Finite Group Databasebeta

← Group #10698072

Character table — Group #10698072

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222222223444466666664444444444666612121212121212121212121212121212121212121212121244441212121212121212888888884444
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
χ51111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ922222222222-2-2-2-222222222222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222-2-2-2-22222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ112222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ122222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ132222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111111122-2-21111-1-1-1-1000000000000
χ142222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-222-1-1-1-11111000000000000
χ152222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ162222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ172222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000
χ182222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000
χ19222222-2-2-2-222222-2-22-2-2220000-2-2000022-2-2000000002222-2-2-2-20000000000000000000022-2-200000000
χ20222222-2-2-2-222222-2-22-2-2220000-2-2000022-2-2000000002222-2-2-2-200000000000000000000-2-22200000000
χ21222222-2-2-2-22-2-2-2-2-2-22-2-222000022000022-2-200000000-2-2-2-222220000000000000000000000002i2i−2i−2i0000
χ22222222-2-2-2-22-2-2-2-2-2-22-2-222000022000022-2-200000000-2-2-2-22222000000000000000000000000−2i−2i2i2i0000
χ232222-2-22-22-2222-2-2222222200002-20000-2-2-2-20000000022-2-222-2-200000000002-22-22-20000000000000000
χ242222-2-22-22-2222-2-2222222200002-20000-2-2-2-20000000022-2-222-2-20000000000-22-22-220000000000000000
χ252222-2-22-22-22-2-22222222220000-220000-2-2-2-200000000-2-222-2-222000000002-20000002-22-2000000000000
χ262222-2-22-22-22-2-22222222220000-220000-2-2-2-200000000-2-222-2-22200000000-22000000-22-22000000000000
χ272222-2-22-22-2-122-2-2-1-1-1-1-1-1-100002-200001111−i3−i3−i3−i3i3i3i3i3-1-111-1-111−i3−i3−i3−i3i3i3i3i3002-2-11-11−i3i3i3−i3000000000000
χ282222-2-22-22-2-122-2-2-1-1-1-1-1-1-100002-200001111−i3−i3−i3−i3i3i3i3i3-1-111-1-111−i3−i3−i3−i3i3i3i3i300-221-11-1i3−i3−i3i3000000000000
χ292222-2-22-22-2-122-2-2-1-1-1-1-1-1-100002-200001111i3i3i3i3−i3−i3−i3−i3-1-111-1-111i3i3i3i3−i3−i3−i3−i3002-2-11-11i3−i3−i3i3000000000000
χ302222-2-22-22-2-122-2-2-1-1-1-1-1-1-100002-200001111i3i3i3i3−i3−i3−i3−i3-1-111-1-111i3i3i3i3−i3−i3−i3−i300-221-11-1−i3i3i3−i3000000000000
χ312222-2-22-22-2-1-2-222-1-1-1-1-1-1-10000-2200001111−i3−i3−i3−i3i3i3i3i311-1-111-1-1i3i3i3i3−i3−i3−i3−i32-200−i3i3i3−i3-11-11000000000000
χ322222-2-22-22-2-1-2-222-1-1-1-1-1-1-10000-2200001111−i3−i3−i3−i3i3i3i3i311-1-111-1-1i3i3i3i3−i3−i3−i3−i3-2200i3−i3−i3i31-11-1000000000000
χ332222-2-22-22-2-1-2-222-1-1-1-1-1-1-10000-2200001111i3i3i3i3−i3−i3−i3−i311-1-111-1-1−i3−i3−i3−i3i3i3i3i32-200i3−i3−i3i3-11-11000000000000
χ342222-2-22-22-2-1-2-222-1-1-1-1-1-1-10000-2200001111i3i3i3i3−i3−i3−i3−i311-1-111-1-1−i3−i3−i3−i3i3i3i3i3-2200−i3i3i3−i31-11-1000000000000
χ352222-2-2-22-22222-2-2-2-22-2-2220000-220000-2-2220000000022-2-2-2-2220000000000000000000000000000002-2
χ362222-2-2-22-22222-2-2-2-22-2-2220000-220000-2-2220000000022-2-2-2-222000000000000000000000000000000-22
χ372222-2-2-22-222-2-222-2-22-2-22200002-20000-2-22200000000-2-22222-2-200000000000000000000000000002-200
χ382222-2-2-22-222-2-222-2-22-2-22200002-20000-2-22200000000-2-22222-2-20000000000000000000000000000-2200
χ3922-2-22-222-2-220000222-2-2-2-222-2-20000002-22-222-2-222-2-200000000000000000000000000002−22−22−22−20000
χ4022-2-22-222-2-220000222-2-2-2-222-2-20000002-22-222-2-222-2-20000000000000000000000000000−22−22−22−220000
χ4122-2-22-222-2-220000222-2-2-2-2-2-2220000002-22-2-2-222-2-22200000000000000000000000000002−22−2−22−220000
χ4222-2-22-222-2-220000222-2-2-2-2-2-2220000002-22-2-2-222-2-2220000000000000000000000000000−22−222−22−20000
χ4322-2-22-2-2-22220000-2-2222-2-20000002i2i−2i−2i2-2-2200000000000000002i2i−2i−2i2i2i−2i−2i0000000000002−2−22−i2i2i2−i20000
χ4422-2-22-2-2-22220000-2-2222-2-20000002i2i−2i−2i2-2-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000−222−2i2−i2−i2i20000
χ4522-2-22-2-2-22220000-2-2222-2-2000000−2i−2i2i2i2-2-220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000002−2−22i2−i2−i2i20000
χ4622-2-22-2-2-22220000-2-2222-2-2000000−2i−2i2i2i2-2-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000−222−2−i2i2i2−i20000
χ47444444-4-4-4-4-2444422-222-2-20000-4-40000-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ48444444-4-4-4-4-2-4-4-4-422-222-2-20000440000-2-222000000002222-2-2-2-200000000000000000000000000000000
χ494444-4-4-44-44-244-4-422-222-2-20000-44000022-2-200000000-2-22222-2-200000000000000000000000000000000
χ504444-4-4-44-44-2-4-44422-222-2-200004-4000022-2-20000000022-2-2-2-22200000000000000000000000000000000
χ5144-4-44-444-4-4-20000-2-2-2222244-4-4000000-22-22-2-222-2-2220000000000000000000000000000000000000000
χ5244-4-44-444-4-4-20000-2-2-22222-4-444000000-22-2222-2-222-2-20000000000000000000000000000000000000000
