Finite Group Databasebeta

← Group #10695467

Character table — Group #10695467

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222222244448888888888888888888888888888888888888888242424242424242448484848
order122222222222366666666666666644442244444444446666121212121212121212121212121212121212121212121212888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ92222222222222222222222222222-2-2-2-2220000-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222222222222222-2-2-2-2-2-20000220000-2-2-2-2-2-2-2-222220000000000000000000000000000
χ11222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ12222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000
χ13222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-22222-2-2-2-2-2-21111-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000000000
χ14222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-222221111-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000
χ15222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2220000-2-20000-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ16222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2220000-2-20000-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ17222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2000022000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3000000000000
χ18222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2000022000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3000000000000
χ1922222222-2-2-2-222222-2-2-2-2-2-222-2-222-22-2000000000000000022-2-200000000000000000000000000002-200
χ2022222222-2-2-2-222222-2-2-2-2-2-222-2-222-22-2000000000000000022-2-20000000000000000000000000000-2200
χ2122222222-2-2-2-222222-2-2-2-2-2-222-2-22-22-220000000000000000-2-2220000000000000000000000000000002-2
χ2222222222-2-2-2-222222-2-2-2-2-2-222-2-22-22-220000000000000000-2-222000000000000000000000000000000-22
χ232222-2-2-2-22-2-22222-2-222-2-2-2-2-2-222200002-2000000000022-2-2000000000000000000000000−i2−i2i2i2−i2−i2i2i20000
χ242222-2-2-2-22-2-22222-2-222-2-2-2-2-2-222200002-2000000000022-2-2000000000000000000000000i2i2−i2−i2i2i2−i2−i20000
χ252222-2-2-2-22-2-22222-2-222-2-2-2-2-2-22220000-220000000000-2-222000000000000000000000000−i2−i2i2i2i2i2−i2−i20000
χ262222-2-2-2-22-2-22222-2-222-2-2-2-2-2-22220000-220000000000-2-222000000000000000000000000i2i2−i2−i2−i2−i2i2i20000
χ272-2-2222-2-222-2-22-2-2222222-2-2-2-2-2-2200000000002i−2i0000000000002i2i−2i−2i00000000000000002−22−2−i2i2−i2i20000
χ282-2-2222-2-222-2-22-2-2222222-2-2-2-2-2-2200000000002i−2i0000000000002i2i−2i−2i0000000000000000−22−22i2−i2i2−i20000
χ292-2-2222-2-222-2-22-2-2222222-2-2-2-2-2-220000000000−2i2i000000000000−2i−2i2i2i00000000000000002−22−2i2−i2i2−i20000
χ302-2-2222-2-222-2-22-2-2222222-2-2-2-2-2-220000000000−2i2i000000000000−2i−2i2i2i0000000000000000−22−22−i2i2−i2i20000
χ312-2-22-2-2222-22-22-2-2-2-222-2-22222-2-2222-2-200000000000000002-22-2000000000000000000002i−2i−2i2i00000000
χ322-2-22-2-2222-22-22-2-2-2-222-2-22222-2-2222-2-200000000000000002-22-200000000000000000000−2i2i2i−2i00000000
χ332-2-22-2-2222-22-22-2-2-2-222-2-22222-2-22-2-2220000000000000000-22-220000000000000000000000002-2-220000
χ342-2-22-2-2222-22-22-2-2-2-222-2-22222-2-22-2-2220000000000000000-22-22000000000000000000000000-222-20000
χ352-2-22-2-222-22-222-2-2-2-2-2-222-2-2222222-2-220022-2-200000000002-2-2200000000000022-2-222-2-2000000000000
χ362-2-22-2-222-22-222-2-2-2-2-2-222-2-2222222-2-2200-2-22200000000002-2-22000000000000-2-222-2-222000000000000
χ372-2-22-2-222-22-222-2-2-2-2-2-222-2-222222-222-20000000022-2-20000-222-2000022-2-222-2-200000000000000000000
χ382-2-22-2-222-22-222-2-2-2-2-2-222-2-222222-222-200000000-2-2220000-222-20000-2-222-2-22200000000000000000000
χ392-2-22-2-222-22-22-1111111-1-111-1-1-1-1-12-2-220022-2-2000000−i3i3−i3i3-111-1−i3i3−i3i3−i3−i3i3i3i3i3−i3−i3-1-111-1-111000000000000
χ402-2-22-2-222-22-22-1111111-1-111-1-1-1-1-12-2-220022-2-2000000i3−i3i3−i3-111-1i3−i3i3−i3i3i3−i3−i3−i3−i3i3i3-1-111-1-111000000000000
χ412-2-22-2-222-22-22-1111111-1-111-1-1-1-1-12-2-2200-2-222000000−i3i3−i3i3-111-1−i3i3−i3i3i3i3−i3−i3−i3−i3i3i311-1-111-1-1000000000000
χ422-2-22-2-222-22-22-1111111-1-111-1-1-1-1-12-2-2200-2-222000000i3−i3i3−i3-111-1i3−i3i3−i3−i3−i3i3i3i3i3−i3−i311-1-111-1-1000000000000
χ432-2-22-2-222-22-22-1111111-1-111-1-1-1-1-1-222-20000000022-2-2−i3i3−i3i31-1-11i3−i3i3−i3-1-111-1-111−i3−i3i3i3i3i3−i3−i3000000000000
χ442-2-22-2-222-22-22-1111111-1-111-1-1-1-1-1-222-20000000022-2-2i3−i3i3−i31-1-11−i3i3−i3i3-1-111-1-111i3i3−i3−i3−i3−i3i3i3000000000000
χ452-2-22-2-222-22-22-1111111-1-111-1-1-1-1-1-222-200000000-2-222−i3i3−i3i31-1-11i3−i3i3−i311-1-111-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ462-2-22-2-222-22-22-1111111-1-111-1-1-1-1-1-222-200000000-2-222i3−i3i3−i31-1-11−i3i3−i3i311-1-111-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ4744444444-4-4-4-4-2-2-2-2-2222222-2-222-24-44-40000000000000000-2-22200000000000000000000000000000000
