Finite Group Databasebeta

← Group #10691293

Character table — Group #10691293

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222444422344444466612121212446612121212121224446688881212121212121212242424242424242488888888246612124444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-11111-1-11111-1-11-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-111-1-1ii−i−iii−i−ii−i
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-11111-1-11111-1-11-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-111-1-1−i−iii−i−iii−ii
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-11111-1-111-1-1111-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11-1-111−i−iiiii−i−i−ii
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-11111-1-111-1-1111-111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11-1-111ii−i−i−i−iiii−i
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-111-1-111-1-111-1-11-1-1-111111111-1-1-1-1iiii−i−i−i−i-11-1-111ii−i−i−i−iii−ii
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-111-1-111-1-111-1-11-1-1-111111111-1-1-1-1−i−i−i−iiiii-11-1-111−i−iiiii−i−ii−i
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-111-1-111-1-1-1-1111-1-1-11111-1-1-1-11111iiii−i−i−i−i1-111-1-1−i−iii−i−iiii−i
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-111-1-111-1-111-1-1-1-1111-1-1-11111-1-1-1-11111−i−i−i−iiiii1-111-1-1ii−i−iii−i−i−ii
χ1722222222222-2-222-2-22222222-2-222-2-2-2-2222-2-22220000-2-2-2-2-2-22200000000000000000000000000000000
χ1822222222222-2-222-2-22222222-2-222-2-2-2-222-222-2-2-20000-2-22222-2-200000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2112222-1-1111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2-1-1111111111111110000000022-1-1-1-10000000000
χ232222222222-1-2-222-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-12-2-22-1-10000111111-1-1−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ242222222222-1-2-222-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-12-2-22-1-10000111111-1-1i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ252222222222-1-2-222-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-1-222-211000011-1-1-1-111−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ262222222222-1-2-222-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-1-222-211000011-1-1-1-111i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ2722222222-2-2222-2-2222222222-2-2-2-22222-2-20000000000-2-20000000000000022-2-222-2-20000000000000000
χ2822222222-2-2222-2-2222222222-2-2-2-22222-2-20000000000-2-200000000000000-2-222-2-2220000000000000000
χ2922222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000022000000000000000000000000000000002i−2i2i−2i00
χ3022222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000002200000000000000000000000000000000−2i2i−2i2i00
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-2-222222-2-2-2-20000000000-22000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-2-222222-2-2-2-20000000000-2200000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-222-2-200000000002-2000000000000000000000000000000002-2-2200
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-222-2-200000000002-200000000000000000000000000000000-222-200
χ352222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-2-2-222222-22-2220000-22-2-222-2-200000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-2-2-22222-22-22-2-20000-2222-2-22200000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-111-1-122-2-2-1-122-2-2-11-1-11111-1-1-1-11111000000002-2-1-1110000000000
χ382222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-111-1-122-2-2-1-1-2-222-11-1-111111111-1-1-1-100000000-2211-1-10000000000
χ392222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-111-1-1-2-2221122-2-2-1111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ402222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-111-1-1-2-22211-2-222-1111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ412222-2-2-2-2-2-2-1-2-22222-1-1-11111-221111-1-1-1-12-22-2-1-100001-111-1-111−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i30000000000
χ422222-2-2-2-2-2-2-1-2-22222-1-1-11111-221111-1-1-1-12-22-2-1-100001-111-1-111i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i30000000000
χ432222-2-2-2-2-2-2-1-2-22222-1-1-11111-221111-1-1-1-1-22-221100001-1-1-111-1-1−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i30000000000
χ442222-2-2-2-2-2-2-1-2-22222-1-1-11111-221111-1-1-1-1-22-221100001-1-1-111-1-1i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i30000000000
χ4522-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i00002-22i−2i000000002−2−i2i2000000002−22−2−i2i2−i2i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000001−i−1+i1+i−1−i000000
