Finite Group Databasebeta

← Group #10828060

Character table — Group #10828060

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212161616161616161616162424242424242424242424242424
order122222223444466624466666612121212244444441212121212121212121222446881212122424242422244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ611111111111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-1-1-111111-1-1-1-111111-1-1-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-11111-1-1-1-1-11111
χ91111-1-11111111111-1-1-111-1-1-1-111111-111-1-1-11-1-11111-1-1-1-1111111-1-11-111-1-1-111-1-1-111-1-111-1-1
χ101111-1-11111111111-1-1-111-1-1-1-111111-111-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-11-111-1-11-1-1111-1-111-1-111
χ111111-1-11111111111-1-1-111-1-1-1-111111-1-1-111-11-1-1-1-1-1-1111111111-11-11-1-1-111-111-1-1-1-1-111-1-111
χ121111-1-11111111111-1-1-111-1-1-1-111111-1-1-111-11-1-1-1-1-1-11111-1-1-1-11-11-11-1-1-1111-1-111111-1-111-1-1
χ131111-1-11111111111-1-1-111-1-1-1-11111-1111-1-11-1-1-11111-1-1-1-11111-1-111-11-1-111-1-1-111-1-1-11111-1-1
χ141111-1-11111111111-1-1-111-1-1-1-11111-1111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-111111-1-1111-1-1-1-111
χ151111-1-11111111111-1-1-111-1-1-1-11111-11-1-1111-1-1-1-1-1-1-111111111-11-11-1111-1-1-1-1-111-111-1-1-1-111
χ161111-1-11111111111-1-1-111-1-1-1-11111-11-1-1111-1-1-1-1-1-1-11111-1-1-1-1-11-11-1111-1-1111-1-11-1-11111-1-1
χ17222222222-2-2-2-22222-2-2222222-2-2-2-200000000-2-2000000000000000000000002-22-2000000000
χ18222222222-2-2-2-22222-2-2222222-2-2-2-200000000-2-200000000000000000000000-22-22000000000
χ1922222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-122-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-122-2-2-2-222-1-1111111110000-1-2-2-1-1-1111100000000000000
χ2122222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-100001-2-2111111100000000000000
χ2222222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000122111-1-1-1-100000000000000
χ23222222-2-222-2-22222-22-2-2-222-2-222-2-2000000002-20000000022-2-2000000000020000-200000000
χ24222222-2-222-2-22222-22-2-2-222-2-222-2-2000000002-200000000-2-2220000000000-20000200000000
χ25222222-2-22-222-2222-2-22-2-222-2-2-2-2222-200002-2-220000000000002002-2-2000000000000000000
χ26222222-2-22-222-2222-2-22-2-222-2-2-2-222-220000-22-22000000000000-200-222000000000000000000
χ27222222-2-2-1-222-2-1-1-1-2-2211-1-11111-1-12-200002-21-1−i3−i3i3i3−i3−i3i3i30000-100-111−i3i3−i3i300000000000000
χ28222222-2-2-1-222-2-1-1-1-2-2211-1-11111-1-12-200002-21-1i3i3−i3−i3i3i3−i3−i30000-100-111i3−i3i3−i300000000000000
χ29222222-2-2-1-222-2-1-1-1-2-2211-1-11111-1-1-220000-221-1−i3−i3i3i3−i3−i3i3i300001001-1-1i3−i3i3−i300000000000000
χ30222222-2-2-1-222-2-1-1-1-2-2211-1-11111-1-1-220000-221-1i3i3−i3−i3i3i3−i3−i300001001-1-1−i3i3−i3i300000000000000
χ312222-2-2222-2-2-2-2222-22222-2-2-2-2-2-2-2-20000000022000000000000000000000002-2-22000000000
χ322222-2-2222-2-2-2-2222-22222-2-2-2-2-2-2-2-2000000002200000000000000000000000-222-2000000000
χ332222-2-222-12222-1-1-1-2-2-2-1-11111-1-1-1-12-222-2-2-2211-1-1-1-111110000-12-21-11-1-11100000000000000
χ342222-2-222-12222-1-1-1-2-2-2-1-11111-1-1-1-12-2-2-222-22111111-1-1-1-10000-1-221-1111-1-100000000000000
χ352222-2-222-12222-1-1-1-2-2-2-1-11111-1-1-1-1-2222-2-22-211-1-1-1-1111100001-22-11-111-1-100000000000000
χ362222-2-222-12222-1-1-1-2-2-2-1-11111-1-1-1-1-22-2-2222-2111111-1-1-1-1000012-2-11-1-1-11100000000000000
χ372222-2-2-2-222-2-222222-22-2-2-2-22222-2-200000000-220000000022-2-20000000000-20000200000000
χ382222-2-2-2-222-2-222222-22-2-2-2-22222-2-200000000-2200000000-2-222000000000020000-200000000
