Finite Group Databasebeta

← Group #10690364

Character table — Group #10690364

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order122244442234466612121212444466121212121212224488888888121224242424242424242424242424242424888866121244448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-11-11-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1-11-111-1-1i−iii−i−i11-1-1
χ101111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-11-11-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii1-11-1-1-111−ii−i−iii-1-111
χ111111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-11-11-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i1-11-1-1-111i−iii−i−i-1-111
χ121111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-11-11-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1-11-111-1-1−ii−i−iii11-1-1
χ131111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-1-11-11ii−i−i−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11-1111-1-1i−i−i−iii-1-111
χ141111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-1-11-11ii−i−i−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii-11-11-1-111−iiii−i−i11-1-1
χ151111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-1-11-11−i−iiiii−i−i1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i-11-11-1-111i−i−i−iii11-1-1
χ161111-1-1-1-1111-1-1111-1-1-1-11-1-111111-1-1-1-1-11-11−i−iiiii−i−i1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii-11-1111-1-1−iiii−i−i-1-111
χ1722222222222222222222-2-2-2-222-2-22-2-22000000000000-2-20000000000000000222200000000-2-200000000
χ1822222222222222222222-2-2-2-222-2-22-2-22000000000000-2-20000000000000000-2-2-2-2000000002200000000
χ192222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ202222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
χ212222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ222222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ2322222222-2-22-2-222222222-22-2-2-222-222-2000000000000-2-20000000000000000000000000000002-22-20000
χ2422222222-2-22-2-222222222-22-2-2-222-222-2000000000000-2-2000000000000000000000000000000-22-220000
χ2522222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-22-2-220000000022000000000000000000002-2-2200000000000000
χ2622222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-2-222-2000000002200000000000000000000-222-200000000000000
χ2722222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111112-2-2200000000-1-133−3−333−3−333−3−333−3−30000-111-100000000000000
χ2822222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111112-2-2200000000-1-1−3−333−3−333−3−333−3−3330000-111-100000000000000
χ2922222222-2-2-1-2-2-1-1-1-1-1-1-1-22-2211111111-222-200000000-1-133−3−333−3−3−3−333−3−33300001-1-1100000000000000
χ3022222222-2-2-1-2-2-1-1-1-1-1-1-1-22-2211111111-222-200000000-1-1−3−333−3−33333−3−333−3−300001-1-1100000000000000
χ312222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-222-2000000000000-2200000000000000002i2i−2i−2i00000000−2i2i00000000
χ322222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-222-2000000000000-220000000000000000−2i−2i2i2i000000002i−2i00000000
χ332222-2-2-2-222-1-2-2-1-1-111112-2-22-1-1-1-111112-22-22i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000-11-1100000000000000
χ342222-2-2-2-222-1-2-2-1-1-111112-2-22-1-1-1-111112-22-2−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000-11-1100000000000000
χ352222-2-2-2-222-1-2-2-1-1-111112-2-22-1-1-1-11111-22-222i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i−i−i−i−iiiii00001-11-100000000000000
χ362222-2-2-2-222-1-2-2-1-1-111112-2-22-1-1-1-11111-22-22−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiiiiiii−i−i−i−i00001-11-100000000000000
χ372222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2222-2-22000000000000-220000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2222-2-22000000000000-22000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2222222-2-2000000002-20000000000000000000022-2-200000000000000
χ402222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22222-2-222000000002-200000000000000000000-2-22200000000000000
χ412222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-122-2-200000000-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000-1-11100000000000000
χ422222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-122-2-200000000-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000-1-11100000000000000
χ432222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-1-2-22200000000-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000011-1-100000000000000
χ442222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-1-2-22200000000-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000011-1-100000000000000