χ5344-4-44-4-4-444-2000022-2-2-2220000004i4i−4i−4i-222-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ5444-4-44-4-4-444-2000022-2-2-222000000−4i−4i4i4i-222-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ5544-4-4-444-4-4440000444-4-4-4-40000000000-44-44000000000000000000000000000000000000000000000000
χ5644-4-4-444-4-44-20000-2-2-2222200000000002-22-2−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000
χ5744-4-4-444-4-44-20000-2-2-2222200000000002-22-22i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000
χ5844-4-4-44-444-440000-4-4444-4-40000000000-444-4000000000000000000000000000000000000000000000000
χ5944-4-4-44-444-4-2000022-2-2-22200000000002-2-2200000000000000002323−23−23−23−232323000000000000000000000000
χ6044-4-4-44-444-4-2000022-2-2-22200000000002-2-220000000000000000−23−2323232323−23−23000000000000000000000000
χ614-44-40000004004-400-4004-42i−2i2i−2i002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i004-400002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ624-44-40000004004-400-4004-4−2i2i−2i2i00−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i004-40000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ634-44-4000000400-4400-4004-42i−2i2i−2i00−2i2i−2i2i00002i−2i2i−2i2i−2i2i−2i00-440000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ644-44-4000000400-4400-4004-4−2i2i−2i2i002i−2i2i−2i0000−2i2i−2i2i−2i2i−2i2i00-4400002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ654-44-4000000-2004-4−2i32i32−2i32i3-222i−2i2i−2i002i−2i2i−2i00002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ2200-2200−2i32i32ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ664-44-4000000-2004-4−2i32i32−2i32i3-22−2i2i−2i2i00−2i2i−2i2i0000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ2200-2200−2i32i3−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ674-44-4000000-2004-42i3−2i322i3−2i3-222i−2i2i−2i002i−2i2i−2i00002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ1400-22002i3−2i32ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ684-44-4000000-2004-42i3−2i322i3−2i3-22−2i2i−2i2i00−2i2i−2i2i0000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ1400-22002i3−2i3−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ694-44-4000000-200-44−2i32i32−2i32i3-222i−2i2i−2i00−2i2i−2i2i00002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22002-2002i3−2i3−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ704-44-4000000-200-44−2i32i32−2i32i3-22−2i2i−2i2i002i−2i2i−2i0000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22002-2002i3−2i32ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ714-44-4000000-200-442i3−2i322i3−2i3-222i−2i2i−2i00−2i2i−2i2i00002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14002-200−2i32i3−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ724-44-4000000-200-442i3−2i322i3−2i3-22−2i2i−2i2i002i−2i2i−2i0000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14002-200−2i32i32ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ734-4-4400000044i−4i0000-400-442i−2i−2i2i002-2-2200002i−2i−2i2i2i−2i−2i2i4i−4i0000002-2-222-2-22000000000000000000000000
χ744-4-4400000044i−4i0000-400-44−2i2i2i−2i00-222-20000−2i2i2i−2i−2i2i2i−2i4i−4i000000-222-2-222-2000000000000000000000000
χ754-4-440000004−4i4i0000-400-442i−2i−2i2i00-222-200002i−2i−2i2i2i−2i−2i2i−4i4i000000-222-2-222-2000000000000000000000000
χ764-4-440000004−4i4i0000-400-44−2i2i2i−2i002-2-220000−2i2i2i−2i−2i2i2i−2i−4i4i0000002-2-222-2-22000000000000000000000000
χ774-4-44000000-24i−4i00−2i32i322i3−2i32-22i−2i−2i2i002-2-2200002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22−2i2i0023−2300−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000
χ784-4-44000000-24i−4i00−2i32i322i3−2i32-2−2i2i2i−2i00-222-20000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2i2i0023−23001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000
χ794-4-44000000-24i−4i002i3−2i32−2i32i32-22i−2i−2i2i002-2-2200002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14−2i2i00−232300−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000000000
χ804-4-44000000-24i−4i002i3−2i32−2i32i32-2−2i2i2i−2i00-222-20000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2i2i00−2323001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000000000000000
χ814-4-44000000-2−4i4i00−2i32i322i3−2i32-22i−2i−2i2i00-222-200002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222i−2i00−2323001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000
χ824-4-44000000-2−4i4i00−2i32i322i3−2i32-2−2i2i2i−2i002-2-220000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222i−2i00−232300−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000
χ834-4-44000000-2−4i4i002i3−2i32−2i32i32-22i−2i−2i2i00-222-200002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142i−2i0023−23001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000000000000000
χ844-4-44000000-2−4i4i002i3−2i32−2i32i32-2−2i2i2i−2i002-2-220000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142i−2i0023−2300−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000000000

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