Finite Group Databasebeta

← Group #10691825

Character table — Group #10691825

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122234444446662444121212121212121212124444688881224242424242424248888441212121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1
χ91111111-1-1-1-1111-111-111-1-1-1-1111111-1-1-111-1-1-11111-1-1-1-1ii−i−i1-11111-1-1-1-1i−iii−i−iii−i−ii−i
χ101111111-1-1-1-1111-111-111-1-1-1-1111111-1-1-111-1-1-11111-1-1-1-1−i−iii1-11111-1-1-1-1−ii−i−iii−i−iii−ii
χ111111111-1-1-1-1111-111-111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-11111ii−i−i-1111-1-1-1-111i−iii−i−i−i−iii−ii
χ121111111-1-1-1-1111-111-111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-11111−i−iii-1111-1-1-1-111−ii−i−iiiii−i−ii−i
χ131111111-1-1-1-1111-111-111-1-1-1-11111-1-111-111-1-1-11111-1-1-1-1ii−i−i-11-1-1-1-11111i−i−i−iiiii−i−i−ii
χ141111111-1-1-1-1111-111-111-1-1-1-11111-1-111-111-1-1-11111-1-1-1-1−i−iii-11-1-1-1-11111−iiii−i−i−i−iiii−i
χ151111111-1-1-1-1111-111-111-1-1-1-11111-1-111-1-1-111-1-1-1-1-11111ii−i−i1-1-1-11111-1-1i−i−i−iii−i−iiii−i
χ161111111-1-1-1-1111-111-111-1-1-1-11111-1-111-1-1-111-1-1-1-1-11111−i−iii1-1-1-11111-1-1−iiii−i−iii−i−i−ii
χ1722222222222222-2-2-2-2-2-2222222-2-20000-20000-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-2-2-2222222-2-20000-20000-200000000-2-2-2-20000000000220000000000
χ192222222-2-2-2-22222-2-22-2-2-2-2-2-222-2-20000200002000000002i2i−2i−2i0000000000−2i2i0000000000
χ202222222-2-2-2-22222-2-22-2-2-2-2-2-222-2-2000020000200000000−2i−2i2i2i00000000002i−2i0000000000
χ2122222-2-222-2-222222-2-22222-2-2-2-2-2-2000020000-20000000000000000000000002i−2i2i−2i000000
χ2222222-2-222-2-222222-2-22222-2-2-2-2-2-2000020000-2000000000000000000000000−2i2i−2i2i000000
χ2322222-2-222-2-2222-2-222-2-222-2-2-2-2222-22-2-200002000000000000002-2002-200000000000000
χ2422222-2-222-2-2222-2-222-2-222-2-2-2-222-22-22-20000200000000000000-2200-2200000000000000
χ2522222-2-2-2-2222222-22-2-2-2-2-222-2-2222-2-2220000-2000000000000002-200-2200000000000000
χ2622222-2-2-2-2222222-22-2-2-2-2-222-2-222-222-220000-200000000000000-22002-200000000000000
χ2722222-2-2-2-222222-22-2222-2-222-2-2-2-20000-2000020000000000000000000000002-2-22000000
χ2822222-2-2-2-222222-22-2222-2-222-2-2-2-20000-200002000000000000000000000000-222-2000000
χ292222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-1111111110000-2-2-1-111-1-111000000000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-11111111100002211-1-111-1-1000000000000
χ332222-122-2-2-2-2-1-1-1-222-2-1-11111-1-1-1-122-2-2122-2-21-1-1-1-1111100002-2-1-1-1-11111000000000000
χ342222-122-2-2-2-2-1-1-1-222-2-1-11111-1-1-1-122-2-21-2-22211111-1-1-1-10000-22-1-11111-1-1000000000000
χ352222-122-2-2-2-2-1-1-1-222-2-1-11111-1-1-1-1-2-222122-2-21-1-1-1-111110000-221111-1-1-1-1000000000000
χ362222-122-2-2-2-2-1-1-1-222-2-1-11111-1-1-1-1-2-2221-2-22211111-1-1-1-100002-211-1-1-1-111000000000000
χ372222-1-2-222-2-2-1-1-1-2-22211-1-11111-1-12-22-210000-1−i3−i3i3i3−i3−i3i3i3000000-11−i3i3-11−i3i3000000000000
χ382222-1-2-222-2-2-1-1-1-2-22211-1-11111-1-12-22-210000-1i3i3−i3−i3i3i3−i3−i3000000-11i3−i3-11i3−i3000000000000
χ392222-1-2-222-2-2-1-1-1-2-22211-1-11111-1-1-22-2210000-1−i3−i3i3i3−i3−i3i3i30000001-1i3−i31-1i3−i3000000000000
χ402222-1-2-222-2-2-1-1-1-2-22211-1-11111-1-1-22-2210000-1i3i3−i3−i3i3i3−i3−i30000001-1−i3i31-1−i3i3000000000000
χ412222-1-2-2-2-222-1-1-12-22-21111-1-111-1-12-2-22-100001−i3−i3i3i3i3i3−i3−i3000000-11−i3i31-1i3−i3000000000000