χ4844444444-4-4-4-4-2-2-2-2-2222222-2-222-2-44-44000000000000000022-2-200000000000000000000000000000000
χ494444-4-4-4-44-4-44-2-2-222-2-2222222-2-2-200004-40000000000-2-222000000000000000000000000000000000000
χ504444-4-4-4-44-4-44-2-2-222-2-2222222-2-2-20000-44000000000022-2-2000000000000000000000000000000000000
χ514444-4-4-4-4-444-4444-4-4-4-44444-4-4-4-4400000000000000000000000000000000000000000000000000000000
χ524444-4-4-4-4-444-4-2-2-22222-2-2-2-22222-200000000000000000000000023−23−23230000000000000000000000000000
χ534444-4-4-4-4-444-4-2-2-22222-2-2-2-22222-2000000000000000000000000−232323−230000000000000000000000000000
χ5444-4-44-44-4000044-44-40000004-400-40000002i−2i2i−2i000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ5544-4-44-44-4000044-44-40000004-400-4000000−2i2i−2i2i00000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ5644-4-44-44-40000-2-22-22−2i32i3−2i32i3−2i32i3-22−2i32i320000002i−2i2i−2i000000000000000000000000002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000
χ5744-4-44-44-40000-2-22-22−2i32i3−2i32i3−2i32i3-22−2i32i32000000−2i2i−2i2i00000000000000000000000000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000
χ5844-4-44-44-40000-2-22-222i3−2i32i3−2i32i3−2i3-222i3−2i320000002i−2i2i−2i000000000000000000000000002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000
χ5944-4-44-44-40000-2-22-222i3−2i32i3−2i32i3−2i3-222i3−2i32000000−2i2i−2i2i00000000000000000000000000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000
χ6044-4-4-44-44000044-4-44000000-4400-40000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ6144-4-4-44-44000044-4-44000000-4400-4000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ6244-4-4-44-440000-2-222-2−2i32i32i3−2i32i3−2i32-2−2i32i320000000000002i−2i2i−2i0000000000002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ1400000000000000000000
χ6344-4-4-44-440000-2-222-2−2i32i32i3−2i32i3−2i32-2−2i32i32000000000000−2i2i−2i2i000000000000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ1400000000000000000000
χ6444-4-4-44-440000-2-222-22i3−2i3−2i32i3−2i32i32-22i3−2i320000000000002i−2i2i−2i0000000000002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ2200000000000000000000
χ6544-4-4-44-440000-2-222-22i3−2i3−2i32i3−2i32i32-22i3−2i32000000000000−2i2i−2i2i000000000000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ2200000000000000000000
χ664-44-44-4-4400004-444-4000000-4400-40000000000002i−2i−2i2i0000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ674-44-44-4-4400004-444-4000000-4400-4000000000000−2i2i2i−2i000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ684-44-44-4-440000-22-2-22−2i32i3−2i32i32i3−2i32-22i3−2i320000000000002i−2i−2i2i0000000000002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ2200000000000000000000
χ694-44-44-4-440000-22-2-22−2i32i3−2i32i32i3−2i32-22i3−2i32000000000000−2i2i2i−2i000000000000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ2200000000000000000000
χ704-44-44-4-440000-22-2-222i3−2i32i3−2i3−2i32i32-2−2i32i320000000000002i−2i−2i2i0000000000002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ1400000000000000000000
χ714-44-44-4-440000-22-2-222i3−2i32i3−2i3−2i32i32-2−2i32i32000000000000−2i2i2i−2i000000000000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ1400000000000000000000
χ724-44-4-444-400004-44-440000004-400-40000002i−2i−2i2i000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ734-44-4-444-400004-44-440000004-400-4000000−2i2i2i−2i00000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ744-44-4-444-40000-22-22-2−2i32i32i3−2i3−2i32i3-222i3−2i320000002i−2i−2i2i000000000000000000000000002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22000000000000
χ754-44-4-444-40000-22-22-2−2i32i32i3−2i3−2i32i3-222i3−2i32000000−2i2i2i−2i00000000000000000000000000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22000000000000
χ764-44-4-444-40000-22-22-22i3−2i3−2i32i32i3−2i3-22−2i32i320000002i−2i−2i2i000000000000000000000000002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14000000000000
χ774-44-4-444-40000-22-22-22i3−2i3−2i32i32i3−2i3-22−2i32i32000000−2i2i2i−2i00000000000000000000000000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14000000000000
χ784-4-4444-4-444-4-4-222-2-2-2-2-2-2222222-200000000004i−4i000000000000−2i−2i2i2i0000000000000000000000000000
χ794-4-4444-4-444-4-4-222-2-2-2-2-2-2222222-20000000000−4i4i0000000000002i2i−2i−2i0000000000000000000000000000
χ804-4-4444-4-4-4-4444-4-444-4-4-4-444-4-444400000000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-4-444-222-2-22222-2-222-2-2-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ824-4-4444-4-4-4-444-222-2-22222-2-222-2-2-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ834-4-44-4-4444-44-4-22222-2-222-2-2-2-222-244-4-40000000000000000-22-2200000000000000000000000000000000
χ844-4-44-4-4444-44-4-22222-2-222-2-2-2-222-2-4-44400000000000000002-22-200000000000000000000000000000000

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