Finite Group Databasebeta

← Group #10691817

Character table — Group #10691817

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122234444446662444121212121212121212126888888881224242424242424248888882424242424242424224488888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ91111111-1-1-1-1111-111-1111111-1-1-1-1-1ii−i−i11-1-1-11111-1-1-1-1ii−i−ii−iii−i−iii−i−i11-1-1i−iii−i−i1-1
χ101111111-1-1-1-1111-111-1111111-1-1-1-1-1ii−i−i11-1-1-11111-1-1-1-1−i−iiii−iii−i−iii−i−i-1-111−ii−i−iii-11
χ111111111-1-1-1-1111-111-1111111-1-1-1-1-1ii−i−i-1-111-1-1-1-1-11111ii−i−i−iiii−i−i−i−iii11-1-1i−i−i−iii-11
χ121111111-1-1-1-1111-111-1111111-1-1-1-1-1ii−i−i-1-111-1-1-1-1-11111−i−iii−iiii−i−i−i−iii-1-111−iiii−i−i1-1
χ131111111-1-1-1-1111-111-1111111-1-1-1-1-1−i−iii11-1-1-11111-1-1-1-1ii−i−i−ii−i−iii−i−iii-1-111i−iii−i−i-11
χ141111111-1-1-1-1111-111-1111111-1-1-1-1-1−i−iii11-1-1-11111-1-1-1-1−i−iii−ii−i−iii−i−iii11-1-1−ii−i−iii1-1
χ151111111-1-1-1-1111-111-1111111-1-1-1-1-1−i−iii-1-111-1-1-1-1-11111ii−i−ii−i−i−iiiii−i−i-1-111i−i−i−iii1-1
χ161111111-1-1-1-1111-111-1111111-1-1-1-1-1−i−iii-1-111-1-1-1-1-11111−i−iiii−i−i−iiiii−i−i11-1-1−iiii−i−i-11
χ1722222222222222-2-2-2-222-2-2-2-22222-200000000-200000000222200000000000000-2-2000000
χ1822222222222222-2-2-2-222-2-2-2-22222-200000000-200000000-2-2-2-20000000000000022000000
χ192222222-2-2-2-22222-2-2222-2-2-2-2-2-2-2-22000000002000000002i2i−2i−2i00000000000000−2i2i000000
χ202222222-2-2-2-22222-2-2222-2-2-2-2-2-2-2-2200000000200000000−2i−2i2i2i000000000000002i−2i000000
χ2122222-2-222-2-222222-2-2-2-222-2-222-2-222i−2i2i−2i0000-2000000000000002i−2i2i−2i0000000000000000
χ2222222-2-222-2-222222-2-2-2-222-2-222-2-22−2i2i−2i2i0000-200000000000000−2i2i−2i2i0000000000000000
χ2322222-2-222-2-2222-2-222-2-2-2-22222-2-2-200000000200000000000000000000002-22-200000000
χ2422222-2-222-2-2222-2-222-2-2-2-22222-2-2-20000000020000000000000000000000-22-2200000000
χ2522222-2-2-2-2222222-22-2-2-2-2-222-2-222200000000-200000000000000000000002-2-2200000000
χ2622222-2-2-2-2222222-22-2-2-2-2-222-2-222200000000-20000000000000000000000-222-200000000
χ2722222-2-2-2-222222-22-22-2-222-2-2-2-222-22-2-2200002000000000000002-2-220000000000000000
χ2822222-2-2-2-222222-22-22-2-222-2-2-2-222-2-222-20000200000000000000-222-20000000000000000
χ292222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1111111110000-2-2-1-1-1-11111000000000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111110000221111-1-1-1-1000000000000
χ332222-122-2-2-2-2-1-1-1-222-2-1-1-1-1-1-1111112i2i−2i−2i22-2-21-1-1-1-1111100002i−2i−i−iii−i−iii000000000000
χ342222-122-2-2-2-2-1-1-1-222-2-1-1-1-1-1-1111112i2i−2i−2i-2-22211111-1-1-1-10000−2i2i−i−iiiii−i−i000000000000
χ352222-122-2-2-2-2-1-1-1-222-2-1-1-1-1-1-111111−2i−2i2i2i22-2-21-1-1-1-111110000−2i2iii−i−iii−i−i000000000000
χ362222-122-2-2-2-2-1-1-1-222-2-1-1-1-1-1-111111−2i−2i2i2i-2-22211111-1-1-1-100002i−2iii−i−i−i−iii000000000000
χ372222-1-2-222-2-2-1-1-122-2-211-1-111-1-111-12i−2i2i−2i0000133−3−333−3−3000000−ii−ii−i3i3−i3i3000000000000
χ382222-1-2-222-2-2-1-1-122-2-211-1-111-1-111-12i−2i2i−2i00001−3−333−3−333000000−ii−iii3−i3i3−i3000000000000
χ392222-1-2-222-2-2-1-1-122-2-211-1-111-1-111-1−2i2i−2i2i0000133−3−333−3−3000000i−ii−ii3−i3i3−i3000000000000
χ402222-1-2-222-2-2-1-1-122-2-211-1-111-1-111-1−2i2i−2i2i00001−3−333−3−333000000i−ii−i−i3i3−i3i3000000000000
χ412222-1-2-2-2-222-1-1-1-22-2211-1-11111-1-112-2-220000-133−3−3−3−333000000-111-1−333−3000000000000
