Finite Group Databasebeta

← Group #10692239

Character table — Group #10692239

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121212121212161616161616161616162424242448484848
order12222234444666224466661212121212126888888881224242424242424242244888844121212122424242424884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ91111-1-1111-1-11111-11-111-1-111-1-1-1-1-1ii−i−iii−i−i1iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−i-11i−ii−i1-1
χ101111-1-1111-1-11111-11-111-1-111-1-1-1-1-1ii−i−iii−i−i1iiii−i−i−i−i-1-111−i−iii1-111-1-1ii−i−i1-1−ii−ii-11
χ111111-1-1111-1-11111-11-111-1-111-1-1-1-1-1ii−i−i−i−iii1−i−i−i−iiiii11-1-1ii−i−i-11-1-111ii−i−i-11i−i−ii-11
χ121111-1-1111-1-11111-11-111-1-111-1-1-1-1-1ii−i−i−i−iii1−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−i1-1−iii−i1-1
χ131111-1-1111-1-11111-11-111-1-111-1-1-1-1-1−i−iiiii−i−i1iiii−i−i−i−i11-1-1−i−iii-11-1-111−i−iii-11−iii−i-11
χ141111-1-1111-1-11111-11-111-1-111-1-1-1-1-1−i−iiiii−i−i1iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii1-1i−i−ii1-1
χ151111-1-1111-1-11111-11-111-1-111-1-1-1-1-1−i−iii−i−iii1−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii-11−ii−ii1-1
χ161111-1-1111-1-11111-11-111-1-111-1-1-1-1-1−i−iii−i−iii1−i−i−i−iiiii-1-111ii−i−i1-111-1-1−i−iii1-1i−ii−i-11
χ17222222222-2-2222-2-2-22-2-2222222-2-2-200000000-20000000022-2-2000000000000002-2000000
χ18222222222-2-2222-2-2-22-2-2222222-2-2-200000000-200000000-2-22200000000000000-22000000
χ192222222-2-222222-2-22-2-2-222-2-2-2-222-20000000020000000000002222000000000000-2-20000
χ202222222-2-222222-2-22-2-2-222-2-2-2-222-2000000002000000000000-2-2-2-2000000000000220000
χ212222222-2-2-2-222222-2-22222-2-2-2-2-2-222i−2i2i−2i0000-200000000000000000000002i−2i2i−2i00000000
χ222222222-2-2-2-222222-2-22222-2-2-2-2-2-22−2i2i−2i2i0000-20000000000000000000000−2i2i−2i2i00000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-100000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-11111111100000000-2-21111-1-1-1-100000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-100000000-2-21111111100000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111110000000022-1-1-1-1111100000000
χ27222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-12i−2i2i−2i0000133−3−333−3−30000000000−i3i3−i3i3−ii−ii00000000
χ28222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-12i−2i2i−2i00001−3−333−3−3330000000000i3−i3i3−i3−ii−ii00000000
χ29222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-1−2i2i−2i2i0000133−3−333−3−30000000000i3−i3i3−i3i−ii−i00000000
χ30222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-1−2i2i−2i2i00001−3−333−3−3330000000000−i3i3−i3i3i−ii−i00000000
χ312222-2-222222222-22-2-2-2-2-2-222-2-222200000000-200000000222200000000000000-2-2000000
χ322222-2-222222222-22-2-2-2-2-2-222-2-222200000000-200000000-2-2-2-20000000000000022000000
χ332222-2-22-2-2222222-2-2222-2-2-2-22222-22-2-220000-200000000000000000000002-2-2200000000
χ342222-2-22-2-2222222-2-2222-2-2-2-22222-2-222-20000-20000000000000000000000-222-200000000
χ352222-2-22-2-2-2-2222-2222-2-2-2-2-2-222-2-220000000020000000000002i2i−2i−2i000000000000−2i2i0000
χ362222-2-22-2-2-2-2222-2222-2-2-2-2-2-222-2-22000000002000000000000−2i−2i2i2i0000000000002i−2i0000
χ372222-2-2-122-2-2-1-1-12-22-2-1-111-1-1111112i2i−2i−2i2i2i−2i−2i-1−i−i−i−iiiii000000002-2-1-111−i−iii00000000
χ382222-2-2-122-2-2-1-1-12-22-2-1-111-1-1111112i2i−2i−2i−2i−2i2i2i-1iiii−i−i−i−i00000000-2211-1-1−i−iii00000000
χ392222-2-2-122-2-2-1-1-12-22-2-1-111-1-111111−2i−2i2i2i2i2i−2i−2i-1−i−i−i−iiiii00000000-2211-1-1ii−i−i00000000
χ402222-2-2-122-2-2-1-1-12-22-2-1-111-1-111111−2i−2i2i2i−2i−2i2i2i-1iiii−i−i−i−i000000002-2-1-111ii−i−i00000000
