Finite Group Databasebeta

← Group #10691321

Character table — Group #10691321

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222444434444444466612121212241212121212121212244466688881212121212121224242424242424248888888844121212128888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11-1-111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-1111-11-1-11111-1-11-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-111-1-1ii−i−iii−i−ii−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-1111-11-1-11111-1-11-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-111-1-1−i−iii−i−iii−ii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-1111-11-1-111-1-1111-1-111-1-1-1-1-1-11111iiii−i−i−i−i-11-1-111−i−iiiii−i−i−ii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-1111-11-1-111-1-1111-1-111-1-1-1-1-1-11111−i−i−i−iiiii-11-1-111ii−i−i−i−iiii−i
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-11-11-1-1-111-1-1111-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-111ii−i−i−i−iii−ii
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-11-11-1-1-111-1-1111-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-111−i−iiiii−i−ii−i
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-11-11-1-1-1-1-111111-1-111-1-1-1-11111iiii−i−i−i−i1-111-1-1−i−iii−i−iiii−i
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-11-11-1-1-1-1-111111-1-111-1-1-1-11111−i−i−i−iiiii1-111-1-1ii−i−iii−i−i−ii
χ1722222222222-2-2-2-2222222222-2-22222-2-2-2-20000-2000000-20000000000000022-2-222-2-20000000000000000
χ1822222222222-2-2-2-2222222222-2-22222-2-2-2-20000-2000000-200000000000000-2-222-2-2220000000000000000
χ19222222222-2-22222-2-22222222-2-2-2-2-2-2222222-2-2-2220000-222-2-2-2-200000000000000000000000000000000
χ20222222222-2-22222-2-22222222-2-2-2-2-2-22222-2-222-2-2-20000-2-2-2222200000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000020000002000000000000000000000000000000002i−2i2i−2i00
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200002000000200000000000000000000000000000000−2i2i−2i2i00
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1112222-1111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-111-2-2-2-2-1111111111111110000000022-1-1-1-10000000000
χ2722222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-21-1-100001-1-11111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-21-1-100001-1-11111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2221110000111-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2221110000111-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22-222-2-222-2-200002000000-2000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22-222-2-222-2-200002000000-200000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-22-2-2-222-2-2222-2-222220000-2-2-2-2-22200000000000000000000000000000000
χ342222-2-2-2-22-2-222-2-222222-2-2-2-22-2-2-222-2-222-222-22-2-20000-22222-2-200000000000000000000000000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-22222-2-20000-20000002000000000000000000000000000000002-2-2200
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-22222-2-20000-2000000200000000000000000000000000000000-222-200
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-12-22-21-1-122-2-2-111-1-111-1-1-1-11111000000002-2-1-1110000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-12-22-21-1-1-2-222-111-1-1111111-1-1-1-100000000-2211-1-10000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-1-22-2211122-2-2-1-1-111-1-1-1-1-1-1111100000000-2211-1-10000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-1-22-22111-2-222-1-1-111-1-11111-1-1-1-1000000002-2-1-1110000000000
χ412222-2-2-2-2-1-2-222-2-222-1-1-111112-211-1-111-1-12-2-22-1-1-1000011111-1-1−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i30000000000
χ422222-2-2-2-2-1-2-222-2-222-1-1-111112-211-1-111-1-12-2-22-1-1-1000011111-1-1i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i30000000000
χ432222-2-2-2-2-1-2-222-2-222-1-1-111112-211-1-111-1-1-222-2-11100001-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i30000000000
χ442222-2-2-2-2-1-2-222-2-222-1-1-111112-211-1-111-1-1-222-2-11100001-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i30000000000
χ452-22-22i−2i2i−2i22-200002i−2i-22-22i2i−2i−2i002-22i−2i000000000002−2−i2i200000002−22−2−i2i2−i2i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000001−i−1+i1+i−1−i000000
χ462-22-22i−2i2i−2i22-200002i−2i-22-22i2i−2i−2i002-22i−2i000000000002−2−i2i200000002−22−2−i2i2−i2i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000−1+i1−i−1−i1+i000000