χ392222-2-2-2-22-222-222222-2-2-2-2-222-2-222220000-2-22-2000000000000200-2-22000000000000000000
χ402222-2-2-2-22-222-222222-2-2-2-2-222-2-222-2-20000222-2000000000000-20022-2000000000000000000
χ412222-2-2-2-2-1-222-2-1-1-122-21111-1-111-1-1220000-2-2-11−i3−i3i3i3i3i3−i3−i30000-10011-1−i3i3i3−i300000000000000
χ422222-2-2-2-2-1-222-2-1-1-122-21111-1-111-1-1220000-2-2-11i3i3−i3−i3−i3−i3i3i30000-10011-1i3−i3−i3i300000000000000
χ432222-2-2-2-2-1-222-2-1-1-122-21111-1-111-1-1-2-2000022-11−i3−i3i3i3i3i3−i3−i30000100-1-11i3−i3−i3i300000000000000
χ442222-2-2-2-2-1-222-2-1-1-122-21111-1-111-1-1-2-2000022-11i3i3−i3−i3−i3−i3i3i30000100-1-11−i3i3i3−i300000000000000
χ452-2-22002-2222-2-2-22-20002-200002-22-200002i−2i000000002i−2i2i−2i2-22-200000000000000000000002i−2i
χ462-2-22002-2222-2-2-22-20002-200002-22-200002i−2i000000002i−2i2i−2i-22-220000000000000000000000−2i2i
χ472-2-22002-2222-2-2-22-20002-200002-22-20000−2i2i00000000−2i2i−2i2i2-22-20000000000000000000000−2i2i
χ482-2-22002-2222-2-2-22-20002-200002-22-20000−2i2i00000000−2i2i−2i2i-22-2200000000000000000000002i−2i
χ492-2-2200-2222-22-2-22-2000-2200002-2-22002i−2i0000002i−2i2i−2i00002-2-22000000000000000000002i−2i00
χ502-2-2200-2222-22-2-22-2000-2200002-2-22002i−2i0000002i−2i2i−2i0000-222-200000000000000000000−2i2i00
χ512-2-2200-2222-22-2-22-2000-2200002-2-2200−2i2i000000−2i2i−2i2i00002-2-2200000000000000000000−2i2i00
χ522-2-2200-2222-22-2-22-2000-2200002-2-2200−2i2i000000−2i2i−2i2i0000-222-2000000000000000000002i−2i00
χ5344444444-2-4-4-4-4-2-2-24-4-4-2-2-2-2-2-222220000000022000000000000000000000000000000000000
χ54444444-4-4-24-4-44-2-2-2-44-422-2-222-2-22200000000-22000000000000000000000000000000000000
χ554444-4-444-2-4-4-4-4-2-2-2-444-2-22222222200000000-2-2000000000000000000000000000000000000
χ564444-4-4-4-4-24-4-44-2-2-24-442222-2-2-2-222000000002-2000000000000000000000000000000000000
χ574-44-44-400400004-4-4000004-4000000000000000000000000000000000000000000002i−2i2i−2i0000
χ584-44-44-400400004-4-4000004-400000000000000000000000000000000000000000000−2i2i−2i2i0000
χ594-44-4-4400400004-4-400000-44000000000000000000000000000000000000000000002i−2i−2i2i0000
χ604-44-4-4400400004-4-400000-4400000000000000000000000000000000000000000000−2i2i2i−2i0000
χ614-4-44004-44-4-444-44-40004-40000-44-440000000000000000000000000000000000000000000000
χ624-4-44004-4-244-4-42-22000-220000-22-2200004i−4i00000000−2i2i−2i2i0000000000000000000000000000
χ634-4-44004-4-244-4-42-22000-220000-22-220000−4i4i000000002i−2i2i−2i0000000000000000000000000000
χ644-4-44004-4-2-4-4442-22000-2200002-22-2000000000023−23−232300000000000000000000000000000000
χ654-4-44004-4-2-4-4442-22000-2200002-22-20000000000−232323−2300000000000000000000000000000000
χ664-4-4400-444-44-44-44-4000-440000-444-40000000000000000000000000000000000000000000000
χ674-4-4400-44-24-44-42-220002-20000-222-2004i−4i000000−2i2i−2i2i00000000000000000000000000000000
χ684-4-4400-44-24-44-42-220002-20000-222-200−4i4i0000002i−2i2i−2i00000000000000000000000000000000
χ694-4-4400-44-2-44-442-220002-200002-2-220000000000000023−23−23230000000000000000000000000000
χ704-4-4400-44-2-44-442-220002-200002-2-2200000000000000−232323−230000000000000000000000000000
χ7188-8-8000080000-8-8800000000000000000000000000000000000000000000000000000000000
χ7288-8-80000-4000044-40000000−4i34i300000000000000000000000000000000000000000000000000
χ7388-8-80000-4000044-400000004i3−4i300000000000000000000000000000000000000000000000000
χ748-88-88-800-40000-44400000-440000000000000000000000000000000000000000000000000000
χ758-88-8-8800-40000-444000004-40000000000000000000000000000000000000000000000000000

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