χ4622-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i00002-22i−2i000000002−2−i2i2000000002−22−2−i2i2−i2i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000−1+i1−i−1−i1+i000000
χ4722-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i00002-22i−2i00000000−22i2−i200000000−22−22i2−i2i2−i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000−1+i1−i−1−i1+i000000
χ4822-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i00002-22i−2i00000000−22i2−i200000000−22−22i2−i2i2−i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000001−i−1+i1+i−1−i000000
χ4922-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i00002-2−2i2i000000002−2i2−i2000000002−22−2i2−i2i2−i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000001+i−1−i1−i−1+i000000
χ5022-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i00002-2−2i2i000000002−2i2−i2000000002−22−2i2−i2i2−i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000−1−i1+i−1+i1−i000000
χ5122-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i00002-2−2i2i00000000−22−i2i200000000−22−22−i2i2−i2i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000−1−i1+i−1+i1−i000000
χ5222-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i00002-2−2i2i00000000−22−i2i200000000−22−22−i2i2−i2i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000001+i−1−i1−i−1+i000000
χ5344444444-4-4-244-4-444-2-2-2-2-2-2-2-4-422-2-2-2-22200000000002200000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000-2-200000000000000000000000000000000000000
χ554444-4-4-4-444-244-4-4-4-4-2-2-22222-44-2-2-2-2222200000000002-200000000000000000000000000000000000000
χ564444-4-4-4-444-2-4-4-4-444-2-2-222224-4-2-222-2-2220000000000-2200000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i004-4400−4i4i4-4-44i4i−4i−4i0000-44−4i4i0000000000000000000000000000000000000000000000000000
χ5844-4-44i−4i4i−4i00-24-4004i−4i-222−2i−2i2i2i0000-22−2i2i0000000022−22−2i22i200000000−22−22i2−i2i2−i2000000000000000000000000
χ5944-4-44i−4i4i−4i00-24-4004i−4i-222−2i−2i2i2i0000-22−2i2i00000000−22222i2−2i2000000002−22−2−i2i2−i2i2000000000000000000000000
χ6044-4-44i−4i4i−4i00-2-4400−4i4i-222−2i−2i2i2i00002-22i−2i00000000000000000000i6−i6−i6i66−6−66000000000000000000000000
χ6144-4-44i−4i4i−4i00-2-4400−4i4i-222−2i−2i2i2i00002-22i−2i00000000000000000000−i6i6i6−i6−666−6000000000000000000000000
χ6244-4-4−4i4i−4i4i004-44004i−4i4-4-4−4i−4i4i4i0000-444i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-4−4i4i−4i4i00-24-400−4i4i-2222i2i−2i−2i0000-222i−2i0000000022−222i2−2i200000000−22−22−i2i2−i2i2000000000000000000000000
χ6444-4-4−4i4i−4i4i00-24-400−4i4i-2222i2i−2i−2i0000-222i−2i00000000−2222−2i22i2000000002−22−2i2−i2i2−i2000000000000000000000000
χ6544-4-4−4i4i−4i4i00-2-44004i−4i-2222i2i−2i−2i00002-2−2i2i00000000000000000000i6−i6−i6i6−666−6000000000000000000000000
χ6644-4-4−4i4i−4i4i00-2-44004i−4i-2222i2i−2i−2i00002-2−2i2i00000000000000000000−i6i6i6−i66−6−66000000000000000000000000
χ674-44-44i−4i−4i4i004000000-44-44i−4i4i−4i0000000000000000000000000000000000002+2i−2−2i002−2i−2+2i000000000000000000
χ684-44-44i−4i−4i4i004000000-44-44i−4i4i−4i000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000
χ694-44-4−4i4i4i−4i004000000-44-4−4i4i−4i4i0000000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000
χ704-44-4−4i4i4i−4i004000000-44-4−4i4i−4i4i000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000
χ714-4-4444-4-44-44004-400-4-444-4-44004-400004-400000000000000000000000000000000000000000000000000
χ724-4-4444-4-44-4-2004-40022-2-222-200-220000-2200000000000023−2323−230000000000000000000000000000000000
χ734-4-4444-4-44-4-2004-40022-2-222-200-220000-22000000000000−2323−23230000000000000000000000000000000000
χ744-4-4444-4-4-44400-4400-4-444-4-4400-440000-4400000000000000000000000000000000000000000000000000
χ754-4-4444-4-4-44-200-440022-2-222-2002-200002-20000−2i32i30000000000−2i32i300000000000000000000000000000000
χ764-4-4444-4-4-44-200-440022-2-222-2002-200002-200002i3−2i300000000002i3−2i300000000000000000000000000000000
χ774-4-44-4-4444-4400-4400-4-44-444-4004-40000-4400000000000000000000000000000000000000000000000000
χ784-4-44-4-4444-4-200-440022-22-2-2200-2200002-20000−2i32i300000000002i3−2i300000000000000000000000000000000
χ794-4-44-4-4444-4-200-440022-22-2-2200-2200002-200002i3−2i30000000000−2i32i300000000000000000000000000000000
χ804-4-44-4-444-444004-400-4-44-444-400-4400004-400000000000000000000000000000000000000000000000000
χ814-4-44-4-444-44-2004-40022-22-2-22002-20000-2200000000000023−23−23230000000000000000000000000000000000
χ824-4-44-4-444-44-2004-40022-22-2-22002-20000-22000000000000−232323−230000000000000000000000000000000000
χ838-88-88i−8i−8i8i00-40000004-44−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ848-88-8−8i8i8i−8i00-40000004-444i−4i4i−4i000000000000000000000000000000000000000000000000000000000000

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