Finite Group Databasebeta

← Group #10853214

Character table — Group #10853214

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order1222222234444666666622441212121212121212444444446688881212121212121212242424242424242444444444121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ41111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ511111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ911111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-11-1-111-1-11-1
χ1011111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-111-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1111-1-1111-1
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111111111-1-11-1-1-111-1-1-11
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-111-11-1-1-1-111-11
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111-11111-1-11-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-111111-1-1-11
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-11-1-1-1-1-1111-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002200000000000000000000222200000000-2-200000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002200000000000000000000-2-2-2-2000000002200000000
χ19222222222-2-2-2-22222222-2-222-2-22222-2-200000000-2-20000000000000000000022-2-2000000002-200000000
χ20222222222-2-2-2-22222222-2-222-2-22222-2-200000000-2-200000000000000000000-2-22200000000-2200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-2-222-1-1-2-2-2-2111111111111111100000000-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-12222-2-2-2-21122-2-21111-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-2-2-22211-2-2221111-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-22222-2-211-2-222-1-1-1-111111111-1-1-1-10000000011-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-2-2-222221122-2-2-1-1-1-11111-1-1-1-1111100000000-1-1110000000000
χ29222-2-2-2-22222-2-222-22-2-2-22-22-22222-2-2-2-2000000002-200000000000000000000000022-2-20000002-2000000
χ30222-2-2-2-22222-2-222-22-2-2-22-22-22222-2-2-2-2000000002-2000000000000000000000000-2-222000000-22000000
χ31222-2-2-2-22222-2-222-22-2-2-2-22-2222-2-222-2-200000000-2200000000000000000000000022-2-2000000-22000000
χ32222-2-2-2-22222-2-222-22-2-2-2-22-2222-2-222-2-200000000-22000000000000000000000000-2-2220000002-2000000
χ33222-2-2-2-222-2-22222-22-2-2-22-2-22-2-2-2-22222002i−2i002i−2i2-200000000000000000000000000002i−2i2i−2i0000000000
χ34222-2-2-2-222-2-22222-22-2-2-22-2-22-2-2-2-2222200−2i2i00−2i2i2-20000000000000000000000000000−2i2i−2i2i0000000000
χ35222-2-2-2-222-2-22222-22-2-2-2-222-2-2-222-2-222002i−2i00−2i2i-220000000000000000000000000000−2i2i2i−2i0000000000
χ36222-2-2-2-222-2-22222-22-2-2-2-222-2-2-222-2-22200−2i2i002i−2i-2200000000000000000000000000002i−2i−2i2i0000000000
χ37222-2-2-2-22-1-2-222-1-11-11112-2-221111-1-1-1-1002i−2i002i−2i-11000033−3−333−3−3−i3−i3i3i3−i3−i3i3i300000000−ii−ii0000000000
χ38222-2-2-2-22-1-2-222-1-11-11112-2-221111-1-1-1-1002i−2i002i−2i-110000−3−333−3−333i3i3−i3−i3i3i3−i3−i300000000−ii−ii0000000000
χ39222-2-2-2-22-1-2-222-1-11-11112-2-221111-1-1-1-100−2i2i00−2i2i-11000033−3−333−3−3i3i3−i3−i3i3i3−i3−i300000000i−ii−i0000000000
χ40222-2-2-2-22-1-2-222-1-11-11112-2-221111-1-1-1-100−2i2i00−2i2i-110000−3−333−3−333−i3−i3i3i3−i3−i3i3i300000000i−ii−i0000000000
χ41222-2-2-2-22-1-2-222-1-11-1111-222-211-1-111-1-1002i−2i00−2i2i1-1000033−3−3−3−333i3i3−i3−i3−i3−i3i3i300000000i−i−ii0000000000
χ42222-2-2-2-22-1-2-222-1-11-1111-222-211-1-111-1-1002i−2i00−2i2i1-10000−3−33333−3−3−i3−i3i3i3i3i3−i3−i300000000i−i−ii0000000000
χ43222-2-2-2-22-1-2-222-1-11-1111-222-211-1-111-1-100−2i2i002i−2i1-1000033−3−3−3−333−i3−i3i3i3i3i3−i3−i300000000−iii−i0000000000
χ44222-2-2-2-22-1-2-222-1-11-1111-222-211-1-111-1-100−2i2i002i−2i1-10000−3−33333−3−3i3i3−i3−i3−i3−i3i3i300000000−iii−i0000000000
χ452-222-22-2-222-2-22-2-2222-2-200002-200002-200002i−2i000000002i−2i2i−2i00000000000000002i−2i2i−2i00000000002-200
χ462-222-22-2-222-2-22-2-2222-2-200002-200002-200002i−2i000000002i−2i2i−2i0000000000000000−2i2i−2i2i0000000000-2200
