Finite Group Databasebeta

← Group #10691826

Character table — Group #10691826

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order122234444446661212121224448888121212126881212122424242424242424448812121212242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-1111-1-1-1-1-111-1ii−i−i11-1-1-1i−i11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101111111-1-1-1-1111-1-1-1-1-111-1ii−i−i11-1-1-1i−i11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ111111111-1-1-1-1111-1-1-1-1-111-1ii−i−i11-1-1-1i−i11-1iiii−i−i−i−i-11−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ121111111-1-1-1-1111-1-1-1-1-111-1ii−i−i11-1-1-1i−i11-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ131111111-1-1-1-1111-1-1-1-1-111-1−i−iii11-1-1-1−ii11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ141111111-1-1-1-1111-1-1-1-1-111-1−i−iii11-1-1-1−ii11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ151111111-1-1-1-1111-1-1-1-1-111-1−i−iii11-1-1-1−ii11-1−i−i−i−iiiii-11i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ161111111-1-1-1-1111-1-1-1-1-111-1−i−iii11-1-1-1−ii11-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-222222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-222-2-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-22-2-222i2i−2i−2i22-2-22−2i2i-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-22-2-22−2i−2i2i2i22-2-222i−2i-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ2122222-2-222-2-2222222222-2-20000-2-2-2-22002-2-20000000000000000000000002i−2i2i−2i00000000
χ2222222-2-222-2-2222222222-2-20000-2-2-2-22002-2-2000000000000000000000000−2i2i−2i2i00000000
χ2322222-2-222-2-22222222-2-2220000-2-2-2-2-200-222000000000000000000002-22-2000000000000
χ2422222-2-222-2-22222222-2-2220000-2-2-2-2-200-22200000000000000000000-22-22000000000000
χ2522222-2-2-2-222222-2-2-2-22-22-20000-2-222200-22-2000000000000000000002-2-22000000000000
χ2622222-2-2-2-222222-2-2-2-22-22-20000-2-222200-22-200000000000000000000-222-2000000000000
χ2722222-2-2-2-222222-2-2-2-2-22-220000-2-222-2002-220000000000000000000000002-2-2200000000
χ2822222-2-2-2-222222-2-2-2-2-22-220000-2-222-2002-22000000000000000000000000-222-200000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ312222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-2-2-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ322222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-2-2-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ332222-1222222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-11-2-2111-1-111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ342222-1222222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-11-2-2111-1-111-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ352222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-112211111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ362222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-112211111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ372222-122-2-2-2-2-1-1-111112-2-222i2i−2i−2i-1-111-1−2i2i11-1−i−iiiii−i−i0000−i3i3i3−i33−3−330000000000000000
χ382222-122-2-2-2-2-1-1-111112-2-222i2i−2i−2i-1-111-1−2i2i11-1−i−iiiii−i−i0000i3−i3−i3i3−333−30000000000000000
χ392222-122-2-2-2-2-1-1-111112-2-22−2i−2i2i2i-1-111-12i−2i11-1ii−i−i−i−iii0000−i3i3i3−i3−333−30000000000000000
χ402222-122-2-2-2-2-1-1-111112-2-22−2i−2i2i2i-1-111-12i−2i11-1ii−i−i−i−iii0000i3−i3−i3i33−3−330000000000000000
χ412222-122-2-2-2-2-1-1-11111-222-22i2i−2i−2i-1-11112i−2i-1-11−i−i−i−iiiii2-22i−2i-1-111−i−iii0000000000000000
χ422222-122-2-2-2-2-1-1-11111-222-22i2i−2i−2i-1-11112i−2i-1-11−i−i−i−iiiii-22−2i2i11-1-1ii−i−i0000000000000000
χ432222-122-2-2-2-2-1-1-11111-222-2−2i−2i2i2i-1-1111−2i2i-1-11iiii−i−i−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ442222-122-2-2-2-2-1-1-11111-222-2−2i−2i2i2i-1-1111−2i2i-1-11iiii−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
χ452-2-2222-22i−2i2i−2i-22-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000000000002−2−i2i21+i−1−i1−i−1+i
χ462-2-2222-22i−2i2i−2i-22-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000000000−22i2−i2−1−i1+i−1+i1−i
χ472-2-2222-22i−2i2i−2i-22-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000000000002−2−i2i2−1−i1+i−1+i1−i
χ482-2-2222-22i−2i2i−2i-22-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000000000−22i2−i21+i−1−i1−i−1+i
χ492-2-2222-2−2i2i−2i2i-22-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000000000002−2i2−i21−i−1+i1+i−1−i
χ502-2-2222-2−2i2i−2i2i-22-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000000000−22−i2i2−1+i1−i−1−i1+i
χ512-2-2222-2−2i2i−2i2i-22-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000000000000002−2i2−i2−1+i1−i−1−i1+i
χ522-2-2222-2−2i2i−2i2i-22-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000000000−22−i2i21−i−1+i1+i−1−i
χ534444-2-4-444-4-4-2-2-2-2-2-2-244-4-400002222-200-222000000000000000000000000000000000000
χ544444-2-4-444-4-4-2-2-2-2-2-2-2-4-444000022222002-2-2000000000000000000000000000000000000
χ554444-2-4-4-4-444-2-2-222224-44-4000022-2-2-2002-22000000000000000000000000000000000000
χ564444-2-4-4-4-444-2-2-22222-44-44000022-2-2200-22-2000000000000000000000000000000000000
χ574-4-444-444i−4i−4i4i-44-44i4i−4i−4i00000000-44−4i4i000000000000000000000000000000000000000000
χ584-4-444-44−4i4i4i−4i-44-4−4i−4i4i4i00000000-444i−4i000000000000000000000000000000000000000000
χ594-4-44-24-44i−4i4i−4i2-22−2i−2i2i2i00004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-22−2i2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000
χ604-4-44-24-44i−4i4i−4i2-22−2i−2i2i2i0000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-22−2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000
χ614-4-44-24-4−4i4i−4i4i2-222i2i−2i−2i0000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23-222i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000
χ624-4-44-24-4−4i4i−4i4i2-222i2i−2i−2i00004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-222i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000
χ634-4-44-2-444i−4i−4i4i2-22−2i−2i2i2i000000002-22i−2i00000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ644-4-44-2-444i−4i−4i4i2-22−2i−2i2i2i000000002-22i−2i000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ654-4-44-2-44−4i4i4i−4i2-222i2i−2i−2i000000002-2−2i2i000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ664-4-44-2-44−4i4i4i−4i2-222i2i−2i−2i000000002-2−2i2i00000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ6788-8-88000000-8-880000000000000000000000000000000000000000000000000000000000
χ6888-8-8-400000044-443−4343−43000000000000000000000000000000000000000000000000000000
χ6988-8-8-400000044-4−4343−4343000000000000000000000000000000000000000000000000000000
χ708-88-880000008-8-80000000000000000000000000000000000000000000000000000000000
χ718-88-8-4000000-444−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000
χ728-88-8-4000000-4444i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000

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