Finite Group Databasebeta

← Group #10691812

Character table — Group #10691812

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order1222344444466612121212244488881212121268812121224242424242424242466881212242424244444888888888888
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
χ51111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-1111-1-1-1-1-111-1ii−i−i11-1-1-1i−i1-11iiii−i−i−i−i1-111i−i-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−i1-11iiii−i−i−i−i1-111i−i-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−i1-11iiii−i−i−i−i-11-1-1−ii11−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−i1-11iiii−i−i−i−i-11-1-1−ii11−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−ii1-11−i−i−i−iiiii1-111−ii-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−ii1-11−i−i−i−iiiii1-111−ii-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−ii1-11−i−i−i−iiiii-11-1-1i−i11ii−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−ii1-11−i−i−i−iiiii-11-1-1i−i11ii−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-22-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-22-2-22−2i−2i2i2i22-2-222i−2i-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ2122222-2-222-2-2222222222-2-20000-2-2-2-2200-2-220000000000000000000000002i−2i2i−2i00000000
χ2222222-2-222-2-2222222222-2-20000-2-2-2-2200-2-22000000000000000000000000−2i2i−2i2i00000000
χ2322222-2-222-2-22222222-2-2220000-2-2-2-2-20022-2000000000000000000002-22-2000000000000
χ2422222-2-222-2-22222222-2-2220000-2-2-2-2-20022-200000000000000000000-22-22000000000000
χ2522222-2-2-2-222222-2-2-2-22-22-20000-2-2222002-2-2000000000000000000002-2-22000000000000
χ2622222-2-2-2-222222-2-2-2-22-22-20000-2-2222002-2-200000000000000000000-222-2000000000000
χ2722222-2-2-2-222222-2-2-2-2-22-220000-2-222-200-2220000000000000000000000002-2-2200000000
χ2822222-2-2-2-222222-2-2-2-2-22-220000-2-222-200-222000000000000000000000000-222-200000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000000000
χ312222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-2-2-1-1-11111111122-1-1-2-2-1-111110000000000000000
χ322222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-2-2-1-1-111111111-2-2112211-1-1-1-10000000000000000
χ332222-1222222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-11-2-2111-1-111-1-11100−i3i300−i3i3−i3i3−i3i30000000000000000
χ342222-1222222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-11-2-2111-1-111-1-11100i3−i300i3−i3i3−i3i3−i30000000000000000
χ352222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-112211111-1-111-1-100−i3i300−i3i3i3−i3i3−i30000000000000000
χ362222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-112211111-1-111-1-100i3−i300i3−i3−i3i3−i3i30000000000000000
χ372222-122-2-2-2-2-1-1-111112-2-222i2i−2i−2i-1-111-1−2i2i1-11−i−iiiii−i−i00−i3i300i3−i33−3−330000000000000000
χ382222-122-2-2-2-2-1-1-111112-2-222i2i−2i−2i-1-111-1−2i2i1-11−i−iiiii−i−i00i3−i300−i3i3−333−30000000000000000
χ392222-122-2-2-2-2-1-1-111112-2-22−2i−2i2i2i-1-111-12i−2i1-11ii−i−i−i−iii00−i3i300i3−i3−333−30000000000000000
χ402222-122-2-2-2-2-1-1-111112-2-22−2i−2i2i2i-1-111-12i−2i1-11ii−i−i−i−iii00i3−i300−i3i33−3−330000000000000000
χ412222-122-2-2-2-2-1-1-11111-222-22i2i−2i−2i-1-11112i−2i-11-1−i−i−i−iiiii2-2-1-12i−2i11−i−iii0000000000000000
χ422222-122-2-2-2-2-1-1-11111-222-22i2i−2i−2i-1-11112i−2i-11-1−i−i−i−iiiii-2211−2i2i-1-1ii−i−i0000000000000000
χ432222-122-2-2-2-2-1-1-11111-222-2−2i−2i2i2i-1-1111−2i2i-11-1iiii−i−i−i−i2-2-1-1−2i2i11ii−i−i0000000000000000
χ442222-122-2-2-2-2-1-1-11111-222-2−2i−2i2i2i-1-1111−2i2i-11-1iiii−i−i−i−i-22112i−2i-1-1−i−iii0000000000000000
χ452-22-222-22i−2i2i−2i2-2-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000000000002−2−i2i21+i−1−i1−i−1+i
χ462-22-222-22i−2i2i−2i2-2-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000000000−22i2−i2−1−i1+i−1+i1−i
χ472-22-222-22i−2i2i−2i2-2-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000000000002−2−i2i2−1−i1+i−1+i1−i
χ482-22-222-22i−2i2i−2i2-2-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000000000−22i2−i21+i−1−i1−i−1+i
χ492-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000000000002−2i2−i21−i−1+i1+i−1−i
χ502-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000000000−22−i2i2−1+i1−i−1−i1+i
χ512-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000000000000002−2i2−i2−1+i1−i−1−i1+i
χ522-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000000000−22−i2i21−i−1+i1+i−1−i
χ534444-2-4-444-4-4-2-2-2-2-2-2-244-4-400002222-20022-2000000000000000000000000000000000000
χ544444-2-4-444-4-4-2-2-2-2-2-2-2-4-44400002222200-2-22000000000000000000000000000000000000
χ554444-2-4-4-4-444-2-2-222224-44-4000022-2-2-200-222000000000000000000000000000000000000
χ564444-2-4-4-4-444-2-2-22222-44-44000022-2-22002-2-2000000000000000000000000000000000000
χ574-44-44-444i−4i−4i4i4-4-44i4i−4i−4i00000000-44−4i4i000000000000000000000000000000000000000000
χ584-44-44-44−4i4i4i−4i4-4-4−4i−4i4i4i00000000-444i−4i000000000000000000000000000000000000000000
χ594-44-4-24-44i−4i4i−4i-222−2i−2i2i2i00004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-22−2i2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000
χ604-44-4-24-44i−4i4i−4i-222−2i−2i2i2i0000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-22−2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000
χ614-44-4-24-4−4i4i−4i4i-2222i2i−2i−2i0000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23-222i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000
χ624-44-4-24-4−4i4i−4i4i-2222i2i−2i−2i00004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-222i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000
χ634-44-4-2-444i−4i−4i4i-222−2i−2i2i2i000000002-22i−2i00000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ644-44-4-2-444i−4i−4i4i-222−2i−2i2i2i000000002-22i−2i000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ654-44-4-2-44−4i4i4i−4i-2222i2i−2i−2i000000002-2−2i2i000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ664-44-4-2-44−4i4i4i−4i-2222i2i−2i−2i000000002-2−2i2i00000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ6788-8-88000000-88-80000000000000000000000000000000000000000000000000000000000
χ6888-8-8-40000004-4443−4343−43000000000000000000000000000000000000000000000000000000
χ6988-8-8-40000004-44−4343−4343000000000000000000000000000000000000000000000000000000
χ708-8-888000000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-88-400000044-4−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000
χ728-8-88-400000044-44i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000

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