Finite Group Databasebeta

← Group #10696040

Character table — Group #10696040

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222222244448888888888888888888888888888888888888888242424242424242448484848
order122244442234466666661212121212121212444444444444444412121212121212121212121212121212121212121212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ92222222222222222222222222222-2-2-2-20000000022-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222222222222222-2-2-2-200000000-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ112222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ122222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000
χ132222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-22222-2-2-2-211111111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ142222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000
χ152222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000022-2-2-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ162222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000022-2-2-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ172222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-2221111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3000000000000
χ182222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-2221111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3000000000000
χ1922222222-2-22-2-22-2-2-2-2222222-2-2-2-22-22-20000000000000000000022-2-20000000000000000000022-2-20000
χ2022222222-2-22-2-22-2-2-2-2222222-2-2-2-22-22-20000000000000000000022-2-200000000000000000000-2-2220000
χ2122222222-2-22-2-22-2-2-2-2222222-2-2-2-2-22-2200000000000000000000-2-222000000000000000022-2-200000000
χ2222222222-2-22-2-22-2-2-2-2222222-2-2-2-2-22-2200000000000000000000-2-2220000000000000000-2-22200000000
χ232222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-2-2222-2-200000000000000002-22-222-2-222-2-200000000000000000000
χ242222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-2-22-2-22200000000000000002-22-2-2-222-2-22200000000000000000000
χ252222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-222-2000022-2-2000000000000-22-220000000022-2-222-2-2000000000000
χ262222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-222-20000-2-222000000000000-22-2200000000-2-222-2-222000000000000
χ272222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112-2-2222-2-200000000−i3−i3i3i3−i3−i3i3i3-11-11-1-111-1-111−i3−i3i3i3i3i3−i3−i3000000000000
χ282222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112-2-2222-2-200000000i3i3−i3−i3i3i3−i3−i3-11-11-1-111-1-111i3i3−i3−i3−i3−i3i3i3000000000000
χ292222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112-2-22-2-22200000000−i3−i3i3i3−i3−i3i3i3-11-1111-1-111-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ302222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112-2-22-2-22200000000i3i3−i3−i3i3i3−i3−i3-11-1111-1-111-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ312222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-222-2000022-2-20000−i3−i3i3i3i3i3−i3−i31-11-1−i3−i3i3i3i3i3−i3−i3-1-111-1-111000000000000
χ322222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-222-2000022-2-20000i3i3−i3−i3−i3−i3i3i31-11-1i3i3−i3−i3−i3−i3i3i3-1-111-1-111000000000000
