Finite Group Databasebeta

← Group #10697821

Character table — Group #10697821

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344444444666121212124444444444661212121212121212121212121212121212121212121212121212246688121224242424888888882244
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ922222222222-2-2-2-22222222-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222-2-2-2-22222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ112222222-2-2-2-222-2-2222-2-2-2-22-200000000222222-2-2-2-2-2-20000000000000000000000000000000000002-200
χ122222222-2-2-2-222-2-2222-2-2-2-22-200000000222222-2-2-2-2-2-2000000000000000000000000000000000000-2200
χ132222222-2-2-2-2-2-222222-2-2-2-2-220000000022-2-2-2-22222-2-2000000000000000000000000000000000000002-2
χ142222222-2-2-2-2-2-222222-2-2-2-2-220000000022-2-2-2-22222-2-200000000000000000000000000000000000000-22
χ15222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-1-1-2-2-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2112211-1-1-1-1000000000000
χ19222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111100−i3i300−i3i3−i3−i3i3i3000000000000
χ20222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111100i3−i300i3−i3i3i3−i3−i3000000000000
χ21222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100−i3i300−i3i3i3i3−i3−i3000000000000
χ22222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100i3−i300i3−i3−i3−i3i3i3000000000000
χ232222-2-2222-2-22222222-2-2-2-2-2-200000000-2-222-2-222-2-22200000000000000002-22200-2-20000000000000000
χ242222-2-2222-2-22222222-2-2-2-2-2-200000000-2-222-2-222-2-2220000000000000000-22-2-200220000000000000000
χ252222-2-2222-2-2-2-2-2-2222-2-2-2-22200000000-2-2-2-222-2-22222000000000000000000002i−2i002i−2i2i−2i000000000000
χ262222-2-2222-2-2-2-2-2-2222-2-2-2-22200000000-2-2-2-222-2-2222200000000000000000000−2i2i00−2i2i−2i2i000000000000
χ272222-2-22-2-22222-2-22222222-2200000000-2-222-2-2-2-222-2-2000000000000000000000000000022-2-200000000
χ282222-2-22-2-22222-2-22222222-2200000000-2-222-2-2-2-222-2-20000000000000000000000000000-2-22200000000
χ292222-2-22-2-222-2-22222222222-200000000-2-2-2-22222-2-2-2-20000000000000000000000000000000022-2-20000
χ302222-2-22-2-222-2-22222222222-200000000-2-2-2-22222-2-2-2-200000000000000000000000000000000-2-2220000
χ312222-2-2-122-2-22222-1-1-11111-2-20000000011-1-111-1-111-1-13333−3−3−3−33333−3−3−3−32-2-1-100113−3−33000000000000
χ322222-2-2-122-2-22222-1-1-11111-2-20000000011-1-111-1-111-1-13333−3−3−3−33333−3−3−3−3-221100-1-1−333−3000000000000
χ332222-2-2-122-2-22222-1-1-11111-2-20000000011-1-111-1-111-1-1−3−3−3−33333−3−3−3−333332-2-1-10011−333−3000000000000
χ342222-2-2-122-2-22222-1-1-11111-2-20000000011-1-111-1-111-1-1−3−3−3−33333−3−3−3−33333-221100-1-13−3−33000000000000
χ352222-2-2-122-2-2-2-2-2-2-1-1-1111122000000001111-1-111-1-1-1-13333−3−3−3−3−3−3−3−3333300−i3i32i−2ii3−i3−ii−ii000000000000
χ362222-2-2-122-2-2-2-2-2-2-1-1-1111122000000001111-1-111-1-1-1-13333−3−3−3−3−3−3−3−3333300i3−i3−2i2i−i3i3i−ii−i000000000000
χ372222-2-2-122-2-2-2-2-2-2-1-1-1111122000000001111-1-111-1-1-1-1−3−3−3−333333333−3−3−3−300−i3i3−2i2ii3−i3i−ii−i000000000000
χ382222-2-2-122-2-2-2-2-2-2-1-1-1111122000000001111-1-111-1-1-1-1−3−3−3−333333333−3−3−3−300i3−i32i−2i−i3i3−ii−ii000000000000
χ392-22-22-222-22-20000-2-2222-2-20000002i2i−2i−2i2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i0000000000002−22−2−i2i2−i2i20000
χ402-22-22-222-22-20000-2-2222-2-20000002i2i−2i−2i2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i000000000000−22−22i2−i2i2−i20000
χ412-22-22-222-22-20000-2-2222-2-2000000−2i−2i2i2i2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i0000000000002−22−2i2−i2i2−i20000
χ422-22-22-222-22-20000-2-2222-2-2000000−2i−2i2i2i2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i000000000000−22−22−i2i2−i2i20000
χ432-22-2-222-222-20000-2-2222-2-2002i2i−2i−2i0000-2200000000-222i2i−2i−2i2i2i−2i−2i000000000000000000002−2−22−i2i2i2−i20000
χ442-22-2-222-222-20000-2-2222-2-2002i2i−2i−2i0000-2200000000-222i2i−2i−2i2i2i−2i−2i00000000000000000000−222−2i2−i2−i2i20000
χ452-22-2-222-222-20000-2-2222-2-200−2i−2i2i2i0000-2200000000-22−2i−2i2i2i−2i−2i2i2i000000000000000000002−2−22i2−i2−i2i20000
χ462-22-2-222-222-20000-2-2222-2-200−2i−2i2i2i0000-2200000000-22−2i−2i2i2i−2i−2i2i2i00000000000000000000−222−2−i2i2i2−i20000
χ47444444-2-4-4-4-444-4-4-2-2-222224-400000000-2-2-2-2-2-22222220000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-444-2-2-22222-4400000000-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ494444-4-4-2-4-44444-4-4-2-2-2-2-2-2-2-440000000022-2-22222-2-2220000000000000000000000000000000000000000
