Finite Group Databasebeta

← Group #10836669

Character table — Group #10836669

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212128888888812122424242424242424444488884412121212242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ611111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1
χ91111111-1-11111111-1-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-111-1-1-1-111-1-11-11-1
χ101111111-1-11111111-1-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-111-1-111-11-11
χ111111111-1-11111111-1-1-1111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-11111-1-111-11-1-111-1-111-1-111-1-1-11-11
χ121111111-1-11111111-1-1-1111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-11111-1-1111-11-1
χ131111111-1-11111111-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111111111-1-1-11-1-11111-1-1-1-1-1-1111-1-11
χ141111111-1-11111111-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-11111-1-11111-1-1-111-1
χ151111111-1-11111111-1-1-1111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111111111-1-1111-111-1-1-1-111-1-1-1-111-111-1
χ161111111-1-11111111-1-1-1111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-111-1-1-1-1111111-1-11-1-11
χ17222222222-2-2-2-22222-2-222-222-2-2-2-2-2002i−2i2i−2i002-200000000000000000000002i−2i2i−2i0000000000
χ18222222222-2-2-2-22222-2-222-222-2-2-2-2-200−2i2i−2i2i002-20000000000000000000000−2i2i−2i2i0000000000
χ192222222-2-2-2-2-2-2222-22222-2-2-222-2-2-2002i−2i−2i2i00-2200000000000000000000002i−2i−2i2i0000000000
χ202222222-2-2-2-2-2-2222-22222-2-2-222-2-2-200−2i2i2i−2i00-220000000000000000000000−2i2i2i−2i0000000000
χ21222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-1-11111111100000000-2-21111-1-1-1-10000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-111110000000000
χ25222222-122-2-2-2-2-1-1-12-2-2-1-11-1-111111002i−2i2i−2i00-1133−3−333−3−30000000000−i3i3−i3i3−ii−ii0000000000
χ26222222-122-2-2-2-2-1-1-12-2-2-1-11-1-111111002i−2i2i−2i00-11−3−333−3−3330000000000i3−i3i3−i3−ii−ii0000000000
χ27222222-122-2-2-2-2-1-1-12-2-2-1-11-1-11111100−2i2i−2i2i00-1133−3−333−3−30000000000i3−i3i3−i3i−ii−i0000000000
χ28222222-122-2-2-2-2-1-1-12-2-2-1-11-1-11111100−2i2i−2i2i00-11−3−333−3−3330000000000−i3i3−i3i3i−ii−i0000000000
χ29222222-1-2-22222-1-1-1-2-2-2-1-1-11111-1-1-12222-2-2-2-211-1-1-1-11111000000002-2-1-111-1-1110000000000
χ30222222-1-2-22222-1-1-1-2-2-2-1-1-11111-1-1-122-2-222-2-211-1-1-1-1111100000000-2211-1-111-1-10000000000
χ31222222-1-2-22222-1-1-1-2-2-2-1-1-11111-1-1-1-2-222-2-222111111-1-1-1-100000000-2211-1-1-1-1110000000000
χ32222222-1-2-22222-1-1-1-2-2-2-1-1-11111-1-1-1-2-2-2-22222111111-1-1-1-1000000002-2-1-11111-1-10000000000
χ33222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-1111002i−2i−2i2i001-133−3−3−3−3330000000000−i3i3i3−i3−iii−i0000000000
χ34222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-1111002i−2i−2i2i001-1−3−33333−3−30000000000i3−i3−i3i3−iii−i0000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-111100−2i2i2i−2i001-133−3−3−3−3330000000000i3−i3−i3i3i−i−ii0000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-111100−2i2i2i−2i001-1−3−33333−3−30000000000−i3i3i3−i3i−i−ii0000000000
χ372222-2-22222-2-22222-22-2-2-2-2222222-200000000-2-20000000022-2-2000000000000002-200000000
χ382222-2-22222-2-22222-22-2-2-2-2222222-200000000-2-200000000-2-22200000000000000-2200000000
χ392222-2-2222-222-2222-2-22-2-2222-2-2-2-2200000000-2200000000000022220000000000000000-2-200