χ472-22-22i−2i2i−2i22-200002i−2i-22-22i2i−2i−2i002-22i−2i00000000000−22i2−i20000000−22−22i2−i2i2−i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000−1+i1−i−1−i1+i000000
χ482-22-22i−2i2i−2i22-200002i−2i-22-22i2i−2i−2i002-22i−2i00000000000−22i2−i20000000−22−22i2−i2i2−i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000001−i−1+i1+i−1−i000000
χ492-22-2−2i2i−2i2i22-20000−2i2i-22-2−2i−2i2i2i002-2−2i2i000000000002−2i2−i200000002−22−2i2−i2i2−i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000001+i−1−i1−i−1+i000000
χ502-22-2−2i2i−2i2i22-20000−2i2i-22-2−2i−2i2i2i002-2−2i2i000000000002−2i2−i200000002−22−2i2−i2i2−i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000−1−i1+i−1+i1−i000000
χ512-22-2−2i2i−2i2i22-20000−2i2i-22-2−2i−2i2i2i002-2−2i2i00000000000−22−i2i20000000−22−22−i2i2−i2i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000−1−i1+i−1+i1−i000000
χ522-22-2−2i2i−2i2i22-20000−2i2i-22-2−2i−2i2i2i002-2−2i2i00000000000−22−i2i20000000−22−22−i2i2−i2i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000001+i−1−i1−i−1+i000000
χ5344444444-244-4-4-4-444-2-2-2-2-2-2-2-4-4-2-2-2-2222200002000000200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000-2000000-200000000000000000000000000000000000000
χ554444-4-4-4-4-244-4-444-4-4-2-2-222224-4-2-222-2-2220000-2000000200000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-4-4-44444-2-2-22222-4422-2-2-2-22200002000000-200000000000000000000000000000000000000
χ5744-4-444-4-44000000004-4-44-44-400000000000000000000000000000000000022−220022−22000000000000000000
χ5844-4-444-4-44000000004-4-44-44-4000000000000000000000000000000000000−222200−2222000000000000000000
χ5944-4-4-4-4444000000004-4-4-44-44000000000000000000000000000000000000−2i22i2002i2−2i2000000000000000000
χ6044-4-4-4-4444000000004-4-4-44-440000000000000000000000000000000000002i2−2i200−2i22i2000000000000000000
χ614-44-44i−4i4i−4i4-440000−4i4i-44-44i4i−4i−4i00-44−4i4i000000000000000000000000000000000000000000000000000000
χ624-44-44i−4i4i−4i-24-400004i−4i2-22−2i−2i2i2i00-22−2i2i0000000000022−22−2i22i20000000−22−22i2−i2i2−i2000000000000000000000000
χ634-44-44i−4i4i−4i-24-400004i−4i2-22−2i−2i2i2i00-22−2i2i00000000000−22222i2−2i200000002−22−2−i2i2−i2i2000000000000000000000000
χ644-44-44i−4i4i−4i-2-440000−4i4i2-22−2i−2i2i2i002-22i−2i0000000000000000000000i6−i6−i6i66−6−66000000000000000000000000
χ654-44-44i−4i4i−4i-2-440000−4i4i2-22−2i−2i2i2i002-22i−2i0000000000000000000000−i6i6i6−i6−666−6000000000000000000000000
χ664-44-4−4i4i−4i4i4-4400004i−4i-44-4−4i−4i4i4i00-444i−4i000000000000000000000000000000000000000000000000000000
χ674-44-4−4i4i−4i4i-24-40000−4i4i2-222i2i−2i−2i00-222i−2i0000000000022−222i2−2i20000000−22−22−i2i2−i2i2000000000000000000000000
χ684-44-4−4i4i−4i4i-24-40000−4i4i2-222i2i−2i−2i00-222i−2i00000000000−2222−2i22i200000002−22−2i2−i2i2−i2000000000000000000000000
χ694-44-4−4i4i−4i4i-2-4400004i−4i2-222i2i−2i−2i002-2−2i2i0000000000000000000000i6−i6−i6i6−666−6000000000000000000000000
χ704-44-4−4i4i−4i4i-2-4400004i−4i2-222i2i−2i−2i002-2−2i2i0000000000000000000000−i6i6i6−i66−6−66000000000000000000000000
χ714-4-444i−4i−4i4i4004-44i−4i00-4-444i−4i−4i4i0000004i−4i4-400000000000000000000000000000000000000000000000000
χ724-4-444i−4i−4i4i400-44−4i4i00-4-444i−4i−4i4i000000−4i4i-4400000000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i-2004-44i−4i0022-2−2i2i2i−2i000000−2i2i-220000000000000023−23−2i32i300000000000000000000000000000000
χ744-4-444i−4i−4i4i-2004-44i−4i0022-2−2i2i2i−2i000000−2i2i-2200000000000000−23232i3−2i300000000000000000000000000000000
χ754-4-444i−4i−4i4i-200-44−4i4i0022-2−2i2i2i−2i0000002i−2i2-200000−2i32i30000023−23000000000000000000000000000000000000
χ764-4-444i−4i−4i4i-200-44−4i4i0022-2−2i2i2i−2i0000002i−2i2-2000002i3−2i300000−2323000000000000000000000000000000000000
χ774-4-44−4i4i4i−4i4004-4−4i4i00-4-44−4i4i4i−4i000000−4i4i4-400000000000000000000000000000000000000000000000000
χ784-4-44−4i4i4i−4i400-444i−4i00-4-44−4i4i4i−4i0000004i−4i-4400000000000000000000000000000000000000000000000000
χ794-4-44−4i4i4i−4i-2004-4−4i4i0022-22i−2i−2i2i0000002i−2i-220000000000000023−232i3−2i300000000000000000000000000000000
χ804-4-44−4i4i4i−4i-2004-4−4i4i0022-22i−2i−2i2i0000002i−2i-2200000000000000−2323−2i32i300000000000000000000000000000000
χ814-4-44−4i4i4i−4i-200-444i−4i0022-22i−2i−2i2i000000−2i2i2-200000−2i32i300000−2323000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i-200-444i−4i0022-22i−2i−2i2i000000−2i2i2-2000002i3−2i30000023−23000000000000000000000000000000000000
χ8388-8-888-8-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-888-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000

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