Finite Group Databasebeta

← Group #10697105

Character table — Group #10697105

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344444444666121212124466888888881212121212121212121224242424242424242424242424242424246688121224242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ9222222222-2-2-2-2-2-2222-2-2-2-22-222000000002222-2-2-2-2-2-2000000000000000000002i−2i002i2i−2i−2i000000000000
χ10222222222-2-2-2-2-2-2222-2-2-2-22-222000000002222-2-2-2-2-2-200000000000000000000−2i2i00−2i−2i2i2i000000000000
χ112222222-2-222-2-2222222222-2-22200000000-2-2-2-2-2-222-2-20000000000000000000000000000000022-2-20000
χ122222222-2-222-2-2222222222-2-22200000000-2-2-2-2-2-222-2-200000000000000000000000000000000-2-2220000
χ132222222-2-2-2-222-2-2222-2-2-2-2-222200000000-2-2-2-222-2-2220000000000000000000000000000000000002-200
χ142222222-2-2-2-222-2-2222-2-2-2-2-222200000000-2-2-2-222-2-222000000000000000000000000000000000000-2200
χ15222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-1-1-2-2-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2112211-1-1-1-1000000000000
χ19222222-122-2-2-2-2-2-2-1-1-111112-2-1-100000000-1-1-1-111111133333333−3−3−3−3−3−3−3−300−i3i32i−2i−i3i3−i−iii000000000000
χ20222222-122-2-2-2-2-2-2-1-1-111112-2-1-100000000-1-1-1-111111133333333−3−3−3−3−3−3−3−300i3−i3−2i2ii3−i3ii−i−i000000000000
χ21222222-122-2-2-2-2-2-2-1-1-111112-2-1-100000000-1-1-1-1111111−3−3−3−3−3−3−3−33333333300−i3i3−2i2i−i3i3ii−i−i000000000000
χ22222222-122-2-2-2-2-2-2-1-1-111112-2-1-100000000-1-1-1-1111111−3−3−3−3−3−3−3−33333333300i3−i32i−2ii3−i3−i−iii000000000000
χ232222-2-222222-2-2-2-22222222-22-2-22222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ242222-2-222222-2-2-2-22222222-22-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ252222-2-2222-2-22222222-2-2-2-2-2-2-2-20000000022-2-22222-2-200000000000000002-22200-2-20000000000000000
χ262222-2-2222-2-22222222-2-2-2-2-2-2-2-20000000022-2-22222-2-20000000000000000-22-2-200220000000000000000
χ272222-2-22-2-22222-2-222222222-2-2-200000000-2-22222-2-2-2-2000000000000000000000000000022-2-200000000
χ282222-2-22-2-22222-2-222222222-2-2-200000000-2-22222-2-2-2-20000000000000000000000000000-2-22200000000
χ292222-2-22-2-2-2-2-2-222222-2-2-2-222-2-200000000-2-222-2-22222000000000000000000000000000000000000002-2
χ302222-2-22-2-2-2-2-2-222222-2-2-2-222-2-200000000-2-222-2-2222200000000000000000000000000000000000000-22
χ312222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-22112222-2-2-2-2-1-1111111-1-1-1-1-1-11111-1-1-1-1111100−i3i300i3−i3−i3i3−i3i3000000000000
χ322222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-22112222-2-2-2-2-1-1111111-1-1-1-1-1-11111-1-1-1-1111100i3−i300−i3i3i3−i3i3−i3000000000000
χ332222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-2211-2-2-2-22222-1-1111111-1-11111-1-1-1-11111-1-1-1-100−i3i300i3−i3i3−i3i3−i3000000000000
χ342222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-2211-2-2-2-22222-1-1111111-1-11111-1-1-1-11111-1-1-1-100i3−i300−i3i3−i3i3−i3i3000000000000
χ352222-2-2-122-2-22222-1-1-11111-2-21100000000-1-111-1-1-1-1113333−3−3−3−3−3−3−3−333332-2-1-100113−3−33000000000000
χ362222-2-2-122-2-22222-1-1-11111-2-21100000000-1-111-1-1-1-1113333−3−3−3−3−3−3−3−33333-221100-1-1−333−3000000000000
χ372222-2-2-122-2-22222-1-1-11111-2-21100000000-1-111-1-1-1-111−3−3−3−333333333−3−3−3−32-2-1-10011−333−3000000000000
χ382222-2-2-122-2-22222-1-1-11111-2-21100000000-1-111-1-1-1-111−3−3−3−333333333−3−3−3−3-221100-1-13−3−33000000000000
χ392-2-222-22002-2002-2-2-2222-2-2002-2−i2−i2i2i2−i2−i2i2i20000002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2002-20000
χ402-2-222-22002-2002-2-2-2222-2-2002-2−i2−i2i2i2−i2−i2i2i20000002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i200-220000
χ412-2-222-22002-2002-2-2-2222-2-2002-2i2i2−i2−i2i2i2−i2−i20000002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i200-220000
χ422-2-222-22002-2002-2-2-2222-2-2002-2i2i2−i2−i2i2i2−i2−i20000002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2002-20000
χ432-2-22-222002-200-22-2-2222-2-200-22−i2−i2i2i2i2i2−i2−i2000000-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i22-2000000
χ442-2-22-222002-200-22-2-2222-2-200-22−i2−i2i2i2i2i2−i2−i2000000-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2-22000000
χ452-2-22-222002-200-22-2-2222-2-200-22i2i2−i2−i2−i2−i2i2i2000000-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2-22000000
χ462-2-22-222002-200-22-2-2222-2-200-22i2i2−i2−i2−i2−i2i2i2000000-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i22-2000000
χ47444444-2-4-444-4-444-2-2-2-2-2-2-2-4-4-2-200000000222222-2-2220000000000000000000000000000000000000000
χ48444444-2-4-4-4-444-4-4-2-2-22222-44-2-2000000002222-2-222-2-20000000000000000000000000000000000000000
χ494444-4-4-2-4-44444-4-4-2-2-2-2-2-2-24-4220000000022-2-2-2-222220000000000000000000000000000000000000000