χ4522-2-222-2-22-22-22-2-2222-2-200002-200-2002000000002−22−2002−22−22−22−2000000002i−2i2i−2i00000000000000−i2i2−i2i2
χ4622-2-222-2-22-22-22-2-2222-2-200002-200-2002000000002−22−2002−22−22−22−200000000−2i2i−2i2i00000000000000i2−i2i2−i2
χ4722-2-222-2-22-22-22-2-2222-2-200002-200-200200000000−22−2200−22−22−22−22000000002i−2i2i−2i00000000000000i2−i2i2−i2
χ4822-2-222-2-22-22-22-2-2222-2-200002-200-200200000000−22−2200−22−22−22−2200000000−2i2i−2i2i00000000000000−i2i2−i2i2
χ4922-2-2-2-2222-222-2-2-22-2-22200002-200200-200000000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000002-2-2200000000000000−i2i2i2−i2
χ5022-2-2-2-2222-222-2-2-22-2-22200002-200200-200000000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000-222-200000000000000i2−i2−i2i2
χ5122-2-2-2-2222-222-2-2-22-2-22200002-200200-200000000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000002-2-2200000000000000i2−i2−i2i2
χ5222-2-2-2-2222-222-2-2-22-2-22200002-200200-200000000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000-222-200000000000000−i2i2i2−i2
χ534444444444-244-2-2-2-2-2-2-2-4-4-4-4-2-222-222-20000000000002200000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-2-2-2-2-2-2-24-44-422-2-22-2-220000000000002200000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-4-2-2-22222-444-4-2-2222-2-220000000000002-200000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-244-2-2-2222244-4-422-2-2-222-20000000000002-200000000000000000000000000000000000000
χ5744-4-444-4-44-4-2-4422-2-2-2220000-2200200-20000000022−2222−2200−22−22−22−22000000000000000000000000000000
χ5844-4-444-4-44-4-2-4422-2-2-2220000-2200200-200000000−2222−2222002−22−22−22−2000000000000000000000000000000
χ5944-4-444-4-4-4444-4-4-4444-4-40000-4400400-40000000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-44-24-422-2-2-22200002-200-2002000000000000006−6−666−6−66000000000000000000000000000000
χ6144-4-444-4-4-44-24-422-2-2-22200002-200-200200000000000000−666−6−666−6000000000000000000000000000000
χ6244-4-4-4-4444-4-24-422-222-2-20000-2200-200200000000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ6344-4-4-4-4444-4-24-422-222-2-20000-2200-2002000000002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ6444-4-4-4-444-444-44-4-44-4-4440000-4400-40040000000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-44-2-4422-222-2-200002-200200-200000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000000000
χ6644-4-4-4-444-44-2-4422-222-2-200002-200200-200000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000000000
χ674-44-44i−4i4i−4i004004-4-44i−4i4i−4i000000000000000000000000000000000000000000000000002-22i−2i0000000000
χ684-44-44i−4i4i−4i004004-4-44i−4i4i−4i00000000000000000000000000000000000000000000000000-22−2i2i0000000000
χ694-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i000000000000000000000000000000000000000000000000002-2−2i2i0000000000
χ704-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i00000000000000000000000000000000000000000000000000-222i−2i0000000000
χ714-4-444i−4i−4i4i00400-44-44i−4i−4i4i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ724-4-444i−4i−4i4i00400-44-44i−4i−4i4i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ734-4-444i−4i−4i4i00-2002-22−2i2i2i−2i00000023−230−2i32i3000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ230000000000000000000000
χ744-4-444i−4i−4i4i00-2002-22−2i2i2i−2i00000023−230−2i32i300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ230000000000000000000000
χ754-4-444i−4i−4i4i00-2002-22−2i2i2i−2i000000−232302i3−2i3000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ230000000000000000000000
χ764-4-444i−4i−4i4i00-2002-22−2i2i2i−2i000000−232302i3−2i300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ230000000000000000000000
χ774-4-44−4i4i4i−4i00400-44-4−4i4i4i−4i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ784-4-44−4i4i4i−4i00400-44-4−4i4i4i−4i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ794-4-44−4i4i4i−4i00-2002-222i−2i−2i2i00000023−2302i3−2i300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ230000000000000000000000
χ804-4-44−4i4i4i−4i00-2002-222i−2i−2i2i00000023−2302i3−2i3000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ230000000000000000000000
χ814-4-44−4i4i4i−4i00-2002-222i−2i−2i2i000000−23230−2i32i300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ230000000000000000000000
χ824-4-44−4i4i4i−4i00-2002-222i−2i−2i2i000000−23230−2i32i3000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ230000000000000000000000
χ838-88-88i−8i8i−8i00-400-444−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ848-88-8−8i8i−8i8i00-400-4444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000

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