Finite Group Databasebeta

← Group #10696159

Character table — Group #10696159

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222222244448888888888888888888888888888888888888888242424242424242448484848
order12224444223446666666121212121212121244442244666688888888121212121212121224242424242424242424242424242424888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ92222222222222222222222222222-2-2-2-200000000000022-2-2-2-2-2-200002222-2-2-2-200000000000000000000
χ102222222222222222222222222222-2-2-2-2000000000000-2-222-2-2-2-20000-2-2-2-2222200000000000000000000
χ112222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ122222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ132222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211112222-2-2-2-2-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000000000
χ142222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-21111-2-2-2-22222-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000
χ152222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000−i3−i3i3i3000022-2-21111−i3−i3i3i3-1-1-1-11111−i3−i3−i3−i3i3i3i3i3000000000000
χ162222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000−i3−i3i3i30000-2-2221111−i3−i3i3i31111-1-1-1-1i3i3i3i3−i3−i3−i3−i3000000000000
χ172222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000i3i3−i3−i3000022-2-21111i3i3−i3−i3-1-1-1-11111i3i3i3i3−i3−i3−i3−i3000000000000
χ182222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000i3i3−i3−i30000-2-2221111i3i3−i3−i31111-1-1-1-1−i3−i3−i3−i3i3i3i3i3000000000000
χ1922222222-2-22-2-2-2-2-2-222222-2-2-2-2222-22-2000000000000000022-2-200000000000000000000000022-2-20000
χ2022222222-2-22-2-2-2-2-2-222222-2-2-2-2222-22-2000000000000000022-2-2000000000000000000000000-2-2220000
χ2122222222-2-22-2-2-2-2-2-222222-2-2-2-222-22-220000000000000000-2-2220000000000000000000022-2-200000000
χ2222222222-2-22-2-2-2-2-2-222222-2-2-2-222-22-220000000000000000-2-22200000000000000000000-2-22200000000
χ232222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-222-2-2000000002i2i−2i−2i00002-22-20000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ242222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-222-2-200000000−2i−2i2i2i00002-22-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ252222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2222200000000-22-22-2-2-2-20000000000000000000000000000
χ262222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-200000000-22-2222220000000000000000000000000000
χ272222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-20000−i3−i3i3i32i2i−2i−2i0000-11-11i3i3−i3−i333−3−333−3−3−i−iii−i−iii000000000000
χ282222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-20000−i3−i3i3i3−2i−2i2i2i0000-11-11i3i3−i3−i3−3−333−3−333ii−i−iii−i−i000000000000
χ292222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-20000i3i3−i3−i32i2i−2i−2i0000-11-11−i3−i3i3i3−3−333−3−333−i−iii−i−iii000000000000
χ302222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-20000i3i3−i3−i3−2i−2i2i2i0000-11-11−i3−i3i3i333−3−333−3−3ii−i−iii−i−i000000000000
χ312222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-1-1-1-1000000001-11-1111133−3−3−3−33333−3−3−3−333000000000000
χ322222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-1-1-1-1000000001-11-11111−3−33333−3−3−3−33333−3−3000000000000
