Finite Group Databasebeta

← Group #10828563

Character table — Group #10828563

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order122222223444466666664444121212121212121244444444888812121212121212121212242424242424242422441212121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-11111
χ511111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-11-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-11111-111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-111111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-111-1-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-111-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-111-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-111
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-20000000000000000-2-200000000000022-2-2000000-200002000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-20000000000000000-2-2000000000000-2-22200000020000-2000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000000002200000000000022-2-200000020000-2000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000000022000000000000-2-222000000-200002000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-21111-1-11111111111110000-1-1-1-100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-10000111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-12222-2-2-2-222-2-2-1-1-1-1111111-1-1-1-111110000-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-10000-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-22222-2-2-2-222-1-1-1-11111111111-1-1-1-1000011-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-2-2-2222222-2-2111111-1-1-1-1-1-1-1-11111000011-1-100000000000000
χ292-2-222-22-222-22-22-2-2-222-22i−2i2i−2i2i2i−2i−2i2-22-200000000000000002i−2i000000000000000000002-20000002i−2i0000
χ302-2-222-22-222-22-22-2-2-222-22i−2i2i−2i2i2i−2i−2i2-22-200000000000000002i−2i00000000000000000000-22000000−2i2i0000
χ312-2-222-22-222-22-22-2-2-222-2−2i2i−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i000000000000000000002-2000000−2i2i0000
χ322-2-222-22-222-22-22-2-2-222-2−2i2i−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i00000000000000000000-220000002i−2i0000
χ332-2-222-22-22-22-222-2-2-222-22i−2i−2i2i2i2i−2i−2i-22-222-2002i−2i0000000000−2i2i00000000000000002-22i−2i00000000000000
χ342-2-222-22-22-22-222-2-2-222-22i−2i−2i2i2i2i−2i−2i-22-22-2200−2i2i0000000000−2i2i0000000000000000-22−2i2i00000000000000
χ352-2-222-22-22-22-222-2-2-222-2−2i2i2i−2i−2i−2i2i2i-22-222-200−2i2i00000000002i−2i00000000000000002-2−2i2i00000000000000
χ362-2-222-22-22-22-222-2-2-222-2−2i2i2i−2i−2i−2i2i2i-22-22-22002i−2i00000000002i−2i0000000000000000-222i−2i00000000000000
χ372-2-222-22-2-1-22-22-1111-1-112i−2i−2i2i−i−iii1-11-12-2002i−2i000000−i3−i3i3i3i−i33−3−3−i3−i3i3i333−3−30000-11−ii00000000000000
χ382-2-222-22-2-1-22-22-1111-1-112i−2i−2i2i−i−iii1-11-12-2002i−2i000000i3i3−i3−i3i−i−3−333i3i3−i3−i3−3−3330000-11−ii00000000000000
χ392-2-222-22-2-1-22-22-1111-1-112i−2i−2i2i−i−iii1-11-1-2200−2i2i000000−i3−i3i3i3i−i33−3−3i3i3−i3−i3−3−33300001-1i−i00000000000000
χ402-2-222-22-2-1-22-22-1111-1-112i−2i−2i2i−i−iii1-11-1-2200−2i2i000000i3i3−i3−i3i−i−3−333−i3−i3i3i333−3−300001-1i−i00000000000000
χ412-2-222-22-2-1-22-22-1111-1-11−2i2i2i−2iii−i−i1-11-12-200−2i2i000000−i3−i3i3i3−ii−3−333−i3−i3i3i3−3−3330000-11i−i00000000000000
χ422-2-222-22-2-1-22-22-1111-1-11−2i2i2i−2iii−i−i1-11-12-200−2i2i000000i3i3−i3−i3−ii33−3−3i3i3−i3−i333−3−30000-11i−i00000000000000
χ432-2-222-22-2-1-22-22-1111-1-11−2i2i2i−2iii−i−i1-11-1-22002i−2i000000−i3−i3i3i3−ii−3−333i3i3−i3−i333−3−300001-1−ii00000000000000
χ442-2-222-22-2-1-22-22-1111-1-11−2i2i2i−2iii−i−i1-11-1-22002i−2i000000i3i3−i3−i3−ii33−3−3−i3−i3i3i3−3−33300001-1−ii00000000000000
χ452-2-2-2-222222-2-22-2-2-22-22200000000-222-2002-2000000002-22-2000000000000002-22-200000002-2000000000
χ462-2-2-2-222222-2-22-2-2-22-22200000000-222-2002-2000000002-22-200000000000000-22-220000000-22000000000
