Finite Group Databasebeta

← Group #10896421

Character table — Group #10896421

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order12222222344446666666444412121212121212122244444466668888121212121212242424242424242444441212121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ911111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1-1-1-11111-1-1
χ1011111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-111111-1-1-1-111
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-111-111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1111111-1-1
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-200000000000000002200000000000022-2-20000200-20000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000000000000022000000000000-2-2220000-20020000000000
χ19222222222-2-2-2-22222222-2-222-2-22222-2-20000000000000000-2-200000000000022-2-20000-20020000000000
χ20222222222-2-2-2-22222222-2-222-2-22222-2-20000000000000000-2-2000000000000-2-2220000200-20000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-2-2221111-2-2-2-2-1-11111111111110000-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-10000111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-12222-2-2-2-2-1-1-1-122-2-2111111-1-1-1-111110000-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-2-2-222-1-1-1-1-2-2221111111111-1-1-1-1000011-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-22222-2-21111-2-22211-1-1-1-11111-1-1-1-10000-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-2-2-22222111122-2-211-1-1-1-1-1-1-1-11111000011-1-100000000000000
χ292-222-22-2-2222-2-222-22-2-2-20000220000-2-22-200000022-2-20000000000000000002-22-2000002-200000000000
χ302-222-22-2-2222-2-222-22-2-2-20000220000-2-22-200000022-2-2000000000000000000-22-2200000-2200000000000
χ312-222-22-2-2222-2-222-22-2-2-20000220000-2-2-22000000-2-2220000000000000000002-22-200000-2200000000000
χ322-222-22-2-2222-2-222-22-2-2-20000220000-2-2-22000000-2-222000000000000000000-22-22000002-200000000000
χ332-222-22-2-22-2-22222-22-2-2-20000-2-200002200002i−2i0000000000002i2i−2i−2i000000002-2-2200000000002i−2i000000
χ342-222-22-2-22-2-22222-22-2-2-20000-2-200002200002i−2i0000000000002i2i−2i−2i00000000-222-20000000000−2i2i000000
χ352-222-22-2-22-2-22222-22-2-2-20000-2-20000220000−2i2i000000000000−2i−2i2i2i000000002-2-220000000000−2i2i000000
χ362-222-22-2-22-2-22222-22-2-2-20000-2-20000220000−2i2i000000000000−2i−2i2i2i00000000-222-200000000002i−2i000000
χ372-2-2-2222-222-22-2-2-222-22-22i−2i2i−2i2-22i2i−2i−2i2-200000000000000002i−2i0000000000000000000000002-2002i−2i0000
χ382-2-2-2222-222-22-2-2-222-22-22i−2i2i−2i2-22i2i−2i−2i2-200000000000000002i−2i000000000000000000000000-2200−2i2i0000
χ392-2-2-2222-222-22-2-2-222-22-2−2i2i−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i0000000000000000000000002-200−2i2i0000
χ402-2-2-2222-222-22-2-2-222-22-2−2i2i−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i000000000000000000000000-22002i−2i0000
χ412-2-2-2222-22-22-22-2-222-22-22i−2i−2i2i-22−2i−2i2i2i-22002-2002i−2i000000002i−2i00000000000000002-22i−2i00000000000000
χ422-2-2-2222-22-22-22-2-222-22-22i−2i−2i2i-22−2i−2i2i2i-2200-2200−2i2i000000002i−2i0000000000000000-22−2i2i00000000000000
χ432-2-2-2222-22-22-22-2-222-22-2−2i2i2i−2i-222i2i−2i−2i-22002-200−2i2i00000000−2i2i00000000000000002-2−2i2i00000000000000
χ442-2-2-2222-22-22-22-2-222-22-2−2i2i2i−2i-222i2i−2i−2i-2200-22002i−2i00000000−2i2i0000000000000000-222i−2i00000000000000
χ452-2-2-2222-2-1-22-2211-1-11-112i−2i−2i2i1-1ii−i−i1-1002-2002i−2i−i3i3−i3i30000−ii3−33−3−i3−i3i3i333−3−30000-11−ii00000000000000
χ462-2-2-2222-2-1-22-2211-1-11-112i−2i−2i2i1-1ii−i−i1-1002-2002i−2ii3−i3i3−i30000−ii−33−33i3i3−i3−i3−3−3330000-11−ii00000000000000
χ472-2-2-2222-2-1-22-2211-1-11-112i−2i−2i2i1-1ii−i−i1-100-2200−2i2i−i3i3−i3i30000−ii3−33−3i3i3−i3−i3−3−33300001-1i−i00000000000000
χ482-2-2-2222-2-1-22-2211-1-11-112i−2i−2i2i1-1ii−i−i1-100-2200−2i2ii3−i3i3−i30000−ii−33−33−i3−i3i3i333−3−300001-1i−i00000000000000