χ422222-1-2-2-2-222-1-1-12-22-21111-1-111-1-12-2-22-100001i3i3−i3−i3−i3−i3i3i3000000-11i3−i31-1−i3i3000000000000
χ432222-1-2-2-2-222-1-1-12-22-21111-1-111-1-1-222-2-100001−i3−i3i3i3i3i3−i3−i30000001-1i3−i3-11−i3i3000000000000
χ442222-1-2-2-2-222-1-1-12-22-21111-1-111-1-1-222-2-100001i3i3−i3−i3−i3−i3i3i30000001-1−i3i3-11i3−i3000000000000
χ452-2-2222-22i−2i2i−2i-2-220000002i−2i2i−2i2-200000002−2−i2i202−22−2−i2i2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000001+i−1−i1−i−1+i00
χ462-2-2222-22i−2i2i−2i-2-220000002i−2i2i−2i2-200000002−2−i2i202−22−2−i2i2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−1−i1+i−1+i1−i00
χ472-2-2222-22i−2i2i−2i-2-220000002i−2i2i−2i2-20000000−22i2−i20−22−22i2−i2i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−1−i1+i−1+i1−i00
χ482-2-2222-22i−2i2i−2i-2-220000002i−2i2i−2i2-20000000−22i2−i20−22−22i2−i2i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000001+i−1−i1−i−1+i00
χ492-2-2222-2−2i2i−2i2i-2-22000000−2i2i−2i2i2-200000002−2i2−i202−22−2i2−i2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000001−i−1+i1+i−1−i00
χ502-2-2222-2−2i2i−2i2i-2-22000000−2i2i−2i2i2-200000002−2i2−i202−22−2i2−i2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−1+i1−i−1−i1+i00
χ512-2-2222-2−2i2i−2i2i-2-22000000−2i2i−2i2i2-20000000−22−i2i20−22−22−i2i2−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−1+i1−i−1−i1+i00
χ522-2-2222-2−2i2i−2i2i-2-22000000−2i2i−2i2i2-20000000−22−i2i20−22−22−i2i2−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000001−i−1+i1+i−1−i00
χ534444-2444444-2-2-2-4-4-4-422-2-2-2-2-2-22200002000020000000000000000000000000000000000
χ544444-244-4-4-4-4-2-2-24-4-44222222-2-2220000-20000-20000000000000000000000000000000000
χ554444-2-4-444-4-4-2-2-244-4-4-2-2-2-22222220000-2000020000000000000000000000000000000000
χ564444-2-4-4-4-444-2-2-2-44-44-2-222-2-22222000020000-20000000000000000000000000000000000
χ574-4-444-444i−4i−4i4i-4-440000004i−4i−4i4i-440000000000000000000000000000000000000000000000
χ584-4-444-44−4i4i4i−4i-4-44000000−4i4i4i−4i-440000000000000000000000000000000000000000000000
χ594-4-44-24-44i−4i4i−4i22-2000000−2i2i−2i2i-22000000022−22−2i22i20−22−22i2−i2i2−i200000000000000000000000000
χ604-4-44-24-44i−4i4i−4i22-2000000−2i2i−2i2i-220000000−22222i2−2i202−22−2−i2i2−i2i200000000000000000000000000
χ614-4-44-24-4−4i4i−4i4i22-20000002i−2i2i−2i-22000000022−222i2−2i20−22−22−i2i2−i2i200000000000000000000000000
χ624-4-44-24-4−4i4i−4i4i22-20000002i−2i2i−2i-220000000−2222−2i22i202−22−2i2−i2i2−i200000000000000000000000000
χ634-4-44-2-444i−4i−4i4i22-2000000−2i2i2i−2i2-2000000000000i6−i6−i6i66−6−6600000000000000000000000000
χ644-4-44-2-444i−4i−4i4i22-2000000−2i2i2i−2i2-2000000000000−i6i6i6−i6−666−600000000000000000000000000
χ654-4-44-2-44−4i4i4i−4i22-20000002i−2i−2i2i2-2000000000000i6−i6−i6i6−666−600000000000000000000000000
χ664-4-44-2-44−4i4i4i−4i22-20000002i−2i−2i2i2-2000000000000−i6i6i6−i66−6−6600000000000000000000000000
χ6788-8-880000008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-8-4000000-4440000−4i34i30000000000000000000000000000000000000000000000000000
χ6988-8-8-4000000-44400004i3−4i30000000000000000000000000000000000000000000000000000
χ708-88-88000000-88-80000000000000000000000000000000000000000000000000000000000
χ718-88-8-40000004-44000000000000−4i34i300000000000000000000000000000000000000000000
χ728-88-8-40000004-440000000000004i3−4i300000000000000000000000000000000000000000000

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