Finite Group Databasebeta

← Group #10686708

Character table — Group #10686708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order122222344444444666224444666666121212121212121212121212224444444466661212121212121212121212121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111
χ8111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ91111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-11-1-111111111-1-111-1-1-1-111-1-1-1-1iiii−i−i−i−iii−i−ii−ii−i
χ101111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-11-1-111111111-1-111-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−iii−ii−ii
χ111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-1-1-11111-1-1-1-11111-1-11111iiii−i−i−i−iii−i−i−ii−ii
χ121111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-1-1-11111-1-1-1-11111-1-11111−i−i−i−iiiii−i−iiii−ii−i
χ131111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-11111-1-111-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−iiii−i−ii
χ141111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-11111-1-111-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i−iii−i
χ151111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1111-1-1-1-11111-1-111-1-1111111-1-1-1-1iiii−i−i−i−i−i−iii−iii−i
χ161111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1111-1-1-1-11111-1-111-1-1111111-1-1-1-1−i−i−i−iiiiiii−i−ii−i−ii
χ1722222222222-2-2-2-222222-2-2222222222222-2-2-2-2222200-2-20000000000-2-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-200220000000000-2-222220000000000000000000000000000
χ192222222-2-2-2-2222222222-2-2-2-2222222-2-2-2-22222-2-2-2-200-220000000000-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-222222222002-20000000000-2-222-2-20000000000000000000000000000
χ21222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-21111-1-1-1-1-1-11111111111110000000000000000
χ23222222-122222222-1-1-1-2-222-2-2-1-11111-1-1-1-1-1-1-1-111112-2-2-2222-2-2-2-1-111-1-11111-1-1-1-1-1-11111110000000000000000
χ24222222-122222222-1-1-1-2-222-2-2-1-11111-1-1-1-1-1-1-1-11111-22-2-2-2-2-222211-1-1-1-11111111111-1-1-1-1-1-10000000000000000
χ25222222-12222-2-2-2-2-1-1-122-2-222-1-1-1-1-1-1-1-1-1-11111-1-1-1-100-2-2000000−i3i3−i3i3111111−i3i3−i3−i3i3i3−i3i3−i3−i3i3i30000000000000000
χ26222222-12222-2-2-2-2-1-1-122-2-222-1-1-1-1-1-1-1-1-1-11111-1-1-1-100-2-2000000i3−i3i3−i3111111i3−i3i3i3−i3−i3i3−i3i3i3−i3−i30000000000000000
χ27222222-12222-2-2-2-2-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-1111111110022000000−i3i3i3−i311-1-1-1-1−i3i3−i3−i3i3i3i3−i3i3i3−i3−i30000000000000000
χ28222222-12222-2-2-2-2-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-1111111110022000000i3−i3−i3i311-1-1-1-1i3−i3i3i3−i3−i3−i3i3−i3−i3i3i30000000000000000
χ29222222-1-2-2-2-22222-1-1-122-2-2-2-2-1-1-1-1-1-11111-1-1-1-1111100-22000000−i3i3−i3i31111-1-1−i3i3i3i3−i3−i3−i3i3i3i3−i3−i30000000000000000
χ30222222-1-2-2-2-22222-1-1-122-2-2-2-2-1-1-1-1-1-11111-1-1-1-1111100-22000000i3−i3i3−i31111-1-1i3−i3−i3−i3i3i3i3−i3−i3−i3i3i30000000000000000
χ31222222-1-2-2-2-22222-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-1002-2000000−i3i3i3−i311-1-111−i3i3i3i3−i3−i3i3−i3−i3−i3i3i30000000000000000
χ32222222-1-2-2-2-22222-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-1002-2000000i3−i3−i3i311-1-111i3−i3−i3−i3i3i3−i3i3i3i3−i3−i30000000000000000
χ33222222-1-2-2-2-2-2-2-2-2-1-1-12222-2-2-1-1-1-1-1-1111111111111222-22-2-22-2-2-1-1-1-1-1-1-1-111-1-11111-1-111110000000000000000
χ34222222-1-2-2-2-2-2-2-2-2-1-1-12222-2-2-1-1-1-1-1-1111111111111-2-22-2-222-2221111-1-1-1-11111-1-1-1-111-1-1-1-10000000000000000
