Finite Group Databasebeta

← Group #10829894

Character table — Group #10829894

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222244444444888888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666121212124444661212444444441212121212121212121212124444881212121224242424222244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ9111111111111111111-1-1-1-111111-11-111-1-1-1-1-1-11111-1-1-1-111111-111-1-111-1-11-111-1-11-1-1-11-1
χ10111111111111111111-1-1-1-111111-11-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-1-11-1-111-1111-11
χ11111111111111111111-1-1-1-111111-11-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1111-1-1-1-1-11-111-11
χ12111111111111111111-1-1-1-111111-11-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-111-111111-11-1-11-1
χ13111111111111111111-1-1-1-11111-11-1111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-111-1111-1-1-11-1-1-11
χ14111111111111111111-1-1-1-11111-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-1111-1-1-1111-1111-1
χ15111111111111111111-1-1-1-11111-11-11-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-11-1-1-1-1-11111-1
χ16111111111111111111-1-1-1-11111-11-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-11111-1-11-111111-1-1-1-11
χ172222222-2-2-2-2222-2-2-2-222-2-222-2-20000000022-2-20000000022-2-2000000000000002-2000000
χ182222222-2-2-2-2222-2-2-2-222-2-222-2-20000000022-2-200000000-2-22200000000000000-22000000
χ192222222-2-2-2-2222-2-2-2-2-2-22222-2-200000000-2-2220000000022-2-200000000000000-22000000
χ202222222-2-2-2-2222-2-2-2-2-2-22222-2-200000000-2-22200000000-2-222000000000000002-2000000
χ21222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-2-2-2-2-1-1-1-1111111110000-2-2-1-1-1-11111000000000000
χ23222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000221111-1-1-1-1000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-22-222-2-21111-1-1-1-1111100002-2-1-111-1-111000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-22-2-2-22211111111-1-1-1-10000-22-1-11111-1-1000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-22-2222-2-21111-1-1-1-111110000-2211-1-111-1-1000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-22-22-2-22211111111-1-1-1-100002-211-1-1-1-111000000000000
χ292222-2-222-22-222222222-22-2-2-2-2-2000000002-22-20000000000000000000000220000-2-20000
χ302222-2-222-22-222222222-22-2-2-2-2-2000000002-22-20000000000000000000000-2-20000220000
χ312222-2-222-22-22222222-22-22-2-2-2-200000000-22-2200000000000000000000002-20000-220000
χ322222-2-222-22-22222222-22-22-2-2-2-200000000-22-220000000000000000000000-2200002-20000
χ332222-2-22-22-22222-2-2-2-22-2-22-2-22222-2-200002-2-22000000000000002-22-20000000000000000
χ342222-2-22-22-22222-2-2-2-22-2-22-2-222-2-22200002-2-2200000000000000-22-220000000000000000
χ352222-2-22-22-22222-2-2-2-2-222-2-2-2222-2-220000-222-2000000000000002-2-220000000000000000
χ362222-2-22-22-22222-2-2-2-2-222-2-2-222-222-20000-222-200000000000000-222-20000000000000000
χ372222-2-2-1-22-22-1-1-111112-2-2211-1-122-2-20000-111-133−3−333−3−3000000-11-113−33−3000000000000
χ382222-2-2-1-22-22-1-1-111112-2-2211-1-122-2-20000-111-1−3−333−3−333000000-11-11−33−33000000000000
χ392222-2-2-1-22-22-1-1-111112-2-2211-1-1-2-2220000-111-133−3−333−3−30000001-11-1−33−33000000000000
χ402222-2-2-1-22-22-1-1-111112-2-2211-1-1-2-2220000-111-1−3−333−3−3330000001-11-13−33−3000000000000
χ412222-2-2-1-22-22-1-1-11111-222-211-1-12-2-2200001-1-1133−3−3−3−333000000-111-13−3−33000000000000
χ422222-2-2-1-22-22-1-1-11111-222-211-1-12-2-2200001-1-11−3−33333−3−3000000-111-1−333−3000000000000
χ432222-2-2-1-22-22-1-1-11111-222-211-1-1-222-200001-1-1133−3−3−3−3330000001-1-11−333−3000000000000
χ442222-2-2-1-22-22-1-1-11111-222-211-1-1-222-200001-1-11−3−33333−3−30000001-1-113−3−33000000000000
χ452-22-22-222-2-222-2-222-2-200002-22-20000002-2000000002-22-22i−2i2i−2i0000000000000000002i−2i00
χ462-22-22-222-2-222-2-222-2-200002-22-20000002-2000000002-22-2−2i2i−2i2i000000000000000000−2i2i00
χ472-22-22-222-2-222-2-222-2-200002-22-2000000-2200000000-22-222i−2i2i−2i000000000000000000−2i2i00
χ482-22-22-222-2-222-2-222-2-200002-22-2000000-2200000000-22-22−2i2i−2i2i0000000000000000002i−2i00
χ492-22-22-22-222-22-2-2-2-22200002-2-2200002i−2i0000002i−2i2i−2i00002i−2i−2i2i0000000000002-200000000
χ502-22-22-22-222-22-2-2-2-22200002-2-2200002i−2i0000002i−2i2i−2i0000−2i2i2i−2i000000000000-2200000000
χ512-22-22-22-222-22-2-2-2-22200002-2-220000−2i2i000000−2i2i−2i2i00002i−2i−2i2i000000000000-2200000000
χ522-22-22-22-222-22-2-2-2-22200002-2-220000−2i2i000000−2i2i−2i2i0000−2i2i2i−2i0000000000002-200000000
χ53444444-2-4-4-4-4-2-2-2222244-4-4-2-22200000000-2-2220000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-22222-4-444-2-2220000000022-2-20000000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-2-2-2-2-24-44-4222200000000-22-220000000000000000000000000000000000
χ564444-4-4-24-44-4-2-2-2-2-2-2-2-44-442222000000002-22-20000000000000000000000000000000000
χ574-44-44-4-24-4-44-222-2-2220000-22-220000004-400000000-22-2200000000000000000000000000
χ584-44-44-4-24-4-44-222-2-2220000-22-22000000-44000000002-22-200000000000000000000000000
χ594-44-44-4-2-444-4-22222-2-20000-222-200004i−4i000000−2i2i−2i2i000000000000000000000000000000
χ604-44-44-4-2-444-4-22222-2-20000-222-20000−4i4i0000002i−2i2i−2i000000000000000000000000000000
χ614-44-4-44444-4-44-4-444-4-40000-44-440000000000000000000000000000000000000000000000
χ624-44-4-444-4-4444-4-4-4-4440000-444-40000000000000000000000000000000000000000000000
χ634-44-4-44-244-4-4-222-2-22200002-22-2000000000000−2i32i32i3−2i3000000000000000000000000000000
χ644-44-4-44-244-4-4-222-2-22200002-22-20000000000002i3−2i3−2i32i3000000000000000000000000000000
χ654-44-4-44-2-4-444-22222-2-200002-2-22000000000000000023−23−232300000000000000000000000000
χ664-44-4-44-2-4-444-22222-2-200002-2-220000000000000000−232323−2300000000000000000000000000
χ6788-8-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000
χ6988-8-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000
χ728-8-8800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000

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