χ402222-2-2222-222-2222-2-22-2-2222-2-2-2-2200000000-22000000000000-2-2-2-200000000000000002200
χ412222-2-22-2-22-2-222222-22-2-2-2-2-2-2-222-200000000220000000022-2-200000000000000-2200000000
χ422222-2-22-2-22-2-222222-22-2-2-2-2-2-2-222-2000000002200000000-2-222000000000000002-200000000
χ432222-2-22-2-2-222-222222-2-2-22-2-222-2-22000000002-200000000000022-2-20000000000000000-2200
χ442222-2-22-2-2-222-222222-2-2-22-2-222-2-22000000002-2000000000000-2-22200000000000000002-200
χ452-22-22-2200-22-222-2-20002-2-200002-222i−2i000000002i−2i2i−2i00002i−2i2i−2i00000000000000002-2000000
χ462-22-22-2200-22-222-2-20002-2-200002-222i−2i000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000-22000000
χ472-22-22-2200-22-222-2-20002-2-200002-22−2i2i00000000−2i2i−2i2i00002i−2i2i−2i0000000000000000-22000000
χ482-22-22-2200-22-222-2-20002-2-200002-22−2i2i00000000−2i2i−2i2i0000−2i2i−2i2i00000000000000002-2000000
χ492-22-2-22200-2-2222-2-2000-22200002-2-20000002-20000002-22-22i−2i−2i2i0000000000000000002i−2i0000
χ502-22-2-22200-2-2222-2-2000-22200002-2-20000002-20000002-22-2−2i2i2i−2i000000000000000000−2i2i0000
χ512-22-2-22200-2-2222-2-2000-22200002-2-2000000-22000000-22-222i−2i−2i2i000000000000000000−2i2i0000
χ522-22-2-22200-2-2222-2-2000-22200002-2-2000000-22000000-22-22−2i2i2i−2i0000000000000000002i−2i0000
χ534444-4-4-2444-4-44-2-2-2-44-4222-2-2-2-2-2-220000000022000000000000000000000000000000000000
χ544444-4-4-244-444-4-2-2-2-4-4422-2-2-22222-2000000002-2000000000000000000000000000000000000
χ554444-4-4-2-4-44-4-44-2-2-24-442222222-2-2200000000-2-2000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-4-2-2-244-422-222-2-222-200000000-22000000000000000000000000000000000000
χ5744-4-40044-40000-44-40000004-400000000000000000000000000022−2222−2200000000000000000000
χ5844-4-40044-40000-44-40000004-4000000000000000000000000000−2222−222200000000000000000000
χ5944-4-4004-440000-44-4000000-4400000000000000000000000000022−22−222200000000000000000000
χ6044-4-4004-440000-44-4000000-44000000000000000000000000000−222222−2200000000000000000000
χ614-44-44-44004-44-44-4-40004-440000-44-40000000000000000000000000000000000000000000000
χ624-44-44-4-2004-44-4-222000-22-200002-220000000000−2i32i32i3−2i300000000000000000000000000000000
χ634-44-44-4-2004-44-4-222000-22-200002-2200000000002i3−2i3−2i32i300000000000000000000000000000000
χ644-44-44-4-200-44-44-222000-2220000-22-24i−4i00000000−2i2i−2i2i00000000000000000000000000000000
χ654-44-44-4-200-44-44-222000-2220000-22-2−4i4i000000002i−2i2i−2i00000000000000000000000000000000
χ664-44-4-4440044-4-44-4-4000-44-40000-4440000000000000000000000000000000000000000000000
χ674-44-4-44-20044-4-4-2220002-2200002-2-20000000000000023−23−23230000000000000000000000000000
χ684-44-4-44-20044-4-4-2220002-2200002-2-200000000000000−232323−230000000000000000000000000000
χ694-44-4-44-200-4-444-2220002-2-20000-2220000004-4000000-22-220000000000000000000000000000
χ704-44-4-44-200-4-444-2220002-2-20000-222000000-440000002-22-20000000000000000000000000000
χ7188-8-800-48-800004-44000000-44000000000000000000000000000000000000000000000000000
χ7288-8-800-4-8800004-440000004-4000000000000000000000000000000000000000000000000000
χ738-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400000044-400000000−4i34i30000000000000000000000000000000000000000000000000
χ758-8-8800-400000044-4000000004i3−4i30000000000000000000000000000000000000000000000000

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