Finite Group Databasebeta

← Group #10896438

Character table — Group #10896438

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
χ31111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-1-11111
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
χ911111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1111-1-111-1-111
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111-1-111-1-1
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-2-2-22222-2-20000000000000000-2-200000000000022-2-20000200-20000000000
χ18222222222-2-2-2-2222222222-2-2-2-22222-2-20000000000000000-2-2000000000000-2-2220000-20020000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000000002200000000000022-2-20000-20020000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000000022000000000000-2-2220000200-20000000000
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
χ29222-22-2-2-2222-2-222-22-2-2-20000220000-2-22-200000022-2-20000000000000000002-22-2000002-200000000000
χ30222-22-2-2-2222-2-222-22-2-2-20000220000-2-22-200000022-2-2000000000000000000-22-2200000-2200000000000
χ31222-22-2-2-2222-2-222-22-2-2-20000220000-2-2-22000000-2-2220000000000000000002-22-200000-2200000000000
χ32222-22-2-2-2222-2-222-22-2-2-20000220000-2-2-22000000-2-222000000000000000000-22-22000002-200000000000
χ33222-22-2-2-22-2-22222-22-2-2-20000-2-200002200002i−2i0000000000002i2i−2i−2i000000002-2-22000000002i−2i00000000
χ34222-22-2-2-22-2-22222-22-2-2-20000-2-200002200002i−2i0000000000002i2i−2i−2i00000000-222-200000000−2i2i00000000
χ35222-22-2-2-22-2-22222-22-2-2-20000-2-20000220000−2i2i000000000000−2i−2i2i2i000000002-2-2200000000−2i2i00000000
χ36222-22-2-2-22-2-22222-22-2-2-20000-2-20000220000−2i2i000000000000−2i−2i2i2i00000000-222-2000000002i−2i00000000
χ372-2-2222-2-222-22-2-2-2222-2-22i−2i2i−2i2-22i2i−2i−2i2-200000000000000002i−2i000000000000000000000000002i−2i2-20000
χ382-2-2222-2-222-22-2-2-2222-2-22i−2i2i−2i2-22i2i−2i−2i2-200000000000000002i−2i00000000000000000000000000−2i2i-220000
χ392-2-2222-2-222-22-2-2-2222-2-2−2i2i−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i000000000000000000000000002i−2i-220000
χ402-2-2222-2-222-22-2-2-2222-2-2−2i2i−2i2i2-2−2i−2i2i2i2-20000000000000000−2i2i00000000000000000000000000−2i2i2-20000
χ412-2-2222-2-22-22-22-2-2222-2-22i−2i−2i2i-222i2i−2i−2i-22002-2002i−2i00000000−2i2i00000000000000002-22i−2i00000000000000
χ422-2-2222-2-22-22-22-2-2222-2-22i−2i−2i2i-222i2i−2i−2i-2200-2200−2i2i00000000−2i2i0000000000000000-22−2i2i00000000000000
χ432-2-2222-2-22-22-22-2-2222-2-2−2i2i2i−2i-22−2i−2i2i2i-22002-200−2i2i000000002i−2i00000000000000002-2−2i2i00000000000000
χ442-2-2222-2-22-22-22-2-2222-2-2−2i2i2i−2i-22−2i−2i2i2i-2200-22002i−2i000000002i−2i0000000000000000-222i−2i00000000000000
χ452-2-2222-2-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-1002-2002i−2i−i3i3−i3i30000i−i3−33−3−i3−i3i3i333−3−30000-11−ii00000000000000
χ462-2-2222-2-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-1002-2002i−2ii3−i3i3−i30000i−i−33−33i3i3−i3−i3−3−3330000-11−ii00000000000000
χ472-2-2222-2-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-100-2200−2i2i−i3i3−i3i30000i−i3−33−3i3i3−i3−i3−3−33300001-1i−i00000000000000
χ482-2-2222-2-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-100-2200−2i2ii3−i3i3−i30000i−i−33−33−i3−i3i3i333−3−300001-1i−i00000000000000
χ492-2-2222-2-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-1002-200−2i2i−i3i3−i3i30000−ii−33−33−i3−i3i3i3−3−3330000-11i−i00000000000000
χ502-2-2222-2-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-1002-200−2i2ii3−i3i3−i30000−ii3−33−3i3i3−i3−i333−3−30000-11i−i00000000000000
