Finite Group Databasebeta

← Group #10896392

Character table — Group #10896392

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order122222223444466666664444444412121212121212121212121244444444441212121212121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1211111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-222-2-22222-2-2-2-2-2-2-2-20000002-20022-2-222-2-200000000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-22222-2-2-2-2000000-220022-2-2-2-22200000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-22222-2-2-2-2-2-2-2-2000000-2200-2-222-2-22200000000000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-222-2-2-2-22222-2-2-2-20000002-200-2-22222-2-200000000000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-122-2-2-2-2-2-222-1-1-1-11111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-2-22222-2-2-2-2-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-211111111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222111111111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-122-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-2-222-2-222221111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1111111110000002-200-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1111111110000002-200-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-11111000000-2200-1-11111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-11111000000-2200-1-11111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-111111111000000-220011-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-111111111000000-220011-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-111110000002-20011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-111110000002-20011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ37222-22-2-2-2222-2-222-2-2-2-222-22-200000000000022-2-2002-22-200002-22-20000000000002-22-22-22-20000000000000000
χ38222-22-2-2-2222-2-222-2-2-2-222-22-200000000000022-2-200-22-2200002-22-2000000000000-22-22-22-220000000000000000
χ39222-22-2-2-2222-2-222-2-2-2-22-22-2200000000000022-2-2002-2-220000-22-220000000000002-22-2-22-220000000000000000
χ40222-22-2-2-2222-2-222-2-2-2-22-22-2200000000000022-2-200-222-20000-22-22000000000000-22-222-22-20000000000000000
χ41222-22-2-2-22-2-22222-2-2-2-222-2-22000000000000-2-2222i−2i0000002i−2i2-2-2200002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ42222-22-2-2-22-2-22222-2-2-2-222-2-22000000000000-2-222−2i2i000000−2i2i2-2-220000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ43222-22-2-2-22-2-22222-2-2-2-22-222-2000000000000-2-2222i−2i000000−2i2i-222-200002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ44222-22-2-2-22-2-22222-2-2-2-22-222-2000000000000-2-222−2i2i0000002i−2i-222-20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ45222-22-2-2-2-122-2-2-1-11111-12-22-2000033−3−333−3−3-1-111002-22-20000-11-113−33−33−3−333−3−33-11-11-11-110000000000000000
χ46222-22-2-2-2-122-2-2-1-11111-12-22-2000033−3−333−3−3-1-11100-22-220000-11-113−33−3−333−3−333−31-11-11-11-10000000000000000
χ47222-22-2-2-2-122-2-2-1-11111-12-22-20000−3−333−3−333-1-111002-22-20000-11-11−33−33−333−3−333−3-11-11-11-110000000000000000
χ48222-22-2-2-2-122-2-2-1-11111-12-22-20000−3−333−3−333-1-11100-22-220000-11-11−33−333−3−333−3−331-11-11-11-10000000000000000
χ49222-22-2-2-2-122-2-2-1-11111-1-22-22000033−3−333−3−3-1-111002-2-2200001-11-1−33−333−3−33−333−3-11-111-11-10000000000000000
χ50222-22-2-2-2-122-2-2-1-11111-1-22-22000033−3−333−3−3-1-11100-222-200001-11-1−33−33−333−33−3−331-11-1-11-110000000000000000
χ51222-22-2-2-2-122-2-2-1-11111-1-22-220000−3−333−3−333-1-111002-2-2200001-11-13−33−3−333−33−3−33-11-111-11-10000000000000000
χ52222-22-2-2-2-122-2-2-1-11111-1-22-220000−3−333−3−333-1-11100-222-200001-11-13−33−33−3−33−333−31-11-1-11-110000000000000000
χ53222-22-2-2-2-1-2-222-1-11111-12-2-22000033−3−3−3−33311-1-12i−2i0000002i−2i-111-13−3−33−ii−ii−ii−ii−i3i3i3−i3−i3i3i3−i30000000000000000
χ54222-22-2-2-2-1-2-222-1-11111-12-2-22000033−3−3−3−33311-1-1−2i2i000000−2i2i-111-13−3−33i−ii−ii−ii−ii3−i3−i3i3i3−i3−i3i30000000000000000
