Finite Group Databasebeta

← Group #10896437

Character table — Group #10896437

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
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-11111
χ511111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-11111-1-1-1-1
χ911111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1
χ1011111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1111111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-111-1-1-111-1-111
χ1211111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1111-1-111-1-1
χ1311111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1
χ1511111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-111-1-111-1-1
χ1611111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-111
χ17222222222-2-2-2-2222222222-2-2-2-2-22222-2000000000000-2-2000000000000000022-2-2000000200-200000000
χ18222222222-2-2-2-2222222222-2-2-2-2-22222-2000000000000-2-20000000000000000-2-222000000-200200000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000022000000000000000022-2-2000000-200200000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-222000000200-200000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-12222-2-2-2-222-2-211-1-1-1-11111-1-1-1-111110000-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-122-2-222-2-2-2-22211-1-1-1-111111111-1-1-1-1000011-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-222-2-222-2-222111111-1-1-1-11111-1-1-1-10000-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-2-2-2222222-2-2111111-1-1-1-1-1-1-1-11111000011-1-100000000000000
χ29222-22-2-2-2222-2-2-2222-2-2-22-22-222-222-2-2-20000000000002-20000000000000000000000002-202-2000000000
χ30222-22-2-2-2222-2-2-2222-2-2-22-22-222-222-2-2-20000000000002-2000000000000000000000000-220-22000000000
χ31222-22-2-2-2222-2-2-2222-2-2-2-22-2222-2-2-222-2000000000000-220000000000000000000000002-20-22000000000
χ32222-22-2-2-2222-2-2-2222-2-2-2-22-2222-2-2-222-2000000000000-22000000000000000000000000-2202-2000000000
χ33222-22-2-2-22-2-222-2222-2-2-22-2-22-2-2222-2-22002i−2i2i−2i000000-22000000000000000000002i−2i2i−2i00000000000000
χ34222-22-2-2-22-2-222-2222-2-2-22-2-22-2-2222-2-2200−2i2i−2i2i000000-2200000000000000000000−2i2i−2i2i00000000000000
χ35222-22-2-2-22-2-222-2222-2-2-2-222-2-2-22-2-2222002i−2i−2i2i0000002-2000000000000000000002i−2i−2i2i00000000000000
χ36222-22-2-2-22-2-222-2222-2-2-2-222-2-2-22-2-222200−2i2i2i−2i0000002-200000000000000000000−2i2i2i−2i00000000000000
χ37222-22-2-2-2-1-2-2221-1-1-11112-2-2211-1-1-111-1002i−2i2i−2i0000001-133−3−333−3−3−i3−i3i3i3−i3−i3i3i30000−ii−ii00000000000000
χ38222-22-2-2-2-1-2-2221-1-1-11112-2-2211-1-1-111-1002i−2i2i−2i0000001-1−3−333−3−333i3i3−i3−i3i3i3−i3−i30000−ii−ii00000000000000
χ39222-22-2-2-2-1-2-2221-1-1-11112-2-2211-1-1-111-100−2i2i−2i2i0000001-133−3−333−3−3i3i3−i3−i3i3i3−i3−i30000i−ii−i00000000000000
χ40222-22-2-2-2-1-2-2221-1-1-11112-2-2211-1-1-111-100−2i2i−2i2i0000001-1−3−333−3−333−i3−i3i3i3−i3−i3i3i30000i−ii−i00000000000000
χ41222-22-2-2-2-1-2-2221-1-1-1111-222-211-111-1-1-1002i−2i−2i2i000000-1133−3−3−3−333−i3−i3i3i3i3i3−i3−i30000−iii−i00000000000000
χ42222-22-2-2-2-1-2-2221-1-1-1111-222-211-111-1-1-1002i−2i−2i2i000000-11−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000−iii−i00000000000000
χ43222-22-2-2-2-1-2-2221-1-1-1111-222-211-111-1-1-100−2i2i2i−2i000000-1133−3−3−3−333i3i3−i3−i3−i3−i3i3i30000i−i−ii00000000000000
χ44222-22-2-2-2-1-2-2221-1-1-1111-222-211-111-1-1-100−2i2i2i−2i000000-11−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000i−i−ii00000000000000
χ452-2-222-22-222-22-222-2-22-2-200002-2-2000020000002i−2i00000000002i−2i2i−2i000000002i−2i2i−2i00000000002-2000000
χ462-2-222-22-222-22-222-2-22-2-200002-2-2000020000002i−2i00000000002i−2i2i−2i00000000−2i2i−2i2i0000000000-22000000
χ472-2-222-22-222-22-222-2-22-2-200002-2-200002000000−2i2i0000000000−2i2i−2i2i000000002i−2i2i−2i0000000000-22000000