χ422222-1-2-2-2-222-1-1-1-22-2211-1-11111-1-112-2-220000-1−3−33333−3−3000000-111-13−3−33000000000000
χ432222-1-2-2-2-222-1-1-1-22-2211-1-11111-1-11-222-20000-133−3−3−3−3330000001-1-113−3−33000000000000
χ442222-1-2-2-2-222-1-1-1-22-2211-1-11111-1-11-222-20000-1−3−33333−3−30000001-1-11−333−3000000000000
χ452-22-222-22i−2i2i−2i2-2-200002-200002i−2i2i−2i000002−2−i2i202−22−2−i2i2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000001+i−1−i1−i−1+i00
χ462-22-222-22i−2i2i−2i2-2-200002-200002i−2i2i−2i000002−2−i2i202−22−2−i2i2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−1−i1+i−1+i1−i00
χ472-22-222-22i−2i2i−2i2-2-200002-200002i−2i2i−2i00000−22i2−i20−22−22i2−i2i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−1−i1+i−1+i1−i00
χ482-22-222-22i−2i2i−2i2-2-200002-200002i−2i2i−2i00000−22i2−i20−22−22i2−i2i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000001+i−1−i1−i−1+i00
χ492-22-222-2−2i2i−2i2i2-2-200002-20000−2i2i−2i2i000002−2i2−i202−22−2i2−i2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000001−i−1+i1+i−1−i00
χ502-22-222-2−2i2i−2i2i2-2-200002-20000−2i2i−2i2i000002−2i2−i202−22−2i2−i2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−1+i1−i−1−i1+i00
χ512-22-222-2−2i2i−2i2i2-2-200002-20000−2i2i−2i2i00000−22−i2i20−22−22−i2i2−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−1+i1−i−1−i1+i00
χ522-22-222-2−2i2i−2i2i2-2-200002-20000−2i2i−2i2i00000−22−i2i20−22−22−i2i2−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000001−i−1+i1+i−1−i00
χ534444-2444444-2-2-2-4-4-4-4-2-22222-2-2-2-220000000020000000000000000000000000000000000
χ544444-244-4-4-4-4-2-2-24-4-44-2-222222222-200000000-20000000000000000000000000000000000
χ554444-2-4-444-4-4-2-2-2-4-4442222-2-2-2-222200000000-20000000000000000000000000000000000
χ564444-2-4-4-4-444-2-2-24-44-42222-2-222-2-2-20000000020000000000000000000000000000000000
χ574-44-44-444i−4i−4i4i4-4-40000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ584-44-44-44−4i4i4i−4i4-4-40000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ594-44-4-24-44i−4i4i−4i-2220000-220000−2i2i−2i2i0000022−22−2i22i20−22−22i2−i2i2−i200000000000000000000000000
χ604-44-4-24-44i−4i4i−4i-2220000-220000−2i2i−2i2i00000−22222i2−2i202−22−2−i2i2−i2i200000000000000000000000000
χ614-44-4-24-4−4i4i−4i4i-2220000-2200002i−2i2i−2i0000022−222i2−2i20−22−22−i2i2−i2i200000000000000000000000000
χ624-44-4-24-4−4i4i−4i4i-2220000-2200002i−2i2i−2i00000−2222−2i22i202−22−2i2−i2i2−i200000000000000000000000000
χ634-44-4-2-444i−4i−4i4i-22200002-20000−2i2i2i−2i00000000006−6−66−i6i6i6−i600000000000000000000000000
χ644-44-4-2-444i−4i−4i4i-22200002-20000−2i2i2i−2i0000000000−666−6i6−i6−i6i600000000000000000000000000
χ654-44-4-2-44−4i4i4i−4i-22200002-200002i−2i−2i2i00000000006−6−66i6−i6−i6i600000000000000000000000000
χ664-44-4-2-44−4i4i4i−4i-22200002-200002i−2i−2i2i0000000000−666−6−i6i6i6−i600000000000000000000000000
χ6788-8-88000000-88-80000000000000000000000000000000000000000000000000000000000
χ6888-8-8-40000004-440000000043−43000000000000000000000000000000000000000000000000
χ6988-8-8-40000004-4400000000−4343000000000000000000000000000000000000000000000000
χ708-8-888000000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-88-400000044-400000043−4300000000000000000000000000000000000000000000000000
χ728-8-88-400000044-4000000−434300000000000000000000000000000000000000000000000000

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