χ504444-4-4-2-4-444-4-444-2-2-2-2-2-2-24-4000000002222-2-2-2-222220000000000000000000000000000000000000000
χ5144-4-400400004-4004-4-40000002i−2i2i−2i2i−2i2i−2i004-4000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5244-4-400400004-4004-4-4000000−2i2i−2i2i−2i2i−2i2i004-400000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5344-4-40040000-44004-4-40000002i−2i2i−2i−2i2i−2i2i00-44000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5444-4-40040000-44004-4-4000000−2i2i−2i2i2i−2i2i−2i00-4400000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5544-4-400-200004-400-22223−2323−23002i−2i2i−2i2i−2i2i−2i00-22000023−2300−ζ4+ζ14+ζ20+ζ22ζ4−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−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ5644-4-400-200004-400-22223−2323−2300−2i2i−2i2i−2i2i−2i2i00-22000023−2300ζ4−ζ14−ζ20−ζ22−ζ4+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+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ5744-4-400-200004-400-222−2323−2323002i−2i2i−2i2i−2i2i−2i00-220000−232300ζ4+ζ14−ζ20+ζ22−ζ4−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−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ5844-4-400-200004-400-222−2323−232300−2i2i−2i2i−2i2i−2i2i00-220000−232300−ζ4−ζ14+ζ20−ζ22ζ4+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+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ5944-4-400-20000-4400-22223−2323−23002i−2i2i−2i−2i2i−2i2i002-20000−232300−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ6044-4-400-20000-4400-22223−2323−2300−2i2i−2i2i2i−2i2i−2i002-20000−232300ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ6144-4-400-20000-4400-222−2323−2323002i−2i2i−2i−2i2i−2i2i002-2000023−2300ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ6244-4-400-20000-4400-222−2323−232300−2i2i−2i2i2i−2i2i−2i002-2000023−2300−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ634-44-44-44-44-440000-4-44-4-44400000000004-400000000-440000000000000000000000000000000000000000
χ644-44-44-4-24-44-4000022-2-2-2220000004i4i−4i−4i-2200000000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ654-44-44-4-24-44-4000022-2-2-222000000−4i−4i4i4i-2200000000-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ664-44-44-4-2-44-44000022-222-2-20000000000-22000000002-2−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000
χ674-44-44-4-2-44-44000022-222-2-20000000000-22000000002-22i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000
χ684-44-4-4444-4-440000-4-44-4-4440000000000-44000000004-40000000000000000000000000000000000000000
χ694-44-4-44-24-4-44000022-222-2-200000000002-200000000-2200000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000
χ704-44-4-44-24-4-44000022-222-2-200000000002-200000000-22000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000
χ714-44-4-44-2-444-4000022-2-2-222004i4i−4i−4i00002-2000000002-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ724-44-4-44-2-444-4000022-2-2-22200−4i−4i4i4i00002-2000000002-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ734-4-440040000004-4-44-40000002-2-222-2-220000004-400002-2-222-2-222-2-222-2-22000000000000000000000000
χ744-4-440040000004-4-44-4000000-222-2-222-20000004-40000-222-2-222-2-222-2-222-2000000000000000000000000
χ754-4-44004000000-44-44-40000002-2-22-222-2000000-4400002-2-222-2-22-222-2-222-2000000000000000000000000
χ764-4-44004000000-44-44-4000000-222-22-2-22000000-440000-222-2-222-22-2-222-2-22000000000000000000000000
χ774-4-4400-20000004-42-2223−23−2323002-2-222-2-22000023−23-220000−1−31+31+3−1−3−1+31−31−3−1+3−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000
χ784-4-4400-20000004-42-2223−23−232300-222-2-222-2000023−23-2200001+3−1−3−1−31+31−3−1+3−1+31−31+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000
χ794-4-4400-20000004-42-22−232323−23002-2-222-2-220000−2323-220000−1+31−31−3−1+3−1−31+31+3−1−3−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000
χ804-4-4400-20000004-42-22−232323−2300-222-2-222-20000−2323-2200001−3−1+3−1+31−31+3−1−3−1−31+31−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000
χ814-4-4400-2000000-442-2223−23−2323002-2-22-222-20000−23232-20000−1−31+31+3−1−3−1+31−31−3−1+31+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000
χ824-4-4400-2000000-442-2223−23−232300-222-22-2-220000−23232-200001+3−1−3−1−31+31−3−1+3−1+31−3−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000
χ834-4-4400-2000000-442-22−232323−23002-2-22-222-2000023−232-20000−1+31−31−3−1+3−1−31+31+3−1−31−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000
χ844-4-4400-2000000-442-22−232323−2300-222-22-2-22000023−232-200001−3−1+3−1+31−31+3−1−3−1−31+3−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000

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