Finite Group Databasebeta

← Group #10848909

Character table — Group #10848909

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222244444444888888888888888888881212121216161616161616161616242424242424242424244848
order1222223444466666664444121212124444444412121212121212121212121244442466121212121212222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ611111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1111111-1-1
χ9111111111111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-111111-111-1-111-1-1-11-1-11-111-1-11-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-111-11-1-111-11
χ11111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-11111-11-1-11111-1-1-11-1-11-1-1-111-11
χ12111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-11111-1-11-111-1111-1-11-1
χ13111111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-111-1-11-1-1111-1-1-11
χ14111111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-111-1-1-1111-1
χ15111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-111111-111-1-1-1-111-1-11-1-11-1-1111-1
χ16111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1-1-11111-111-111-1-1-11
χ172222222-2-2-2-2222222222-2-2-2-2-2-22-22-200002200000000-2-200000000002-22-2000000000000
χ182222222-2-2-2-2222222222-2-2-2-2-2-2-22-2200002200000000-2-20000000000-22-22000000000000
χ192222222-2-2-2-22222222-2-222-2-2-2-22-2-220000-2-2000000002200000000002-2-22000000000000
χ202222222-2-2-2-22222222-2-222-2-2-2-2-222-20000-2-200000000220000000000-222-2000000000000
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
χ22222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-2-2-2-2-1-111111111-1-10000-2-21111-1-1-1-1000000000000
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
χ24222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-1000022-1-1-1-11111000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-222-2-211-1-1-1-111111100002-2-1-111-1-111000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-222111111-1-1-1-1110000-2211-1-1-1-111000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22222-2-211-1-1-1-11111110000-2211-1-111-1-1000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-222111111-1-1-1-11100002-2-1-11111-1-1000000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-122-2-211112-22-20000-1-1−i3−i3i3i3−i3−i3i3i311000000−i3i3−i3i3-11-11000000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-122-2-211112-22-20000-1-1i3i3−i3−i3i3i3−i3−i311000000i3−i3i3−i3-11-11000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111-22-220000-1-1−i3−i3i3i3−i3−i3i3i311000000i3−i3i3−i31-11-1000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111-22-220000-1-1i3i3−i3−i3i3i3−i3−i311000000−i3i3−i3i31-11-1000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22211112-2-22000011−i3−i3i3i3i3i3−i3−i3-1-1000000−i3i3i3−i3-111-1000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22211112-2-22000011i3i3−i3−i3−i3−i3i3i3-1-1000000i3−i3−i3i3-111-1000000000000
χ35222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2221111-222-2000011−i3−i3i3i3i3i3−i3−i3-1-1000000i3−i3−i3i31-1-11000000000000
χ36222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2221111-222-2000011i3i3−i3−i3−i3−i3i3i3-1-1000000−i3i3i3−i31-1-11000000000000
χ372222-2-222-2-222-2-2-2-2222-22-222-2-2000000002-2000000002-222-2-20000000000200-200000000
χ382222-2-222-2-222-2-2-2-2222-22-222-2-2000000002-2000000002-2-2-2220000000000-200200000000
χ392222-2-222-2-222-2-2-2-222-22-2222-2-200000000-2200000000-2222-2-20000000000-200200000000
χ402222-2-222-2-222-2-2-2-222-22-2222-2-200000000-2200000000-22-2-2220000000000200-200000000
χ412222-2-22-222-22-2-2-2-2222-2-22-2-222000000002-200000000-22000000000000000220-2-2000000
χ422222-2-22-222-22-2-2-2-2222-2-22-2-222000000002-200000000-22000000000000000-2-2022000000
χ432222-2-22-222-22-2-2-2-222-222-2-2-22200000000-22000000002-20000000000000002-20-22000000
χ442222-2-22-222-22-2-2-2-222-222-2-2-22200000000-22000000002-2000000000000000-2202-2000000
χ452-2-222-2222-2-2-222-2-22-200002-22-20000002i−2i0000002i−2i2i−2i002i−2i2i−2i0000000000000000002-200
χ462-2-222-2222-2-2-222-2-22-200002-22-20000002i−2i0000002i−2i2i−2i00−2i2i−2i2i000000000000000000-2200
χ472-2-222-2222-2-2-222-2-22-200002-22-2000000−2i2i000000−2i2i−2i2i002i−2i2i−2i000000000000000000-2200
χ482-2-222-2222-2-2-222-2-22-200002-22-2000000−2i2i000000−2i2i−2i2i00−2i2i−2i2i0000000000000000002-200
χ492-2-22-2222-22-2-2-2-2222-200002-2-2200002i−2i00002i−2i2i−2i0000002i−2i−2i2i00000000000000002-20000
χ502-2-22-2222-22-2-2-2-2222-200002-2-2200002i−2i00002i−2i2i−2i000000−2i2i2i−2i0000000000000000-220000
χ512-2-22-2222-22-2-2-2-2222-200002-2-220000−2i2i0000−2i2i−2i2i0000002i−2i−2i2i0000000000000000-220000
χ522-2-22-2222-22-2-2-2-2222-200002-2-220000−2i2i0000−2i2i−2i2i000000−2i2i2i−2i00000000000000002-20000
χ534444-4-4-24-4-44-22222-2-24-44-4-2-22200000000-2200000000-2200000000000000000000000000
χ544444-4-4-24-4-44-22222-2-2-44-44-2-222000000002-2000000002-200000000000000000000000000
χ554444-4-4-2-444-4-22222-2-24-4-4422-2-200000000-22000000002-200000000000000000000000000
χ564444-4-4-2-444-4-22222-2-2-444-422-2-2000000002-200000000-2200000000000000000000000000
χ574-4-444-44-4-444-444-4-44-40000-44-440000000000000000000000000000000000000000000000
χ584-4-444-4-244-4-42-2-222-220000-22-220000004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ594-4-444-4-244-4-42-2-222-220000-22-22000000−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ604-4-444-4-2-4-4442-2-222-2200002-22-20000000000000023−23−23230000000000000000000000000000
χ614-4-444-4-2-4-4442-2-222-2200002-22-200000000000000−232323−230000000000000000000000000000
χ624-4-44-444-44-44-4-4-4444-40000-444-40000000000000000000000000000000000000000000000
χ634-4-44-44-24-44-4222-2-2-220000-222-200004i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ644-4-44-44-24-44-4222-2-2-220000-222-20000−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ654-4-44-44-2-44-44222-2-2-2200002-2-22000000000023−23−232300000000000000000000000000000000
χ664-4-44-44-2-44-44222-2-2-2200002-2-220000000000−232323−2300000000000000000000000000000000
χ6788-8-8008000080000-8-8000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-4−4i34i3−4i34i344000000000000000000000000000000000000000000000000000000
χ6988-8-800-40000-44i3−4i34i3−4i344000000000000000000000000000000000000000000000000000000
χ708-88-80080000-80000-88000000000000000000000000000000000000000000000000000000
χ718-88-800-400004−4i34i34i3−4i34-4000000000000000000000000000000000000000000000000000000
χ728-88-800-4000044i3−4i3−4i34i34-4000000000000000000000000000000000000000000000000000000

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