χ492-2-2-2222-2-1-22-2211-1-11-11−2i2i2i−2i1-1−i−iii1-1002-200−2i2i−i3i3−i3i30000i−i−33−33−i3−i3i3i3−3−3330000-11i−i00000000000000
χ502-2-2-2222-2-1-22-2211-1-11-11−2i2i2i−2i1-1−i−iii1-1002-200−2i2ii3−i3i3−i30000i−i3−33−3i3i3−i3−i333−3−30000-11i−i00000000000000
χ512-2-2-2222-2-1-22-2211-1-11-11−2i2i2i−2i1-1−i−iii1-100-22002i−2i−i3i3−i3i30000i−i−33−33i3i3−i3−i333−3−300001-1−ii00000000000000
χ522-2-2-2222-2-1-22-2211-1-11-11−2i2i2i−2i1-1−i−iii1-100-22002i−2ii3−i3i3−i30000i−i3−33−3−i3−i3i3i3−3−33300001-1−ii00000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222222220000000000000000-2-20000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422-2-2-2-2220000000000000000220000000000000000000000000000000000
χ55444-44-4-4-4400004-4-4-444-400000000000000000000000022−220000000022−2222−2200000000000000000000000000
χ56444-44-4-4-4400004-4-4-444-4000000000000000000000000−222200000000−2222−222200000000000000000000000000
χ57444-44-4-4-4-20000-2222-2-2200000023−2323−230000000000000022−2200000000−22−226−66−60000000000000000000000
χ58444-44-4-4-4-20000-2222-2-2200000023−2323−2300000000000000−2222000000002−22−2−66−660000000000000000000000
χ59444-44-4-4-4-20000-2222-2-22000000−2323−23230000000000000022−2200000000−22−22−66−660000000000000000000000
χ60444-44-4-4-4-20000-2222-2-22000000−2323−232300000000000000−2222000000002−22−26−66−60000000000000000000000
χ6144-44-4-44-440000-444-44-4-40000000000000000000000000000000000000000000000000000000000000022−22
χ6244-44-4-44-440000-444-44-4-400000000000000000000000000000000000000000000000000000000000000−2222
χ6344-4-4-44-4444-4-44-4-4-444-4400004-40000-440000000000000000000000000000000000000000000000000000
χ6444-4-4-44-444-444-4-4-4-444-440000-4400004-40000000000000000000000000000000000000000000000000000
χ6544-4-4-44-44-24-4-44222-2-22-20000-2200002-2000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6644-4-4-44-44-24-4-44222-2-22-20000-2200002-20000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ6744-4-4-44-44-2-444-4222-2-22-200002-20000-2200000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ6844-4-4-44-44-2-444-4222-2-22-200002-20000-22000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ694-444-44-4-4-244-4-4-2-22-22220000-2-20000224-4000000-2-2220000000000000000000000000000000000000000
χ704-444-44-4-4-244-4-4-2-22-22220000-2-2000022-4400000022-2-20000000000000000000000000000000000000000
χ714-444-44-4-4-2-4-444-2-22-22220000220000-2-200004i−4i000000000000−2i−2i2i2i000000000000000000000000000000
χ724-444-44-4-4-2-4-444-2-22-22220000220000-2-20000−4i4i0000000000002i2i−2i−2i000000000000000000000000000000
χ734-44-4-4-444400004-44-4-4-4400000000000000000000000000000000000000000000000000000000000022−2200
χ744-44-4-4-444400004-44-4-4-44000000000000000000000000000000000000000000000000000000000000−222200
χ754-4-444-4-4440000-44-4-4-4440000000000000000000000000022−22000000000022−22−22220000000000000000000000
χ764-4-444-4-4440000-44-4-4-44400000000000000000000000000−22220000000000−222222−220000000000000000000000
χ774-4-444-4-44-200002-2222-2-2000000−2i32i32i3−2i3000000000000000022−22000000i6−i6−i6i6−222−20000000000000000000000
χ784-4-444-4-44-200002-2222-2-2000000−2i32i32i3−2i30000000000000000−2222000000−i6i6i6−i62−2−220000000000000000000000
χ794-4-444-4-44-200002-2222-2-20000002i3−2i3−2i32i3000000000000000022−22000000−i6i6i6−i6−222−20000000000000000000000
χ804-4-444-4-44-200002-2222-2-20000002i3−2i3−2i32i30000000000000000−2222000000i6−i6−i6i62−2−220000000000000000000000
χ814-4-4-4444-4-24-44-422-2-22-224i−4i4i−4i-22−2i−2i2i2i-220000000000000000−2i2i0000000000000000000000000000000000
χ824-4-4-4444-4-24-44-422-2-22-22−4i4i−4i4i-222i2i−2i−2i-2200000000000000002i−2i0000000000000000000000000000000000
χ8388-88-8-88-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-8-888-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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