Finite Group Databasebeta

← Group #10844981

Character table — Group #10844981

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212124444888812122424242424242424888888884412121212121212124444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-1
χ91111111-1-11111111-1-1-111-1-1-1-111111-11-111-1-1-1-11111-1-1-1-1111111-1-11-111-1-111-1-111-1-1-1-11-11-1
χ101111111-1-11111111-1-1-111-1-1-1-111111-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-11111-11-11
χ111111111-1-11111111-1-1-111-1-1-1-111111-11-1-1-111-1-1-1-1-1-11111111111-1-1-1111-1-1-1-111-1-111-1-11-1-11
χ121111111-1-11111111-1-1-111-1-1-1-111111-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1111-1-1-1-11111-1-111-111-1
χ131111111-1-11111111-1-1-111-1-1-1-11111-11-1111-1-1-1-11111-1-1-1-11111-1-111-11-1-111-1-11111-1-1-1-1-11-11
χ141111111-1-11111111-1-1-111-1-1-1-11111-11-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-111-1-111111-11-1
χ151111111-1-11111111-1-1-111-1-1-1-11111-11-11-1-111-1-1-1-1-1-111111111-1-1111-1-1-11111-1-1-1-111-1-1-111-1
χ161111111-1-11111111-1-1-111-1-1-1-11111-11-11-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-11111-1-111-1-1111-1-11
χ17222222222-2-2-2-22222-2-22222-2-2-2-2-2-2000000002-2000000002i2i−2i−2i0000000000000000002i−2i0000
χ18222222222-2-2-2-22222-2-22222-2-2-2-2-2-2000000002-200000000−2i−2i2i2i000000000000000000−2i2i0000
χ192222222-2-2-2-2-2-2222-22222-2-222-2-2-2-200000000-22000000002i2i−2i−2i000000000000000000−2i2i0000
χ202222222-2-2-2-2-2-2222-22222-2-222-2-2-2-200000000-2200000000−2i−2i2i2i0000000000000000002i−2i0000
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
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-1-1-1-111110000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000221111-1-1-1-10000000000
χ25222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-12-22-222-2-211-1-1-1-11111000000002-2-1-111-1-1110000000000
χ26222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-12-22-2-2-222111111-1-1-1-100000000-22-1-11111-1-10000000000
χ27222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-1-22-2222-2-211-1-1-1-1111100000000-2211-1-111-1-10000000000
χ28222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-1-22-22-2-222111111-1-1-1-1000000002-211-1-1-1-1110000000000
χ292222-2-22222-22-2222-22-2-2-22222-2-22222-2-20000-2-20000000000000000002-22-200000000000000
χ302222-2-22222-22-2222-22-2-2-22222-2-222-2-2220000-2-2000000000000000000-22-2200000000000000
χ312222-2-2222-22-22222-2-22-2-222-2-222-2-200000000-2200000000000022220000000000000000-2-200
χ322222-2-2222-22-22222-2-22-2-222-2-222-2-200000000-22000000000000-2-2-2-200000000000000002200
χ332222-2-22-2-22-22-22222-22-2-2-2-2-2-2-2-2222-2-220000220000000000000000002-2-2200000000000000
χ342222-2-22-2-22-22-22222-22-2-2-2-2-2-2-2-222-222-2000022000000000000000000-222-200000000000000
χ352222-2-22-2-2-22-2222222-2-2-2-2-22222-2-2000000002-200000000000022-2-20000000000000000-2200
χ362222-2-22-2-2-22-2222222-2-2-2-2-22222-2-2000000002-2000000000000-2-22200000000000000002-200
χ372222-2-2-1222-22-2-1-1-1-22-211-1-1-1-111-1-122-2-2000011−i3−i3i3i3−i3−i3i3i30000000000-11-11−i3i3−i3i30000000000
χ382222-2-2-1222-22-2-1-1-1-22-211-1-1-1-111-1-122-2-2000011i3i3−i3−i3i3i3−i3−i30000000000-11-11i3−i3i3−i30000000000
χ392222-2-2-1222-22-2-1-1-1-22-211-1-1-1-111-1-1-2-222000011−i3−i3i3i3−i3−i3i3i300000000001-11-1i3−i3i3−i30000000000
χ402222-2-2-1222-22-2-1-1-1-22-211-1-1-1-111-1-1-2-222000011i3i3−i3−i3i3i3−i3−i300000000001-11-1−i3i3−i3i30000000000