χ332222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-222-20000-2-2220000−i3−i3i3i3i3i3−i3−i31-11-1i3i3−i3−i3−i3−i3i3i311-1-111-1-1000000000000
χ342222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-222-20000-2-2220000i3i3−i3−i3−i3−i3i3i31-11-1−i3−i3i3i3i3i3−i3−i311-1-111-1-1000000000000
χ352222-2-2-2-2-2-22222-2-2-2-222-2-2-2-2222222-2-2000000000000000000002-2-22000000000000000000000000002i−2i
χ362222-2-2-2-2-2-22222-2-2-2-222-2-2-2-2222222-2-2000000000000000000002-2-2200000000000000000000000000−2i2i
χ372222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222-2-22200000000000000000000-222-20000000000000000000000002-200
χ382222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222-2-22200000000000000000000-222-2000000000000000000000000-2200
χ392-2-22-2-2222-222-2222-2-2-2-222-2-222-2-2000000000000002-200002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ402-2-22-2-2222-222-2222-2-2-2-222-2-222-2-2000000000000002-200002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ412-2-22-2-2222-222-2222-2-2-2-222-2-222-2-200000000000000-220000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ422-2-22-2-2222-222-2222-2-2-2-222-2-222-2-200000000000000-220000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ432-2-22-2-222-222-222-2-222-2-222-2-2-2-2220000000000002-2002-22-2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ442-2-22-2-222-222-222-2-222-2-222-2-2-2-2220000000000002-2002-22-2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ452-2-22-2-222-222-222-2-222-2-222-2-2-2-222000000000000-2200-22-22000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ462-2-22-2-222-222-222-2-222-2-222-2-2-2-222000000000000-2200-22-22000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ4744444444-4-4-2-4-4-22222-2-2-2-2-2-222224-44-400000000000000000000-2-2220000000000000000000000000000
χ4844444444-4-4-2-4-4-22222-2-2-2-2-2-22222-44-440000000000000000000022-2-20000000000000000000000000000
χ494444-4-4-4-4-4-4-244-22222-2-22222-2-2-2-244-4-400000000000000000000-222-20000000000000000000000000000
χ504444-4-4-4-4-4-4-244-22222-2-22222-2-2-2-2-4-444000000000000000000002-2-220000000000000000000000000000
χ5144-4-44i−4i4i−4i00400-400004-44i−4i4i−4i000000002-22i−2i000000000000000000002-22i−2i2-22i−2i00000000000000000000
χ5244-4-44i−4i4i−4i00400-400004-44i−4i4i−4i00000000-22−2i2i00000000000000000000-22−2i2i-22−2i2i00000000000000000000
χ5344-4-44i−4i4i−4i00-2002−2i32i3−2i32i3-22−2i2i−2i2i23−2323−2300002-22i−2i00000000000000000000−1+i31−i32ζ14−2ζ14−1−i31+i32ζ22−2ζ2200000000000000000000
χ5444-4-44i−4i4i−4i00-2002−2i32i3−2i32i3-22−2i2i−2i2i23−2323−230000-22−2i2i000000000000000000001−i3−1+i3−2ζ142ζ141+i3−1−i3−2ζ222ζ2200000000000000000000
χ5544-4-44i−4i4i−4i00-20022i3−2i32i3−2i3-22−2i2i−2i2i−2323−232300002-22i−2i00000000000000000000−1−i31+i32ζ22−2ζ22−1+i31−i32ζ14−2ζ1400000000000000000000
χ5644-4-44i−4i4i−4i00-20022i3−2i32i3−2i3-22−2i2i−2i2i−2323−23230000-22−2i2i000000000000000000001+i3−1−i3−2ζ222ζ221−i3−1+i3−2ζ142ζ1400000000000000000000
χ5744-4-4−4i4i−4i4i00400-400004-4−4i4i−4i4i000000002-2−2i2i000000000000000000002-2−2i2i2-2−2i2i00000000000000000000
χ5844-4-4−4i4i−4i4i00400-400004-4−4i4i−4i4i00000000-222i−2i00000000000000000000-222i−2i-222i−2i00000000000000000000