χ482-2-222-22-222-22-222-2-22-2-200002-2-200002000000−2i2i0000000000−2i2i−2i2i00000000−2i2i−2i2i00000000002-2000000
χ492-2-222-22-22-22-2222-2-22-2-20000-2220000-22-20000000000002-22-20000000000002i−2i−2i2i0000000000002i−2i0000
χ502-2-222-22-22-22-2222-2-22-2-20000-2220000-22-20000000000002-22-2000000000000−2i2i2i−2i000000000000−2i2i0000
χ512-2-222-22-22-22-2222-2-22-2-20000-2220000-2-22000000000000-22-220000000000002i−2i−2i2i000000000000−2i2i0000
χ522-2-222-22-22-22-2222-2-22-2-20000-2220000-2-22000000000000-22-22000000000000−2i2i2i−2i0000000000002i−2i0000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222-2-2-2-220000000000002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422222222000000000000-2-200000000000000000000000000000000000000
χ55444-44-4-4-4-244-4-42-2-2-22224-44-4-2-22-2-2222000000000000-2200000000000000000000000000000000000000
χ56444-44-4-4-4-244-4-42-2-2-2222-44-44-2-2222-2-220000000000002-200000000000000000000000000000000000000
χ5744-44-44-4-440000-4-44-44-4400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ5844-44-44-4-440000-4-44-44-44000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ5944-4-4-4-444400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000−2i22i200
χ6044-4-4-4-444400004-44-4-44-40000000000000000000000000000000000000000000000000000000000002i2−2i200
χ614-444-4-4-4440000-4-4-4444-40000000000000000000000−2i22i200000000000000−2i22i2−2i22i20000000000000000000000
χ624-444-4-4-4440000-4-4-4444-400000000000000000000002i2−2i2000000000000002i2−2i22i2−2i20000000000000000000000
χ634-444-4-4-44-20000222-2-2-220000000−2i32i3−2i32i300000000000−2i22i200000000006−66−6i2−i2i2−i20000000000000000000000
χ644-444-4-4-44-20000222-2-2-220000000−2i32i3−2i32i3000000000002i2−2i20000000000−66−66−i2i2−i2i20000000000000000000000
χ654-444-4-4-44-20000222-2-2-2200000002i3−2i32i3−2i300000000000−2i22i20000000000−66−66i2−i2i2−i20000000000000000000000
χ664-444-4-4-44-20000222-2-2-2200000002i3−2i32i3−2i3000000000002i2−2i200000000006−66−6−i2i2−i2i20000000000000000000000
χ674-44-4-444-4400004-4-44-4-4400000000000000000000−2i22i2000000000000−2i22i22i2−2i200000000000000000000000000
χ684-44-4-444-4400004-4-44-4-44000000000000000000002i2−2i20000000000002i2−2i2−2i22i200000000000000000000000000
χ694-44-4-444-4-20000-222-222-20000000−2i32i32i3−2i3000000000−2i22i2000000000000i2−i2−i2i26−6−660000000000000000000000
χ704-44-4-444-4-20000-222-222-20000000−2i32i32i3−2i30000000002i2−2i2000000000000−i2i2i2−i2−666−60000000000000000000000
χ714-44-4-444-4-20000-222-222-200000002i3−2i3−2i32i3000000000−2i22i2000000000000i2−i2−i2i2−666−60000000000000000000000
χ724-44-4-444-4-20000-222-222-200000002i3−2i3−2i32i30000000002i2−2i2000000000000−i2i2i2−i26−6−660000000000000000000000
χ734-4-444-44-4-24-44-4-2-222-2220000-2220000-20000004i−4i0000000000−2i2i−2i2i000000000000000000000000000000
χ744-4-444-44-4-24-44-4-2-222-2220000-2220000-2000000−4i4i00000000002i−2i2i−2i000000000000000000000000000000
χ754-4-444-44-4-2-44-44-2-222-22200002-2-2000024-4000000000000-22-220000000000000000000000000000000000
χ764-4-444-44-4-2-44-44-2-222-22200002-2-200002-440000000000002-22-20000000000000000000000000000000000
χ774-4-4-444-4444-4-44-44-4-4-44400004-440000-40000000000000000000000000000000000000000000000000000
χ784-4-4-444-444-444-4-44-4-4-4440000-44-4000040000000000000000000000000000000000000000000000000000
χ794-4-4-444-44-24-4-442-2222-2-20000-22-2000020000000000000023−23−23230000000000000000000000000000000000
χ804-4-4-444-44-24-4-442-2222-2-20000-22-20000200000000000000−232323−230000000000000000000000000000000000
χ814-4-4-444-44-2-444-42-2222-2-200002-220000-2000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ824-4-4-444-44-2-444-42-2222-2-200002-220000-20000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ8388-88-88-8-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-888-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000

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