χ35222222-1-2-2-2-2-2-2-2-2-1-1-1-2-22222-1-1111111111111-1-1-1-12-2-222-2-2-222-1-111-1-111-1-1-1-1111111-1-1-1-10000000000000000
χ36222222-1-2-2-2-2-2-2-2-2-1-1-1-2-22222-1-1111111111111-1-1-1-1-22-22-2222-2-211-1-1-1-111-1-111-1-1-1-1-1-111110000000000000000
χ372222-2-2222-2-222-2-2222002-200-2-2000022-2-222-2-200000200000-22-200222-20000000000-2-22-22-20000000000000000
χ382222-2-2222-2-222-2-2222002-200-2-2000022-2-222-2-200000-2000002-2200-2-22-2000000000022-22-220000000000000000
χ392222-2-2222-2-2-2-22222200-2200-2-2000022-2-2-2-22200002000-22-20002200-220000-2-22-22-20000000000000000000000
χ402222-2-2222-2-2-2-22222200-2200-2-2000022-2-2-2-2220000-20002-22000-2-200-22000022-22-220000000000000000000000
χ412222-2-22-2-22222-2-222200-2200-2-20000-2-22222-2-200002000-2-220002200-220000-2-2-22-220000000000000000000000
χ422222-2-22-2-22222-2-222200-2200-2-20000-2-22222-2-20000-200022-2000-2-200-220000222-22-20000000000000000000000
χ432222-2-22-2-222-2-222222002-200-2-20000-2-222-2-22200000200000-2-2200222-20000000000-2-2-22-220000000000000000
χ442222-2-22-2-222-2-222222002-200-2-20000-2-222-2-22200000-20000022-200-2-22-20000000000222-22-20000000000000000
χ452222-2-2-122-2-222-2-2-1-1-1002-20011−i3−i3i3i3-1-111-1-111−i3−i3i3i30200000-22-2−i3i3-1-1-11−i3i3−i3i3i3−i3−i3i3i3−i311-11-110000000000000000
χ462222-2-2-122-2-222-2-2-1-1-1002-20011−i3−i3i3i3-1-111-1-111−i3−i3i3i30-2000002-22i3−i311-11−i3i3−i3i3−i3i3i3−i3−i3i3-1-11-11-10000000000000000
χ472222-2-2-122-2-222-2-2-1-1-1002-20011i3i3−i3−i3-1-111-1-111i3i3−i3−i30200000-22-2i3−i3-1-1-11i3−i3i3−i3−i3i3i3−i3−i3i311-11-110000000000000000
χ482222-2-2-122-2-222-2-2-1-1-1002-20011i3i3−i3−i3-1-111-1-111i3i3−i3−i30-2000002-22−i3i311-11i3−i3i3−i3i3−i3−i3i3i3−i3-1-11-11-10000000000000000
χ492222-2-2-122-2-2-2-222-1-1-100-220011−i3−i3i3i3-1-11111-1-1−i3−i3i3i32000-22-2000-1-1−i3i31-1i3−i3i3−i311-11-11i3−i3−i3i3i3−i30000000000000000
χ502222-2-2-122-2-2-2-222-1-1-100-220011−i3−i3i3i3-1-11111-1-1−i3−i3i3i3-20002-2200011i3−i31-1i3−i3i3−i3-1-11-11-1−i3i3i3−i3−i3i30000000000000000
χ512222-2-2-122-2-2-2-222-1-1-100-220011i3i3−i3−i3-1-11111-1-1i3i3−i3−i32000-22-2000-1-1i3−i31-1−i3i3−i3i311-11-11−i3i3i3−i3−i3i30000000000000000
χ522222-2-2-122-2-2-2-222-1-1-100-220011i3i3−i3−i3-1-11111-1-1i3i3−i3−i3-20002-2200011−i3i31-1−i3i3−i3i3-1-11-11-1i3−i3−i3i3i3−i30000000000000000
χ532222-2-2-1-2-22222-2-2-1-1-100-220011−i3−i3i3i311-1-1-1-111i3i3−i3−i32000-2-22000-1-1−i3i31-1i3−i3−i3i3111-11-1i3−i3i3−i3−i3i30000000000000000
χ542222-2-2-1-2-22222-2-2-1-1-100-220011−i3−i3i3i311-1-1-1-111i3i3−i3−i3-200022-200011i3−i31-1i3−i3−i3i3-1-1-11-11−i3i3−i3i3i3−i30000000000000000
χ552222-2-2-1-2-22222-2-2-1-1-100-220011i3i3−i3−i311-1-1-1-111−i3−i3i3i32000-2-22000-1-1i3−i31-1−i3i3i3−i3111-11-1−i3i3−i3i3i3−i30000000000000000
χ562222-2-2-1-2-22222-2-2-1-1-100-220011i3i3−i3−i311-1-1-1-111−i3−i3i3i3-200022-200011−i3i31-1−i3i3i3−i3-1-1-11-11i3−i3i3−i3−i3i30000000000000000
χ572222-2-2-1-2-222-2-222-1-1-1002-20011−i3−i3i3i311-1-111-1-1i3i3−i3−i30200000-2-22−i3i3-1-1-11−i3i3i3−i3i3−i3i3−i3−i3i3111-11-10000000000000000
χ582222-2-2-1-2-222-2-222-1-1-1002-20011−i3−i3i3i311-1-111-1-1i3i3−i3−i30-20000022-2i3−i311-11−i3i3i3−i3−i3i3−i3i3i3−i3-1-1-11-110000000000000000
χ592222-2-2-1-2-222-2-222-1-1-1002-20011i3i3−i3−i311-1-111-1-1−i3−i3i3i30200000-2-22i3−i3-1-1-11i3−i3−i3i3−i3i3−i3i3i3−i3111-11-10000000000000000
χ602222-2-2-1-2-222-2-222-1-1-1002-20011i3i3−i3−i311-1-111-1-1−i3−i3i3i30-20000022-2−i3i311-11i3−i3−i3i3i3−i3i3−i3−i3i3-1-1-11-110000000000000000