χ55222-22-2-2-2-1-2-222-1-11111-12-2-220000−3−33333−3−311-1-12i−2i0000002i−2i-111-1−333−3−ii−ii−ii−iii3−i3−i3i3i3−i3−i3i30000000000000000
χ56222-22-2-2-2-1-2-222-1-11111-12-2-220000−3−33333−3−311-1-1−2i2i000000−2i2i-111-1−333−3i−ii−ii−ii−i−i3i3i3−i3−i3i3i3−i30000000000000000
χ57222-22-2-2-2-1-2-222-1-11111-1-222-2000033−3−3−3−33311-1-12i−2i000000−2i2i1-1-11−333−3−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i30000000000000000
χ58222-22-2-2-2-1-2-222-1-11111-1-222-2000033−3−3−3−33311-1-1−2i2i0000002i−2i1-1-11−333−3i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i30000000000000000
χ59222-22-2-2-2-1-2-222-1-11111-1-222-20000−3−33333−3−311-1-12i−2i000000−2i2i1-1-113−3−33−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i30000000000000000
χ60222-22-2-2-2-1-2-222-1-11111-1-222-20000−3−33333−3−311-1-1−2i2i0000002i−2i1-1-113−3−33i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i30000000000000000
χ612-2-2-2222-222-22-2-2-222-2-2200002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000002-22i−2i0000000000
χ622-2-2-2222-222-22-2-2-222-2-2200002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000000000000000-22−2i2i0000000000
χ632-2-2-2222-222-22-2-2-222-2-220000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000002-2−2i2i0000000000
χ642-2-2-2222-222-22-2-2-222-2-220000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2000000000000000000000000000000000000-222i−2i0000000000
χ652-2-2-2222-22-22-22-2-222-2-2200002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000000000000000002-200002i−2i00000000
χ662-2-2-2222-22-22-22-2-222-2-2200002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i-22-220000000000000000000000000000000000-220000−2i2i00000000
χ672-2-2-2222-22-22-22-2-222-2-220000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000000000000000002-20000−2i2i00000000
χ682-2-2-2222-22-22-22-2-222-2-220000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i-22-220000000000000000000000000000000000-2200002i−2i00000000
χ6944-44-44-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000022−22000000
χ7044-44-44-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000000000−2222000000
χ7144-4-4-4-444400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ7244-4-4-4-444400004-4-44-44-400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ734-444-4-44-440000-44-444-4-40000000000000000000000000000000000000000000000000000000000000000000022−22
χ744-444-4-44-440000-44-444-4-400000000000000000000000000000000000000000000000000000000000000000000−2222
χ754-44-4-44-4440000-444-4-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ764-44-4-44-4440000-444-4-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ774-4-444-4-4444-4-44-4-4-4-444400000000000000004-4-4400000000000000000000000000000000000000000000000000
χ784-4-444-4-444-444-4-4-4-4-44440000000000000000-444-400000000000000000000000000000000000000000000000000
χ794-4-444-4-44-24-4-442222-2-2-200000000−2i32i32i3−2i3−2i32i32i3−2i3-222-200000000000000000000000000000000000000000000000000
χ804-4-444-4-44-24-4-442222-2-2-2000000002i3−2i3−2i32i32i3−2i3−2i32i3-222-200000000000000000000000000000000000000000000000000
χ814-4-444-4-44-2-444-42222-2-2-200000000−2i32i32i3−2i32i3−2i3−2i32i32-2-2200000000000000000000000000000000000000000000000000
χ824-4-444-4-44-2-444-42222-2-2-2000000002i3−2i3−2i32i3−2i32i32i3−2i32-2-2200000000000000000000000000000000000000000000000000
χ834-4-4-4444-4-24-44-422-2-222-200004i−4i4i−4i−2i2i−2i2i−2i2i−2i2i-22-2200000000000000000000000000000000000000000000000000
χ844-4-4-4444-4-24-44-422-2-222-20000−4i4i−4i4i2i−2i2i−2i2i−2i2i−2i-22-2200000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2-44-4422-2-222-200004i−4i−4i4i−2i2i−2i2i2i−2i2i−2i2-22-200000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-2-44-4422-2-222-20000−4i4i4i−4i2i−2i2i−2i−2i2i−2i2i2-22-200000000000000000000000000000000000000000000000000
χ8788-88-88-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-8-888-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-8-88-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000

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