χ504444-4-4-2-4-4-4-4-4-444-2-2-2222244220000000022-2-222-2-2-2-20000000000000000000000000000000000000000
χ5144-4-40044-40000004-4-400000000000022−2222−224-400000000000022−2222−22000022−2222−22000000000000000000000000
χ5244-4-40044-40000004-4-4000000000000−2222−22224-4000000000000−2222−22220000−2222−2222000000000000000000000000
χ5344-4-4004-440000004-4-40000000022−2222−220000-440000000022−2222−22000022−2222−220000000000000000000000000000
χ5444-4-4004-440000004-4-400000000−2222−22220000-4400000000−2222−22220000−2222−22220000000000000000000000000000
χ5544-4-400-24-4000000-22223−2323−230000000022−2222−22-2200000023−2300002ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ2300002ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000
χ5644-4-400-24-4000000-22223−2323−2300000000−2222−2222-2200000023−230000−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ230000−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000
χ5744-4-400-24-4000000-222−2323−23230000000022−2222−22-22000000−232300002ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ700002ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000
χ5844-4-400-24-4000000-222−2323−232300000000−2222−2222-22000000−23230000−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ70000−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000
χ5944-4-400-2-44000000-22223−2323−23000022−2222−2200002-2000000−23232ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ700002ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000
χ6044-4-400-2-44000000-22223−2323−230000−2222−222200002-2000000−2323−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ70000−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000
χ6144-4-400-2-44000000-222−2323−2323000022−2222−2200002-200000023−232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ2300002ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000
χ6244-4-400-2-44000000-222−2323−23230000−2222−222200002-200000023−23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ230000−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000
χ634-44-400400004-400-44-4000000002i−2i−2i2i2i−2i−2i2i00004-400002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ644-44-400400004-400-44-400000000−2i2i2i−2i−2i2i2i−2i00004-40000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ654-44-40040000-4400-44-4000000002i−2i−2i2i−2i2i2i−2i0000-4400002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ664-44-40040000-4400-44-400000000−2i2i2i−2i2i−2i−2i2i0000-440000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ674-44-400-200004-4002-2223−23−232300002i−2i−2i2i2i−2i−2i2i0023−23-220000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ684-44-400-200004-4002-2223−23−23230000−2i2i2i−2i−2i2i2i−2i0023−23-220000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ694-44-400-200004-4002-22−232323−2300002i−2i−2i2i2i−2i−2i2i00−2323-220000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ704-44-400-200004-4002-22−232323−230000−2i2i2i−2i−2i2i2i−2i00−2323-220000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ714-44-400-20000-44002-2223−23−232300002i−2i−2i2i−2i2i2i−2i00−23232-20000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ724-44-400-20000-44002-2223−23−23230000−2i2i2i−2i2i−2i−2i2i00−23232-20000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ734-44-400-20000-44002-22−232323−2300002i−2i−2i2i−2i2i2i−2i0023−232-20000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ744-44-400-20000-44002-22−232323−230000−2i2i2i−2i2i−2i−2i2i0023−232-20000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ754-4-444-4400-4400-44-4-44-4-444004-400000000000000-44000000000000000000000000000000000000000000
χ764-4-444-4-2004-4004-422-2-2-22200-22−2i2−2i22i22i2−2i2−2i22i22i2000000-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ774-4-444-4-2004-4004-422-2-2-22200-222i22i2−2i2−2i22i22i2−2i2−2i2000000-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ784-4-444-4-200-4400-4422-222-2-200-22000000000000002-200i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6000000000000000000000000
χ794-4-444-4-200-4400-4422-222-2-200-22000000000000002-200−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6000000000000000000000000
χ804-4-44-44400-44004-4-4-44-4-44400-44000000000000004-4000000000000000000000000000000000000000000
χ814-4-44-44-2004-400-4422-2-2-222002-2−2i2−2i22i22i22i22i2−2i2−2i20000002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ824-4-44-44-2004-400-4422-2-2-222002-22i22i2−2i2−2i2−2i2−2i22i22i20000002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ834-4-44-44-200-44004-422-222-2-2002-200000000000000-2200i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ844-4-44-44-200-44004-422-222-2-2002-200000000000000-2200−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000

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