χ6122-2-22-222i−2i2i−2i00002-2-22-2002i−2i2-22-22-22i−2i2i−2i00002i−2i2i−2i000000000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1−i−1+i0000
χ6222-2-22-222i−2i2i−2i00002-2-22-2002i−2i2-22-22-22i−2i2i−2i00002i−2i2i−2i00000000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1+i1−i0000
χ6322-2-22-222i−2i2i−2i00002-2-2-2200−2i2i2-2-22-222i−2i2i−2i0000−2i2i−2i2i000000000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1+i1−i0000
χ6422-2-22-222i−2i2i−2i00002-2-2-2200−2i2i2-2-22-222i−2i2i−2i0000−2i2i−2i2i00000000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1−i−1+i0000
χ6522-2-22-22−2i2i−2i2i00002-2-22-200−2i2i2-22-22-2−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1+i−1−i0000
χ6622-2-22-22−2i2i−2i2i00002-2-22-200−2i2i2-22-22-2−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1−i1+i0000
χ6722-2-22-22−2i2i−2i2i00002-2-2-22002i−2i2-2-22-22−2i2i−2i2i00002i−2i2i−2i000000000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1−i1+i0000
χ6822-2-22-22−2i2i−2i2i00002-2-2-22002i−2i2-2-22-22−2i2i−2i2i00002i−2i2i−2i00000000000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1+i−1−i0000
χ6944-4-44-4-24i−4i4i−4i0000-2224-4004i−4i-22-22-22−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7044-4-44-4-24i−4i4i−4i0000-222-4400−4i4i-222-22-2−2i2i−2i2i00002i−2i2i−2i000000000000000000000000000000000000000000000000
χ7144-4-44-4-2−4i4i−4i4i0000-2224-400−4i4i-22-22-222i−2i2i−2i00002i−2i2i−2i000000000000000000000000000000000000000000000000
χ7244-4-44-4-2−4i4i−4i4i0000-222-44004i−4i-222-22-22i−2i2i−2i0000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ7344-4-4-4444i−4i−4i4i00004-4-4000000-4400004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ7444-4-4-444−4i4i4i−4i00004-4-4000000-440000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-24i−4i−4i4i0000-2220000002-2−2i32i32i3−2i3−2i2i2i−2i000023−23−2323000000000000000000000000000000000000000000000000
χ7644-4-4-44-24i−4i−4i4i0000-2220000002-22i3−2i3−2i32i3−2i2i2i−2i0000−232323−23000000000000000000000000000000000000000000000000
χ7744-4-4-44-2−4i4i4i−4i0000-2220000002-2−2i32i32i3−2i32i−2i−2i2i0000−232323−23000000000000000000000000000000000000000000000000
χ7844-4-4-44-2−4i4i4i−4i0000-2220000002-22i3−2i3−2i32i32i−2i−2i2i000023−23−2323000000000000000000000000000000000000000000000000
χ794-44-40040000004i−4i-44-40000000000000000004i−4i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000
χ804-44-40040000004i−4i-44-40000000000000000004i−4i000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000
χ814-44-4004000000−4i4i-44-4000000000000000000−4i4i000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000
χ824-44-4004000000−4i4i-44-4000000000000000000−4i4i0000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000
χ834-4-4400400004i−4i00-4-4400000000000000004i−4i000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000
χ844-4-4400400004i−4i00-4-4400000000000000004i−4i00000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000
χ854-4-440040000−4i4i00-4-440000000000000000−4i4i00000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000
χ864-4-440040000−4i4i00-4-440000000000000000−4i4i000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000
χ878-88-800-40000008i−8i4-44000000000000000000−4i4i0000000000000000000000000000000000000000000000000000
χ888-88-800-4000000−8i8i4-440000000000000000004i−4i0000000000000000000000000000000000000000000000000000
χ898-8-8800-400008i−8i0044-40000000000000000−4i4i000000000000000000000000000000000000000000000000000000
χ908-8-8800-40000−8i8i0044-400000000000000004i−4i000000000000000000000000000000000000000000000000000000

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