Finite Group Databasebeta

← Group #10896416

Character table — Group #10896416

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order122222223444466666664444121212121212121244444444888812121212121212121212242424242424242444441212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111
χ17222222222-2-2-2-2222222222-2-2-2-22222-2-2000000000000-2-2000000000000000022-2-20000002-20000000000
χ18222222222-2-2-2-2222222222-2-2-2-22222-2-2000000000000-2-20000000000000000-2-222000000-220000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000022000000000000000022-2-2000000-220000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2220000002-20000000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
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
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-12222-2-2-2-222-2-211-1-1-1-11111-1-1-1-11111000011-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-1000011-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-10000-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-2-2-2222222-2-2111111-1-1-1-1-1-1-1-111110000-1-11100000000000000
χ292222-2-2-2-2222-2-222-2-22-2-20000220000-2-2002-2000000000022-2-20000000000002-22-200002-2000000000000
χ302222-2-2-2-2222-2-222-2-22-2-20000220000-2-2002-2000000000022-2-2000000000000-22-220000-22000000000000
χ312222-2-2-2-2222-2-222-2-22-2-20000220000-2-200-220000000000-2-2220000000000002-22-20000-22000000000000
χ322222-2-2-2-2222-2-222-2-22-2-20000220000-2-200-220000000000-2-222000000000000-22-2200002-2000000000000
χ332222-2-2-2-22-2-22222-2-22-2-20000-2-20000220000002i−2i00000000002i2i−2i−2i000000002-2-220000000000002i−2i0000
χ342222-2-2-2-22-2-22222-2-22-2-20000-2-20000220000002i−2i00000000002i2i−2i−2i00000000-222-2000000000000−2i2i0000
χ352222-2-2-2-22-2-22222-2-22-2-20000-2-2000022000000−2i2i0000000000−2i−2i2i2i000000002-2-22000000000000−2i2i0000
χ362222-2-2-2-22-2-22222-2-22-2-20000-2-2000022000000−2i2i0000000000−2i−2i2i2i00000000-222-20000000000002i−2i0000
χ3722-2-22-22-222-22-2-2-2222-2-22i−2i2i−2i2-22i2i−2i−2i2-20000000000002i−2i00000000000000000000000000002-22i−2i000000
χ3822-2-22-22-222-22-2-2-2222-2-22i−2i2i−2i2-22i2i−2i−2i2-20000000000002i−2i0000000000000000000000000000-22−2i2i000000
χ3922-2-22-22-222-22-2-2-2222-2-2−2i2i−2i2i2-2−2i−2i2i2i2-2000000000000−2i2i00000000000000000000000000002-2−2i2i000000
χ4022-2-22-22-222-22-2-2-2222-2-2−2i2i−2i2i2-2−2i−2i2i2i2-2000000000000−2i2i0000000000000000000000000000-222i−2i000000
χ4122-2-22-22-22-22-22-2-2222-2-22i−2i−2i2i-222i2i−2i−2i-222i−2i002-2000000−2i2i000000000000000000002-22i−2i00000000000000
χ4222-2-22-22-22-22-22-2-2222-2-22i−2i−2i2i-222i2i−2i−2i-22−2i2i00-22000000−2i2i00000000000000000000-22−2i2i00000000000000
χ4322-2-22-22-22-22-22-2-2222-2-2−2i2i2i−2i-22−2i−2i2i2i-222i−2i00-220000002i−2i00000000000000000000-222i−2i00000000000000
χ4422-2-22-22-22-22-22-2-2222-2-2−2i2i2i−2i-22−2i−2i2i2i-22−2i2i002-20000002i−2i000000000000000000002-2−2i2i00000000000000
χ4522-2-22-22-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-12i−2i002-2000000i−i−i3i3−i3i33−33−333−3−3−i3−i3i3i30000-11−ii00000000000000
χ4622-2-22-22-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-12i−2i002-2000000i−ii3−i3i3−i3−33−33−3−333i3i3−i3−i30000-11−ii00000000000000
χ4722-2-22-22-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-1−2i2i00-22000000i−i−i3i3−i3i33−33−3−3−333i3i3−i3−i300001-1i−i00000000000000
χ4822-2-22-22-2-1-22-2211-1-1-1112i−2i−2i2i1-1−i−iii1-1−2i2i00-22000000i−ii3−i3i3−i3−33−3333−3−3−i3−i3i3i300001-1i−i00000000000000
χ4922-2-22-22-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-12i−2i00-22000000−ii−i3i3−i3i3−33−3333−3−3i3i3−i3−i300001-1−ii00000000000000
