Finite Group Databasebeta

← Group #10849688

Character table — Group #10849688

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212161616161616161616162424242424242424242424242424
order122222344444466644466121212121212121222448888121224242424242424244444446612121212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111
χ91111111-1-11111111-1-1-111-1-111-1-1111-11-111-1-1-1-11111-1-1-1-111111-11-11-111-1-1-1-11-11-111-1-111-1-1
χ101111111-1-11111111-1-1-111-1-111-1-1111-11-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-111-1-111-11-11-1-111-1-111
χ111111111-1-11111111-1-1-111-1-111-1-1111-11-1-1-111-1-1-1-1-1-111111111-111-11-1-1-111-1-11-11-1-1-111-1-111
χ121111111-1-11111111-1-1-111-1-111-1-1111-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-11-1-1-11111-11-1111-1-111-1-1
χ131111111-1-11111111-1-1-111-1-111-1-111-11-1111-1-1-1-11111-1-1-1-11111-11-11-11-1-111-1-1-11-11-1-11111-1-1
χ141111111-1-11111111-1-1-111-1-111-1-111-11-1111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-1-111111-11-111-1-1-1-111
χ151111111-1-11111111-1-1-111-1-111-1-111-11-11-1-111-1-1-1-1-1-1111111111-1-11-1111-1-1-1-1-11-1111-1-1-1-111
χ161111111-1-11111111-1-1-111-1-111-1-111-11-11-1-111-1-1-1-1-1-11111-1-1-1-11-1-11-1111-1-1111-11-1-1-11111-1-1
χ17222222222-2-2-2-2222-2-222222-2-2-2-2-2-2000000002-20000000022-2-200000000002-2000000000000
χ18222222222-2-2-2-2222-2-222222-2-2-2-2-2-2000000002-200000000-2-2220000000000-22000000000000
χ192222222-2-2-2-2-2-222222-222-2-2-2-222-2-200000000-220000000022-2-20000000000-22000000000000
χ202222222-2-2-2-2-2-222222-222-2-2-2-222-2-200000000-2200000000-2-22200000000002-2000000000000
χ21222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-1111100000000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-21111111100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-100000000000000
χ25222222-1-2-22222-1-1-1-2-2-2-1-111-1-111-1-12-22-222-2-211-1-1-1-1111100002-2-11-11-1-11100000000000000
χ26222222-1-2-22222-1-1-1-2-2-2-1-111-1-111-1-12-22-2-2-222111111-1-1-1-10000-22-11-1111-1-100000000000000
χ27222222-1-2-22222-1-1-1-2-2-2-1-111-1-111-1-1-22-2222-2-211-1-1-1-111110000-221-11-111-1-100000000000000
χ28222222-1-2-22222-1-1-1-2-2-2-1-111-1-111-1-1-22-22-2-222111111-1-1-1-100002-21-11-1-1-11100000000000000
χ292222-2-222222-2-22222-2-2-2-222-2-2222222-2-20000-2-20000000000000022-2-2000000000000000000
χ302222-2-222222-2-22222-2-2-2-222-2-22222-2-2220000-2-200000000000000-2-222000000000000000000
χ312222-2-2222-2-222222-22-2-2-22222-2-2-2-200000000-2200000000000000000000000022-2-200000000
χ322222-2-2222-2-222222-22-2-2-22222-2-2-2-200000000-22000000000000000000000000-2-22200000000
χ332222-2-22-2-222-2-2222-222-2-2-2-2-2-2-2-2222-2-22000022000000000000002-2-22000000000000000000
χ342222-2-22-2-222-2-2222-222-2-2-2-2-2-2-2-222-222-200002200000000000000-222-2000000000000000000
χ352222-2-22-2-2-2-2222222-22-2-2-2-22222-2-2000000002-20000000000000000000000002-2-2200000000
χ362222-2-22-2-2-2-2222222-22-2-2-2-22222-2-2000000002-2000000000000000000000000-222-200000000
χ372222-2-2-12222-2-2-1-1-12-2-211-1-111-1-1-1-122-2-2000011−i3−i3i3i3−i3−i3i3i3000000-1-111−i3i3−i3i300000000000000
χ382222-2-2-12222-2-2-1-1-12-2-211-1-111-1-1-1-122-2-2000011i3i3−i3−i3i3i3−i3−i3000000-1-111i3−i3i3−i300000000000000
χ392222-2-2-12222-2-2-1-1-12-2-211-1-111-1-1-1-1-2-222000011−i3−i3i3i3−i3−i3i3i300000011-1-1i3−i3i3−i300000000000000
χ402222-2-2-12222-2-2-1-1-12-2-211-1-111-1-1-1-1-2-222000011i3i3−i3−i3i3i3−i3−i300000011-1-1−i3i3−i3i300000000000000
