i002-2
χ332-2-22-2-222222-2-2-2-22-2-2222-22-2000022-2-2-22-220000002-20000000000000000000000000000002-22-2000000
χ342-2-22-2-222222-2-2-2-22-2-2222-22-2000022-2-2-22-220000002-2000000000000000000000000000000-22-22000000
χ352-2-22-2-222222-2-2-2-22-2-222-22-220000-2-222-22-22000000-220000000000000000000000000000002-2-22000000
χ362-2-22-2-222222-2-2-2-22-2-222-22-220000-2-222-22-22000000-22000000000000000000000000000000-222-2000000
χ372-2-22-2-2222-2-222-2-22-2-2222-2-222-22-222-2-22-22-22-20000-222-22-222-2-200000000000000000000000000000000
χ382-2-22-2-2222-2-222-2-22-2-2222-2-22-22-2222-2-22-22-2-220000-22-22-22-2-22200000000000000000000000000000000
χ392-2-22-2-2222-2-222-2-22-2-222-222-22-22-2-2-2222-22-2-2200002-22-22-2-2-22200000000000000000000000000000000
χ402-2-22-2-2222-2-222-2-22-2-222-222-2-22-22-2-2222-22-22-200002-2-22-2222-2-200000000000000000000000000000000
χ412-2-22-2-222-1-2-22211-111-1-12-2-222-22-2-1-111-11-112-200001-1-11-11-1-11133−3−333−3−30000003−33−300000000000000
χ422-2-22-2-222-1-2-22211-111-1-12-2-222-22-2-1-111-11-112-200001-1-11-11-1-111−3−333−3−333000000−33−3300000000000000
χ432-2-22-2-222-1-2-22211-111-1-12-2-22-22-22-1-111-11-11-2200001-11-11-111-1-133−3−333−3−3000000−33−3300000000000000
χ442-2-22-2-222-1-2-22211-111-1-12-2-22-22-22-1-111-11-11-2200001-11-11-111-1-1−3−333−3−3330000003−33−300000000000000
χ452-2-22-2-222-1-2-22211-111-1-1-222-22-22-211-1-1-11-11-220000-11-11-1111-1-133−3−3−3−3330000003−3−3300000000000000
χ462-2-22-2-222-1-2-22211-111-1-1-222-22-22-211-1-1-11-11-220000-11-11-1111-1-1−3−33333−3−3000000−333−300000000000000
χ472-2-22-2-222-1-2-22211-111-1-1-222-2-22-2211-1-1-11-112-20000-111-11-1-1-11133−3−3−3−333000000−333−300000000000000
χ482-2-22-2-222-1-2-22211-111-1-1-222-2-22-2211-1-1-11-112-20000-111-11-1-1-111−3−33333−3−30000003−3−3300000000000000
χ492-2-2-2222-222-22-2-2-2-2222-200002i−2i−2i2i000022-2-2000000002i−2i−2i2i00000000000000000000002-2000000002i−2i00
χ502-2-2-2222-222-22-2-2-2-2222-200002i−2i−2i2i000022-2-2000000002i−2i−2i2i0000000000000000000000-2200000000−2i2i00
χ512-2-2-2222-222-22-2-2-2-2222-20000−2i2i2i−2i000022-2-200000000−2i2i2i−2i00000000000000000000002-200000000−2i2i00
χ522-2-2-2222-222-22-2-2-2-2222-20000−2i2i2i−2i000022-2-200000000−2i2i2i−2i0000000000000000000000-22000000002i−2i00
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000-2-2-2-22222000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022222222000000-2-20000000000000000000000000000000000000000
χ55444-4-4-44-444-4-4444-4-4-44-4000000000000-444-4000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-24-4-44-2-2222-220000000000002-2-22000000000000−2i32i3−2i32i300000000000000000000000000000000
χ57444-4-4-44-4-24-4-44-2-2222-220000000000002-2-220000000000002i3−2i32i3−2i300000000000000000000000000000000
χ58444-4-4-44-4-2-444-4-2-2222-2200004i4i−4i−4i0000-222-200000000−2i−2i2i2i000000000000000000000000000000000000
χ59444-4-4-44-4-2-444-4-2-2222-220000−4i−4i4i4i0000-222-2000000002i2i−2i−2i000000000000000000000000000000000000
χ6044-444-4-4-4400004-444-4-4-40000000000000000000000000000000000000000004-400000000000000000000
χ6144-444-4-4-4400004-444-4-4-4000000000000000000000000000000000000000000-4400000000000000000000
χ6244-4-4-44-44400004-4-4-44-4400000000000000000022−2200000000000022−2222−220000000000000000000000000000
χ6344-4-4-44-44400004-4-4-44-44000000000000000000−2222000000000000−2222−22220000000000000000000000000000
χ6444-4-4-44-44-20000-2222-22-20000000023−2323−2300000022−22000000000000−22−226−66−6000000000000000000000000
χ6544-4-4-44-44-20000-2222-22-20000000023−2323−23000000−22220000000000002−22−2−66−66000000000000000000000000
χ6644-4-4-44-44-20000-2222-22-200000000−2323−232300000022−22000000000000−22−22−66−66000000000000000000000000
χ6744-4-4-44-44-20000-2222-22-200000000−2323−2323000000−22220000000000002−22−26−66−6000000000000000000000000
χ684-444-44-4-440000-444-44-4-400000000000000000000000000000000000000004-40000000000000000000000
χ694-444-44-4-440000-444-44-4-40000000000000000000000000000000000000000-440000000000000000000000
χ704-44-44-4-4440000-44-44-4-440000000000000000000022−220000000000000022−22−2222000000000000000000000000
χ714-44-44-4-4440000-44-44-4-4400000000000000000000−222200000000000000−222222−22000000000000000000000000
χ724-44-44-4-44-200002-22-222-20000000023−23−23230000000022−220000000000−666−6−222−2000000000000000000000000
χ734-44-44-4-44-200002-22-222-20000000023−23−232300000000−222200000000006−6−662−2−22000000000000000000000000
χ744-44-44-4-44-200002-22-222-200000000−232323−230000000022−2200000000006−6−66−222−2000000000000000000000000
χ754-44-44-4-44-200002-22-222-200000000−232323−2300000000−22220000000000−666−62−2−22000000000000000000000000
χ764-4-44-4-444-244-4-422-222-2-24-44-40000-2-2222-22-2000000-220000000000000000000000000000000000000000
χ774-4-44-4-444-244-4-422-222-2-2-44-44000022-2-22-22-20000002-20000000000000000000000000000000000000000
χ784-4-4-4444-44-44-44-4-4-4444-4000000000000-4-444000000000000000000000000000000000000000000000000
χ794-4-4-4444-4-24-44-4222-2-2-2200004i−4i−4i4i0000-2-22200000000−2i2i2i−2i000000000000000000000000000000000000
χ804-4-4-4444-4-24-44-4222-2-2-220000−4i4i4i−4i0000-2-222000000002i−2i−2i2i000000000000000000000000000000000000
χ814-4-4-4444-4-2-44-44222-2-2-2200000000000022-2-2000000000000−2i32i32i3−2i300000000000000000000000000000000
χ824-4-4-4444-4-2-44-44222-2-2-2200000000000022-2-20000000000002i3−2i3−2i32i300000000000000000000000000000000
χ8388-888-8-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000

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