χ412222-2-2-1-2-222-1-1-12-2-22-1-11111-1-1-1-112-2-2200001−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i3-111-100000000
χ422222-2-2-1-2-222-1-1-12-2-22-1-11111-1-1-1-112-2-2200001i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i3-111-100000000
χ432222-2-2-1-2-222-1-1-12-2-22-1-11111-1-1-1-11-222-200001−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i31-1-1100000000
χ442222-2-2-1-2-222-1-1-12-2-22-1-11111-1-1-1-11-222-200001i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i31-1-1100000000
χ45444444-244-4-4-2-2-2-4-4-4422-2-2-2-2-2-22220000000020000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-4-44-422-2-22222-2-2200000000-20000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-44-4-42222-2-222-2-2-20000000020000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2-4444222222-2-222-200000000-20000000000000000000000000000000000
χ4944-4-44-4400004-4-40000004-4000000000000000000000000000022−2222−22000000000000000000
χ5044-4-44-4400004-4-40000004-40000000000000000000000000000−2222−2222000000000000000000
χ5144-4-4-44400004-4-4000000-440000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ5244-4-4-44400004-4-4000000-4400000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ534-44-4004004i−4i-44-40000000000004i−4i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1302ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ544-44-4004004i−4i-44-40000000000004i−4i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ554-44-400400−4i4i-44-4000000000000−4i4i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ564-44-400400−4i4i-44-4000000000000−4i4i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2302ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ574-44-400-2004i−4i2-220000−2i32i3000023−23−2i2i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130−2ζ72ζ7−2ζ232ζ232ζ5−2ζ52ζ13−2ζ1300000000000000000000000000
χ584-44-400-2004i−4i2-220000−2i32i3000023−23−2i2i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1302ζ7−2ζ72ζ23−2ζ23−2ζ52ζ5−2ζ132ζ1300000000000000000000000000
χ594-44-400-2004i−4i2-2200002i3−2i30000−2323−2i2i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130−2ζ232ζ23−2ζ72ζ72ζ13−2ζ132ζ5−2ζ500000000000000000000000000
χ604-44-400-2004i−4i2-2200002i3−2i30000−2323−2i2i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1302ζ23−2ζ232ζ7−2ζ7−2ζ132ζ13−2ζ52ζ500000000000000000000000000
χ614-44-400-200−4i4i2-220000−2i32i30000−23232i−2i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2302ζ13−2ζ132ζ5−2ζ5−2ζ232ζ23−2ζ72ζ700000000000000000000000000
χ624-44-400-200−4i4i2-220000−2i32i30000−23232i−2i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230−2ζ132ζ13−2ζ52ζ52ζ23−2ζ232ζ7−2ζ700000000000000000000000000
χ634-44-400-200−4i4i2-2200002i3−2i3000023−232i−2i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2302ζ5−2ζ52ζ13−2ζ13−2ζ72ζ7−2ζ232ζ2300000000000000000000000000
χ644-44-400-200−4i4i2-2200002i3−2i3000023−232i−2i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230−2ζ52ζ5−2ζ132ζ132ζ7−2ζ72ζ23−2ζ2300000000000000000000000000
χ654-4-440044-400-4-44000000004-40000000000000000000000004-40000000000000000000000
χ664-4-440044-400-4-44000000004-4000000000000000000000000-440000000000000000000000
χ674-4-44004-4400-4-4400000000-4400000000000000000000004-4000000000000000000000000
χ684-4-44004-4400-4-4400000000-440000000000000000000000-44000000000000000000000000
χ6988-8-88-8-40000-444000000-4400000000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-4440000004-400000000000000000000000000000000000000000000000000
χ718-8-8800-48-80044-400000000-44000000000000000000000000000000000000000000000000
χ728-8-8800-4-880044-4000000004-4000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.