χ332222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-222-2-2221111000000001-11-1-1-1-1-133−3−3−3−333−3−33333−3−3000000000000
χ342222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-222-2-2221111000000001-11-1-1-1-1-1−3−33333−3−333−3−3−3−333000000000000
χ352222-2-2-2-2-2-2222-2-2-2-2222-2-22222-2-22-2-2200000000000000002-2-220000000000000000000000000000200-2
χ362222-2-2-2-2-2-2222-2-2-2-2222-2-22222-2-22-2-2200000000000000002-2-220000000000000000000000000000-2002
χ372222-2-2-2-2-2-2222-2-2-2-2222-2-22222-2-2-222-20000000000000000-222-2000000000000000000000000000002-20
χ382222-2-2-2-2-2-2222-2-2-2-2222-2-22222-2-2-222-20000000000000000-222-200000000000000000000000000000-220
χ392-2-2222-2-22-222-222-2-2-2-222222-2-2-2-20000000000000000002i−2i0000000000002i−2i2i−2i000000002−22−2−i2i2−i2i20000
χ402-2-2222-2-22-222-222-2-2-2-222222-2-2-2-20000000000000000002i−2i0000000000002i−2i2i−2i00000000−22−22i2−i2i2−i20000
χ412-2-2222-2-22-222-222-2-2-2-222222-2-2-2-2000000000000000000−2i2i000000000000−2i2i−2i2i000000002−22−2i2−i2i2−i20000
χ422-2-2222-2-22-222-222-2-2-2-222222-2-2-2-2000000000000000000−2i2i000000000000−2i2i−2i2i00000000−22−22−i2i2−i2i20000
χ432-2-2222-2-2-222-22-2-222-2-2222-2-222-2-200000000000000002i−2i00000000002i−2i2i−2i0000000000002−2−22−i2i2i2−i20000
χ442-2-2222-2-2-222-22-2-222-2-2222-2-222-2-200000000000000002i−2i00000000002i−2i2i−2i000000000000−222−2i2−i2−i2i20000
χ452-2-2222-2-2-222-22-2-222-2-2222-2-222-2-20000000000000000−2i2i0000000000−2i2i−2i2i0000000000002−2−22i2−i2−i2i20000
χ462-2-2222-2-2-222-22-2-222-2-2222-2-222-2-20000000000000000−2i2i0000000000−2i2i−2i2i000000000000−222−2−i2i2i2−i20000
χ4744444444-4-4-2-4-42222-2-2-2-2-22222-2-24-44-40000000000000000-2-22200000000000000000000000000000000
χ4844444444-4-4-2-4-42222-2-2-2-2-22222-2-2-44-44000000000000000022-2-200000000000000000000000000000000
χ494444-4-4-4-4-4-4-2442222-2-2-222-2-2-2-2224-4-440000000000000000-222-200000000000000000000000000000000
χ504444-4-4-4-4-4-4-2442222-2-2-222-2-2-2-222-444-400000000000000002-2-2200000000000000000000000000000000
χ5144-4-44i−4i4i−4i0040000004-4-44i−4i00004i−4i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ5244-4-44i−4i4i−4i0040000004-4-44i−4i00004i−4i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ5344-4-44i−4i4i−4i00-200−2i32i3−2i32i3-222−2i2i23−2323−23−2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−2ζ232ζ232ζ5−2ζ5−2ζ72ζ72ζ13−2ζ13000000000000
χ5444-4-44i−4i4i−4i00-200−2i32i3−2i32i3-222−2i2i23−2323−23−2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000002ζ23−2ζ23−2ζ52ζ52ζ7−2ζ7−2ζ132ζ13000000000000
χ5544-4-44i−4i4i−4i00-2002i3−2i32i3−2i3-222−2i2i−2323−2323−2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−2ζ72ζ72ζ13−2ζ13−2ζ232ζ232ζ5−2ζ5000000000000
χ5644-4-44i−4i4i−4i00-2002i3−2i32i3−2i3-222−2i2i−2323−2323−2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000002ζ7−2ζ7−2ζ132ζ132ζ23−2ζ23−2ζ52ζ5000000000000
χ5744-4-4−4i4i−4i4i0040000004-4-4−4i4i0000−4i4i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ5844-4-4−4i4i−4i4i0040000004-4-4−4i4i0000−4i4i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ5944-4-4−4i4i−4i4i00-200−2i32i3−2i32i3-2222i−2i−2323−23232i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000002ζ5−2ζ5−2ζ232ζ232ζ13−2ζ13−2ζ72ζ7000000000000