χ472-2-2-2-222222-2-22-2-2-22-22200000000-222-200-2200000000-22-22000000000000002-22-20000000-22000000000
χ482-2-2-2-222222-2-22-2-2-22-22200000000-222-200-2200000000-22-2200000000000000-22-2200000002-2000000000
χ492-2-2-2-22222-222-2-2-2-22-222000000002-2-220000002-200000000002-22-2000000002-2-220000000002-20000000
χ502-2-2-2-22222-222-2-2-2-22-222000000002-2-220000002-200000000002-22-200000000-222-2000000000-220000000
χ512-2-2-2-22222-222-2-2-2-22-222000000002-2-22000000-220000000000-22-22000000002-2-22000000000-220000000
χ522-2-2-2-22222-222-2-2-2-22-222000000002-2-22000000-220000000000-22-2200000000-222-20000000002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-222220000000000000000220000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222222220000000000000000-2-20000000000000000000000000000000000
χ55444-4-4-44-4444-4-4-444-4-44-400000000-4-4440000000000000000000000000000000000000000000000000000
χ56444-4-4-44-44-4-444-444-4-44-40000000044-4-40000000000000000000000000000000000000000000000000000
χ57444-4-4-44-4-244-4-42-2-222-220000000022-2-200000000000000000023−23−2323000000000000000000000000000000
χ58444-4-4-44-4-244-4-42-2-222-220000000022-2-2000000000000000000−232323−23000000000000000000000000000000
χ59444-4-4-44-4-2-4-4442-2-222-2200000000-2-222000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ60444-4-4-44-4-2-4-4442-2-222-2200000000-2-2220000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ6144-44-44-4-440000-44-444-4-400000000000000000000000000000000000000000000000000000000000022−2200
χ6244-44-44-4-440000-44-444-4-4000000000000000000000000000000000000000000000000000000000000−222200
χ6344-4-44-4-444000044-4-4-4-440000000000000000000000−2i22i200000000000000−2i22i2−2i22i20000000000000000000000
χ6444-4-44-4-444000044-4-4-4-4400000000000000000000002i2−2i2000000000000002i2−2i22i2−2i20000000000000000000000
χ6544-4-44-4-44-20000-2-22222-2000023−2323−2300000000000000−2i22i20000000000i6−i6i6−i6i2−i2i2−i20000000000000000000000
χ6644-4-44-4-44-20000-2-22222-2000023−2323−23000000000000002i2−2i20000000000−i6i6−i6i6−i2i2−i2i20000000000000000000000
χ6744-4-44-4-44-20000-2-22222-20000−2323−232300000000000000−2i22i20000000000−i6i6−i6i6i2−i2i2−i20000000000000000000000
χ6844-4-44-4-44-20000-2-22222-20000−2323−2323000000000000002i2−2i20000000000i6−i6i6−i6−i2i2−i2i20000000000000000000000
χ694-444-4-4-4440000-4-44-44-4400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ704-444-4-4-4440000-4-44-44-44000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ714-44-444-4-4400004-444-4-4-40000000000000000000022−2200000000000022−22−222200000000000000000000000000
χ724-44-444-4-4400004-444-4-4-400000000000000000000−2222000000000000−222222−2200000000000000000000000000
χ734-44-444-4-4-20000-22-2-22220000−2i32i32i3−2i300000000000022−22000000000000−222−2−i6i6i6−i60000000000000000000000
χ744-44-444-4-4-20000-22-2-22220000−2i32i32i3−2i3000000000000−22220000000000002−2−22i6−i6−i6i60000000000000000000000
χ754-44-444-4-4-20000-22-2-222200002i3−2i3−2i32i300000000000022−22000000000000−222−2i6−i6−i6i60000000000000000000000
χ764-44-444-4-4-20000-22-2-222200002i3−2i3−2i32i3000000000000−22220000000000002−2−22−i6i6i6−i60000000000000000000000
χ774-4-444-44-4-24-44-4-2222-2-224i−4i4i−4i−2i−2i2i2i-22-220000000000000000−2i2i0000000000000000000000000000000000
χ784-4-444-44-4-24-44-4-2222-2-22−4i4i−4i4i2i2i−2i−2i-22-2200000000000000002i−2i0000000000000000000000000000000000
χ794-4-4-4-4444-24-4-44222-22-2-2000000002-2-22004-400000000-22-22000000000000000000000000000000000000
χ804-4-4-4-4444-24-4-44222-22-2-2000000002-2-2200-44000000002-22-2000000000000000000000000000000000000
χ814-4-4-4-4444-2-444-4222-22-2-200000000-222-20000004-40000000000-22-22000000000000000000000000000000
χ824-4-4-4-4444-2-444-4222-22-2-200000000-222-2000000-4400000000002-22-2000000000000000000000000000000
χ8388-88-88-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000

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