χ512-2-2222-2-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-100-22002i−2i−i3i3−i3i30000−ii−33−33i3i3−i3−i333−3−300001-1−ii00000000000000
χ522-2-2222-2-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-100-22002i−2ii3−i3i3−i30000−ii3−33−3−i3−i3i3i3−3−33300001-1−ii00000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422-2-2-2-2220000000000000000220000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222222220000000000000000-2-20000000000000000000000000000000000
χ55444-44-4-4-4-244-4-4-2-22-22220000-2-20000224-4000000-2-2220000000000000000000000000000000000000000
χ56444-44-4-4-4-244-4-4-2-22-22220000-2-2000022-4400000022-2-20000000000000000000000000000000000000000
χ57444-44-4-4-4-2-4-444-2-22-22220000220000-2-200004i−4i000000000000−2i−2i2i2i000000000000000000000000000000
χ58444-44-4-4-4-2-4-444-2-22-22220000220000-2-20000−4i4i0000000000002i2i−2i−2i000000000000000000000000000000
χ5944-44-4-44-4400004-4-4-444-4000000000000000000000000000000000000000000000000000000000000−2i22i200
χ6044-44-4-44-4400004-4-4-444-40000000000000000000000000000000000000000000000000000000000002i2−2i200
χ6144-4-4-44-44400004-44-4-4-44000000000000000000000000−2i22i200000000−2i22i2−2i22i200000000000000000000000000
χ6244-4-4-44-44400004-44-4-4-440000000000000000000000002i2−2i2000000002i2−2i22i2−2i200000000000000000000000000
χ6344-4-4-44-44-20000-22-2222-200000023−2323−2300000000000000−2i22i200000000i2−i2i2−i2i6−i6i6−i60000000000000000000000
χ6444-4-4-44-44-20000-22-2222-200000023−2323−23000000000000002i2−2i200000000−i2i2−i2i2−i6i6−i6i60000000000000000000000
χ6544-4-4-44-44-20000-22-2222-2000000−2323−232300000000000000−2i22i200000000i2−i2i2−i2−i6i6−i6i60000000000000000000000
χ6644-4-4-44-44-20000-22-2222-2000000−2323−2323000000000000002i2−2i200000000−i2i2−i2i2i6−i6i6−i60000000000000000000000
χ674-444-4-4-4440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ684-444-4-4-4440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ694-44-4-444-440000-444-4-44-400000000000000000000000000−2i22i20000000000−2i22i22i2−2i20000000000000000000000
χ704-44-4-444-440000-444-4-44-4000000000000000000000000002i2−2i200000000002i2−2i2−2i22i20000000000000000000000
χ714-44-4-444-4-200002-2-222-22000000−2i32i32i3−2i30000000000000000−2i22i20000006−6−66i2−i2−i2i20000000000000000000000
χ724-44-4-444-4-200002-2-222-22000000−2i32i32i3−2i300000000000000002i2−2i2000000−666−6−i2i2i2−i20000000000000000000000
χ734-44-4-444-4-200002-2-222-220000002i3−2i3−2i32i30000000000000000−2i22i2000000−666−6i2−i2−i2i20000000000000000000000
χ744-44-4-444-4-200002-2-222-220000002i3−2i3−2i32i300000000000000002i2−2i20000006−6−66−i2i2i2−i20000000000000000000000
χ754-4-4444-4-4-24-44-422-2-2-2224i−4i4i−4i-22−2i−2i2i2i-220000000000000000−2i2i0000000000000000000000000000000000
χ764-4-4444-4-4-24-44-422-2-2-222−4i4i−4i4i-222i2i−2i−2i-2200000000000000002i−2i0000000000000000000000000000000000
χ774-4-4-44-44444-4-44-4-4-44-44400004-40000-440000000000000000000000000000000000000000000000000000
χ784-4-4-44-4444-444-4-4-4-44-4440000-4400004-40000000000000000000000000000000000000000000000000000
χ794-4-4-44-444-24-4-44222-22-2-20000-2200002-2000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ804-4-4-44-444-24-4-44222-22-2-20000-2200002-20000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ814-4-4-44-444-2-444-4222-22-2-200002-20000-2200000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ824-4-4-44-444-2-444-4222-22-2-200002-20000-22000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ8388-88-8-88-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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