χ5022-2-22-22-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-12i−2i00-22000000−iii3−i3i3−i33−33−3−3−333−i3−i3i3i300001-1−ii00000000000000
χ5122-2-22-22-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-1−2i2i002-2000000−ii−i3i3−i3i3−33−33−3−333−i3−i3i3i30000-11i−i00000000000000
χ5222-2-22-22-2-1-22-2211-1-1-111−2i2i2i−2i1-1ii−i−i1-1−2i2i002-2000000−iii3−i3i3−i33−33−333−3−3i3i3−i3−i30000-11i−i00000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422-2-2-2-2220000000000002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422222222000000000000-2-200000000000000000000000000000000000000
χ554444-4-4-4-4-244-4-4-2-222-2220000-2-2000022004-40000000000-2-2220000000000000000000000000000000000
χ564444-4-4-4-4-244-4-4-2-222-2220000-2-200002200-44000000000022-2-20000000000000000000000000000000000
χ574444-4-4-4-4-2-4-444-2-222-2220000220000-2-20000004i−4i0000000000−2i−2i2i2i000000000000000000000000000000
χ584444-4-4-4-4-2-4-444-2-222-2220000220000-2-2000000−4i4i00000000002i2i−2i−2i000000000000000000000000000000
χ5944-4-44-44-4-24-44-422-2-2-2224i−4i4i−4i-22−2i−2i2i2i-22000000000000−2i2i00000000000000000000000000000000000000
χ6044-4-44-44-4-24-44-422-2-2-222−4i4i−4i4i-222i2i−2i−2i-220000000000002i−2i00000000000000000000000000000000000000
χ6144-4-4-44-4444-4-44-4-4-4-444400004-40000-440000000000000000000000000000000000000000000000000000
χ6244-4-4-44-444-444-4-4-4-4-44440000-4400004-40000000000000000000000000000000000000000000000000000
χ6344-4-4-44-44-24-4-442222-2-2-20000-2200002-2000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6444-4-4-44-44-24-4-442222-2-2-20000-2200002-20000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ6544-4-4-44-44-2-444-42222-2-2-200002-20000-2200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ6644-4-4-44-44-2-444-42222-2-2-200002-20000-22000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ674-44-444-4-4400004-44-4-44-400000000000000000000000000000000000000000000000000000000000022−2200
χ684-44-444-4-4400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000−222200
χ694-44-4-4-444400004-4-44-4-440000000000000000000022−2200000000000022−2222−2200000000000000000000000000
χ704-44-4-4-444400004-4-44-4-4400000000000000000000−2222000000000000−2222−222200000000000000000000000000
χ714-44-4-4-444-20000-222-222-200000023−2323−23000000000022−22000000000000−22−226−66−60000000000000000000000
χ724-44-4-4-444-20000-222-222-200000023−2323−230000000000−22220000000000002−22−2−66−660000000000000000000000
χ734-44-4-4-444-20000-222-222-2000000−2323−2323000000000022−22000000000000−22−22−66−660000000000000000000000
χ744-44-4-4-444-20000-222-222-2000000−2323−23230000000000−22220000000000002−22−26−66−60000000000000000000000
χ754-4-444-4-4440000-444-4-4-4400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ764-4-444-4-4440000-444-4-4-44000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ774-4-44-444-440000-44-44-44-40000000000000000000000−2i22i200000000000000−2i22i22i2−2i20000000000000000000000
χ784-4-44-444-440000-44-44-44-400000000000000000000002i2−2i2000000000000002i2−2i2−2i22i20000000000000000000000
χ794-4-44-444-4-200002-22-22-22000000−2i32i32i3−2i3000000000000−2i22i200000000006−6−66i2−i2−i2i20000000000000000000000
χ804-4-44-444-4-200002-22-22-22000000−2i32i32i3−2i30000000000002i2−2i20000000000−666−6−i2i2i2−i20000000000000000000000
χ814-4-44-444-4-200002-22-22-220000002i3−2i3−2i32i3000000000000−2i22i20000000000−666−6i2−i2−i2i20000000000000000000000
χ824-4-44-444-4-200002-22-22-220000002i3−2i3−2i32i30000000000002i2−2i200000000006−6−66−i2i2i2−i20000000000000000000000
χ838-88-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000

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