χ5944-4-4−4i4i−4i4i00-2002−2i32i3−2i32i3-222i−2i2i−2i−2323−232300002-2−2i2i00000000000000000000−1+i31−i3−2ζ142ζ14−1−i31+i3−2ζ222ζ2200000000000000000000
χ6044-4-4−4i4i−4i4i00-2002−2i32i3−2i32i3-222i−2i2i−2i−2323−23230000-222i−2i000000000000000000001−i3−1+i32ζ14−2ζ141+i3−1−i32ζ22−2ζ2200000000000000000000
χ6144-4-4−4i4i−4i4i00-20022i3−2i32i3−2i3-222i−2i2i−2i23−2323−2300002-2−2i2i00000000000000000000−1−i31+i3−2ζ222ζ22−1+i31−i3−2ζ142ζ1400000000000000000000
χ6244-4-4−4i4i−4i4i00-20022i3−2i32i3−2i3-222i−2i2i−2i23−2323−230000-222i−2i000000000000000000001+i3−1−i32ζ22−2ζ221−i3−1+i32ζ14−2ζ1400000000000000000000
χ634-44-44i−4i−4i4i00400-40000-44−4i4i4i−4i0000000000002i−2i2-20000000000000000000000002i−2i2-22i−2i2-2000000000000
χ644-44-44i−4i−4i4i00400-40000-44−4i4i4i−4i000000000000−2i2i-22000000000000000000000000−2i2i-22−2i2i-22000000000000
χ654-44-44i−4i−4i4i00-2002−2i32i32i3−2i32-22i−2i−2i2i−232323−23000000002i−2i2-20000000000000000000000002ζ22−2ζ22−1−i31+i32ζ14−2ζ14−1+i31−i3000000000000
χ664-44-44i−4i−4i4i00-2002−2i32i32i3−2i32-22i−2i−2i2i−232323−2300000000−2i2i-22000000000000000000000000−2ζ222ζ221+i3−1−i3−2ζ142ζ141−i3−1+i3000000000000
χ674-44-44i−4i−4i4i00-20022i3−2i3−2i32i32-22i−2i−2i2i23−23−2323000000002i−2i2-20000000000000000000000002ζ14−2ζ14−1+i31−i32ζ22−2ζ22−1−i31+i3000000000000
χ684-44-44i−4i−4i4i00-20022i3−2i3−2i32i32-22i−2i−2i2i23−23−232300000000−2i2i-22000000000000000000000000−2ζ142ζ141−i3−1+i3−2ζ222ζ221+i3−1−i3000000000000
χ694-44-4−4i4i4i−4i00400-40000-444i−4i−4i4i0000000000002i−2i-220000000000000000000000002i−2i-222i−2i-22000000000000
χ704-44-4−4i4i4i−4i00400-40000-444i−4i−4i4i000000000000−2i2i2-2000000000000000000000000−2i2i2-2−2i2i2-2000000000000
χ714-44-4−4i4i4i−4i00-2002−2i32i32i3−2i32-2−2i2i2i−2i23−23−2323000000002i−2i-220000000000000000000000002ζ22−2ζ221+i3−1−i32ζ14−2ζ141−i3−1+i3000000000000
χ724-44-4−4i4i4i−4i00-2002−2i32i32i3−2i32-2−2i2i2i−2i23−23−232300000000−2i2i2-2000000000000000000000000−2ζ222ζ22−1−i31+i3−2ζ142ζ14−1+i31−i3000000000000
χ734-44-4−4i4i4i−4i00-20022i3−2i3−2i32i32-2−2i2i2i−2i−232323−23000000002i−2i-220000000000000000000000002ζ14−2ζ141−i3−1+i32ζ22−2ζ221+i3−1−i3000000000000
χ744-44-4−4i4i4i−4i00-20022i3−2i3−2i32i32-2−2i2i2i−2i−232323−2300000000−2i2i2-2000000000000000000000000−2ζ142ζ14−1+i31−i3−2ζ222ζ22−1−i31+i3000000000000
χ754-4-4444-4-44-44-44444-4-4-4-4-4-444-4-44400000000000000000000000000000000000000000000000000000000
χ764-4-4444-4-44-4-2-44-2-2-2222222-2-222-2-200000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ774-4-4444-4-44-4-2-44-2-2-2222222-2-222-2-2000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ784-4-4444-4-4-4444-44-4-444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-4-44-24-4-222-2-22222-2-2-2-2220000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ804-4-4444-4-4-44-24-4-222-2-22222-2-2-2-22200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ814-4-44-4-4444-4-24-4-2-2-22222-2-222-2-222000000000000004-40000-22-2200000000000000000000000000000000
χ824-4-44-4-4444-4-24-4-2-2-22222-2-222-2-22200000000000000-4400002-22-200000000000000000000000000000000
χ834-4-44-4-444-44-2-44-222-2-222-2-22222-2-20000000000004-400-22-22000000000000000000000000000000000000
χ844-4-44-4-444-44-2-44-222-2-222-2-22222-2-2000000000000-44002-22-2000000000000000000000000000000000000

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