χ412222-2-2-1-2-222-2-2-1-1-1-22211111111-1-12-2-220000-1-1−i3−i3i3i3i3i3−i3−i3000000-111-1−i3i3i3−i300000000000000
χ422222-2-2-1-2-222-2-2-1-1-1-22211111111-1-12-2-220000-1-1i3i3−i3−i3−i3−i3i3i3000000-111-1i3−i3−i3i300000000000000
χ432222-2-2-1-2-222-2-2-1-1-1-22211111111-1-1-222-20000-1-1−i3−i3i3i3i3i3−i3−i30000001-1-11i3−i3−i3i300000000000000
χ442222-2-2-1-2-222-2-2-1-1-1-22211111111-1-1-222-20000-1-1i3i3−i3−i3−i3−i3i3i30000001-1-11−i3i3i3−i300000000000000
χ4522-2-2-222002-22-2-22-20002-2002-2002-20000002i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000000000002-2
χ4622-2-2-222002-22-2-22-20002-2002-2002-20000002i−2i0000002i−2i2i−2i−2i2i−2i2i0000000000000000000000-22
χ4722-2-2-222002-22-2-22-20002-2002-2002-2000000−2i2i000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000-22
χ4822-2-2-222002-22-2-22-20002-2002-2002-2000000−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000000000002-2
χ4922-2-2-22200-22-22-22-20002-200-2200-2200002i−2i00002i−2i2i−2i00002i−2i−2i2i000000000000000000002-200
χ5022-2-2-22200-22-22-22-20002-200-2200-2200002i−2i00002i−2i2i−2i0000−2i2i2i−2i00000000000000000000-2200
χ5122-2-2-22200-22-22-22-20002-200-2200-220000−2i2i0000−2i2i−2i2i00002i−2i−2i2i00000000000000000000-2200
χ5222-2-2-22200-22-22-22-20002-200-2200-220000−2i2i0000−2i2i−2i2i0000−2i2i2i−2i000000000000000000002-200
χ53444444-244-4-4-4-4-2-2-2-4-44-2-2-2-222222200000000-22000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-244-4-2-22222-2-222000000002-2000000000000000000000000000000000000
χ554444-4-4-244-4-444-2-2-2-44-422-2-2-2-22222000000002-2000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-444-2-2-24-442222-2-2-2-22200000000-22000000000000000000000000000000000000
χ5744-4-44-44004-4-44-44-4000-4400-44004-40000000000000000000000000000000000000000000000
χ5844-4-44-4400-444-4-44-4000-44004-400-440000000000000000000000000000000000000000000000
χ5944-4-44-4-2004-4-442-220002-2002-200-220000000000000023−23−23230000000000000000000000000000
χ6044-4-44-4-2004-4-442-220002-2002-200-2200000000000000−232323−230000000000000000000000000000
χ6144-4-44-4-200-444-42-220002-200-22002-2000000000023−23−232300000000000000000000000000000000
χ6244-4-44-4-200-444-42-220002-200-22002-20000000000−232323−2300000000000000000000000000000000
χ6344-4-4-44-2004-44-42-22000-2200-2200-220000004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ6444-4-4-44-2004-44-42-22000-2200-2200-22000000−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ6544-4-4-44-200-44-442-22000-22002-2002-200004i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ6644-4-4-44-200-44-442-22000-22002-2002-20000−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ674-4-440044-400004-4-4000004-4000000000000000000000000000000000000000000002i−2i2i−2i0000
χ684-4-440044-400004-4-4000004-400000000000000000000000000000000000000000000−2i2i−2i2i0000
χ694-4-44004-4400004-4-400000-44000000000000000000000000000000000000000000002i−2i−2i2i0000
χ704-4-44004-4400004-4-400000-4400000000000000000000000000000000000000000000−2i2i2i−2i0000
χ718-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ728-88-800-400000044-4000000000−4i34i3000000000000000000000000000000000000000000000000
χ738-88-800-400000044-40000000004i3−4i3000000000000000000000000000000000000000000000000
χ748-8-8800-48-80000-44400000-440000000000000000000000000000000000000000000000000000
χ758-8-8800-4-880000-444000004-40000000000000000000000000000000000000000000000000000

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