χ472-222-22-2-222-2-22-2-2222-2-200002-200002-20000−2i2i00000000−2i2i−2i2i00000000000000002i−2i2i−2i0000000000-2200
χ482-222-22-2-222-2-22-2-2222-2-200002-200002-20000−2i2i00000000−2i2i−2i2i0000000000000000−2i2i−2i2i00000000002-200
χ492-22-22-22-222-22-2-2-2-22-22200002-20000-222-200000000000000002-22-20000000000002i−2i−2i2i000000002i−2i0000
χ502-22-22-22-222-22-2-2-2-22-22200002-20000-222-200000000000000002-22-2000000000000−2i2i2i−2i00000000−2i2i0000
χ512-22-22-22-222-22-2-2-2-22-22200002-20000-22-220000000000000000-22-220000000000002i−2i−2i2i00000000−2i2i0000
χ522-22-22-22-222-22-2-2-2-22-22200002-20000-22-220000000000000000-22-22000000000000−2i2i2i−2i000000002i−2i0000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-42222222200000000-2-2000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422-2-2-2-2220000000022000000000000000000000000000000000000000000
χ55444-4-4-4-44-244-4-4-2-22-22224-44-4-2-2-2-2222200000000-22000000000000000000000000000000000000000000
χ56444-4-4-4-44-244-4-4-2-22-2222-44-44-2-222-2-222000000002-2000000000000000000000000000000000000000000
χ5744-44-4-44-4400004-44-4-44-40000000000000000000000000000000000000000004-400000000000000000000
χ5844-44-4-44-4400004-44-4-44-4000000000000000000000000000000000000000000-4400000000000000000000
χ5944-4-444-4-4400004-4-4-44-44000000000000000000000000000000000000000000004i−4i000000000000000000
χ6044-4-444-4-4400004-4-4-44-4400000000000000000000000000000000000000000000−4i4i000000000000000000
χ614-444-44-4-44-444-4-4-4444-4-40000-440000-440000000000000000000000000000000000000000000000000000
χ624-444-44-4-4-24-4-4422-2-2-2220000-220000-2200004i−4i00000000−2i2i−2i2i0000000000000000000000000000000000
χ634-444-44-4-4-24-4-4422-2-2-2220000-220000-220000−4i4i000000002i−2i2i−2i0000000000000000000000000000000000
χ644-444-44-4-4-2-444-422-2-2-22200002-200002-200000000000000000023−23−2323000000000000000000000000000000
χ654-444-44-4-4-2-444-422-2-2-22200002-200002-2000000000000000000−232323−23000000000000000000000000000000
χ664-44-44-44-44-44-44-4-4-44-4440000-4400004-40000000000000000000000000000000000000000000000000000
χ674-44-44-44-4-24-44-4222-22-2-20000-2200002-24-40000000000000000-22-22000000000000000000000000000000
χ684-44-44-44-4-24-44-4222-22-2-20000-2200002-2-4400000000000000002-22-2000000000000000000000000000000
χ694-44-44-44-4-2-44-44222-22-2-200002-20000-2200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ704-44-44-44-4-2-44-44222-22-2-200002-20000-22000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ714-4-444-4-4440000-444-4-4-44000000000000000000000000−2i22i2000000000000−2i22i2−2i22i20000000000000000000000
χ724-4-444-4-4440000-444-4-4-440000000000000000000000002i2−2i20000000000002i2−2i22i2−2i20000000000000000000000
χ734-4-444-4-44-200002-2-2222-200000023−2323−2300000000000000−2i22i200000000i6−i6i6−i6i2−i2i2−i20000000000000000000000
χ744-4-444-4-44-200002-2-2222-200000023−2323−23000000000000002i2−2i200000000−i6i6−i6i6−i2i2−i2i20000000000000000000000
χ754-4-444-4-44-200002-2-2222-2000000−2323−232300000000000000−2i22i200000000−i6i6−i6i6i2−i2i2−i20000000000000000000000
χ764-4-444-4-44-200002-2-2222-2000000−2323−2323000000000000002i2−2i200000000i6−i6i6−i6−i2i2−i2i20000000000000000000000
χ774-4-4-4-444440000-44-4-444-4000000000000000000000022−22000000000022−22−222200000000000000000000000000
χ784-4-4-4-444440000-44-4-444-40000000000000000000000−22220000000000−222222−2200000000000000000000000000
χ794-4-4-4-4444-200002-222-2-2200000023−23−232300000000000022−220000000000−222−2−666−60000000000000000000000
χ804-4-4-4-4444-200002-222-2-2200000023−23−2323000000000000−222200000000002−2−226−6−660000000000000000000000
χ814-4-4-4-4444-200002-222-2-22000000−232323−2300000000000022−220000000000−222−26−6−660000000000000000000000
χ824-4-4-4-4444-200002-222-2-22000000−232323−23000000000000−222200000000002−2−22−666−60000000000000000000000
χ8388-88-8-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-888-8-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000

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