χ6044-4-4−4i4i−4i4i00-200−2i32i3−2i32i3-2222i−2i−2323−23232i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−2ζ52ζ52ζ23−2ζ23−2ζ132ζ132ζ7−2ζ7000000000000
χ6144-4-4−4i4i−4i4i00-2002i3−2i32i3−2i3-2222i−2i23−2323−232i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000002ζ13−2ζ13−2ζ72ζ72ζ5−2ζ5−2ζ232ζ23000000000000
χ6244-4-4−4i4i−4i4i00-2002i3−2i32i3−2i3-2222i−2i23−2323−232i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−2ζ132ζ132ζ7−2ζ7−2ζ52ζ52ζ23−2ζ23000000000000
χ634-44-44i−4i−4i4i004000000-44-44i−4i0000−4i4i00002-22i−2i2-22-20000000000002i−2i2i−2i0000000000000000000000000000
χ644-44-44i−4i−4i4i004000000-44-44i−4i0000−4i4i0000-22−2i2i-22-22000000000000−2i2i−2i2i0000000000000000000000000000
χ654-44-44i−4i−4i4i00-200−2i32i32i3−2i32-22−2i2i23−23−23232i−2i00002-22i−2i−1−i31+i3−1+i31−i30000000000002ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ664-44-44i−4i−4i4i00-200−2i32i32i3−2i32-22−2i2i23−23−23232i−2i0000-22−2i2i1+i3−1−i31−i3−1+i3000000000000−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ674-44-44i−4i−4i4i00-2002i3−2i3−2i32i32-22−2i2i−232323−232i−2i00002-22i−2i−1+i31−i3−1−i31+i30000000000002ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ684-44-44i−4i−4i4i00-2002i3−2i3−2i32i32-22−2i2i−232323−232i−2i0000-22−2i2i1−i3−1+i31+i3−1−i3000000000000−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ694-44-4−4i4i4i−4i004000000-44-4−4i4i00004i−4i00002-2−2i2i2-22-2000000000000−2i2i−2i2i0000000000000000000000000000
χ704-44-4−4i4i4i−4i004000000-44-4−4i4i00004i−4i0000-222i−2i-22-220000000000002i−2i2i−2i0000000000000000000000000000
χ714-44-4−4i4i4i−4i00-200−2i32i32i3−2i32-222i−2i−232323−23−2i2i00002-2−2i2i−1−i31+i3−1+i31−i3000000000000−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ724-44-4−4i4i4i−4i00-200−2i32i32i3−2i32-222i−2i−232323−23−2i2i0000-222i−2i1+i3−1−i31−i3−1+i30000000000002ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ734-44-4−4i4i4i−4i00-2002i3−2i3−2i32i32-222i−2i23−23−2323−2i2i00002-2−2i2i−1+i31−i3−1−i31+i3000000000000−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ744-44-4−4i4i4i−4i00-2002i3−2i3−2i32i32-222i−2i23−23−2323−2i2i0000-222i−2i1−i3−1+i31+i3−1−i30000000000002ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ754-4-4444-4-44-4-24-4-2-22222-2-2-2-2-222220000000000000000004i−4i000000000000−2i2i−2i2i00000000000000000000
χ764-4-4444-4-44-4-24-4-2-22222-2-2-2-2-22222000000000000000000−4i4i0000000000002i−2i2i−2i00000000000000000000
χ774-4-4444-4-4-44-2-4422-2-222-2-2-222-2-22200000000000000004i−4i0000000000−2i2i−2i2i000000000000000000000000
χ784-4-4444-4-4-44-2-4422-2-222-2-2-222-2-2220000000000000000−4i4i00000000002i−2i2i−2i000000000000000000000000
χ794-4-44-4-4444-44-4444-4-4-4-44-4-4-4-4444400000000000000000000000000000000000000000000000000000000
χ804-4-44-4-4444-4-2-44-2-22222-22222-2-2-2-200000000000000000000000000000000−2i32i32i3−2i300000000000000000000
χ814-4-44-4-4444-4-2-44-2-22222-22222-2-2-2-2000000000000000000000000000000002i3−2i3−2i32i300000000000000000000
χ824-4-44-4-444-4444-4-4-444-4-44-4-444-4-44400000000000000000000000000000000000000000000000000000000
χ834-4-44-4-444-44-24-422-2-222-222-2-222-2-20000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ844-4-44-4-444-44-24-422-2-222-222-2-222-2-200000000000000000000000000002i3−2i3−2i32i3000000000000000000000000

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