χ412222-2-2-1-2-22-22-2-1-1-12-2211111111-1-12-2-220000-1-1−i3−i3i3i3i3i3−i3−i30000000000-111-1−i3i3i3−i30000000000
χ422222-2-2-1-2-22-22-2-1-1-12-2211111111-1-12-2-220000-1-1i3i3−i3−i3−i3−i3i3i30000000000-111-1i3−i3−i3i30000000000
χ432222-2-2-1-2-22-22-2-1-1-12-2211111111-1-1-222-20000-1-1−i3−i3i3i3i3i3−i3−i300000000001-1-11i3−i3−i3i30000000000
χ442222-2-2-1-2-22-22-2-1-1-12-2211111111-1-1-222-20000-1-1i3i3−i3−i3−i3−i3i3i300000000001-1-11−i3i3i3−i30000000000
χ452-2-222-22002-2-22-2-220002-200002-22-20000002i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000002-2000000
χ462-2-222-22002-2-22-2-220002-200002-22-20000002i−2i0000002i−2i2i−2i−2i2i−2i2i0000000000000000-22000000
χ472-2-222-22002-2-22-2-220002-200002-22-2000000−2i2i000000−2i2i−2i2i2i−2i2i−2i0000000000000000-22000000
χ482-2-222-22002-2-22-2-220002-200002-22-2000000−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000002-2000000
χ492-2-222-2200-222-2-2-220002-20000-22-2200002i−2i00002i−2i2i−2i00002-2-22000000000000002i−2i00000000
χ502-2-222-2200-222-2-2-220002-20000-22-2200002i−2i00002i−2i2i−2i0000-222-200000000000000−2i2i00000000
χ512-2-222-2200-222-2-2-220002-20000-22-220000−2i2i0000−2i2i−2i2i00002-2-2200000000000000−2i2i00000000
χ522-2-222-2200-222-2-2-220002-20000-22-220000−2i2i0000−2i2i−2i2i0000-222-2000000000000002i−2i00000000
χ53444444-244-4-4-4-4-2-2-24-4-4-2-2-2-222222200000000-22000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-444-2-222-2-22222000000002-2000000000000000000000000000000000000
χ554444-4-4-244-44-44-2-2-2-4-4422-2-222-2-222000000002-2000000000000000000000000000000000000
χ564444-4-4-2-4-4-44-44-2-2-244-42222-2-2-2-22200000000-22000000000000000000000000000000000000
χ5744-4-40044-400004-4-4000004-4000000000000000000000000000022−2222−2200000000000000000000
χ5844-4-40044-400004-4-4000004-40000000000000000000000000000−2222−222200000000000000000000
χ5944-4-4004-4400004-4-400000-44000000000000000000000000000022−22−222200000000000000000000
χ6044-4-4004-4400004-4-400000-440000000000000000000000000000−222222−2200000000000000000000
χ614-4-444-4-2004-4-4422-2000-220000-22-220000004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ624-4-444-4-2004-4-4422-2000-220000-22-22000000−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ634-4-444-4-200-444-422-2000-2200002-22-200004i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ644-4-444-4-200-444-422-2000-2200002-22-20000−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ654-4-44-4440044-4-4-4-44000-440000-444-40000000000000000000000000000000000000000000000
χ664-4-44-44400-4-444-4-44000-4400004-4-440000000000000000000000000000000000000000000000
χ674-4-44-44-20044-4-422-20002-200002-2-220000000000000023−23−23230000000000000000000000000000
χ684-4-44-44-20044-4-422-20002-200002-2-2200000000000000−232323−230000000000000000000000000000
χ694-4-44-44-200-4-44422-20002-20000-222-2000000000023−23−232300000000000000000000000000000000
χ704-4-44-44-200-4-44422-20002-20000-222-20000000000−232323−2300000000000000000000000000000000
χ7188-8-800-48-80000-44400000-440000000000000000000000000000000000000000000000000000
χ7288-8-800-4-880000-444000004-40000000000000000000000000000000000000000000000000000
χ738-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ748-88-800-40000004-440000000−4i34i300000000000000000000000000000000000000000000000000
χ758-88-800-40000004-4400000004i3−4i300000000000000000000000000000000000000000000000000

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