Finite Group Databasebeta

← Group #10698048

Character table — Group #10698048

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222222234444666666644444444446666121212121212121212121212121212121212121212121212244466121212121212888888882444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1
χ922222222222-2-2-2-22222222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
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
χ132222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-11111-1-1000000000000
χ142222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-22211-1-1-1-111000000000000
χ152222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000−i3i3−i3−i3i3i3−i3i3000000000000
χ162222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000i3−i3i3i3−i3−i3i3−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−i3i3i3i3−i3−i3−i3i3000000000000
χ182222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000i3−i3−i3−i3i3i3i3−i3000000000000
χ19222222-2-2-2-222222-2-222-2-22-2-20000000022-2-22222-2-2-2-2000000000000000000000000000022-2-200000000
χ20222222-2-2-2-222222-2-222-2-22-2-20000000022-2-22222-2-2-2-20000000000000000000000000000-2-22200000000
χ21222222-2-2-2-22-2-2-2-2-2-222-2-22220000000022-2-2-2-2-2-22222000000000000000000000000000000002i2i−2i−2i0000
χ22222222-2-2-2-22-2-2-2-2-2-222-2-22220000000022-2-2-2-2-2-2222200000000000000000000000000000000−2i−2i2i2i0000
χ232222-2-22-22-2222-2-222222222-200000000-2-2-2-222-2-222-2-20000000000000000002-2002-22-200000000000000
χ242222-2-22-22-2222-2-222222222-200000000-2-2-2-222-2-222-2-2000000000000000000-2200-22-2200000000000000
χ252222-2-22-22-22-2-2222222222-2200000000-2-2-2-2-2-222-2-22200000000000000002-200220000-2-2000000000000
χ262222-2-22-22-22-2-2222222222-2200000000-2-2-2-2-2-222-2-2220000000000000000-2200-2-2000022000000000000
χ272222-2-22-22-2-122-2-2-1-1-1-1-1-1-12-2000000001111-1-111-1-111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3002-2−i3i3-11-11i3−i3000000000000
χ282222-2-22-22-2-122-2-2-1-1-1-1-1-1-12-2000000001111-1-111-1-111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i300-22i3−i31-11-1−i3i3000000000000
χ292222-2-22-22-2-122-2-2-1-1-1-1-1-1-12-2000000001111-1-111-1-111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3002-2i3−i3-11-11−i3i3000000000000
χ302222-2-22-22-2-122-2-2-1-1-1-1-1-1-12-2000000001111-1-111-1-111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i300-22−i3i31-11-1i3−i3000000000000
χ312222-2-22-22-2-1-2-222-1-1-1-1-1-1-1-2200000000111111-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-200-1-1−i3i3i3−i311000000000000
χ322222-2-22-22-2-1-2-222-1-1-1-1-1-1-1-2200000000111111-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-220011i3−i3−i3i3-1-1000000000000
χ332222-2-22-22-2-1-2-222-1-1-1-1-1-1-1-2200000000111111-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-200-1-1i3−i3−i3i311000000000000
χ342222-2-22-22-2-1-2-222-1-1-1-1-1-1-1-2200000000111111-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-220011−i3i3i3−i3-1-1000000000000
χ352222-2-2-22-22222-2-2-2-222-2-22-2200000000-2-22222-2-2-2-222000000000000000000000000000000000000002-2
χ362222-2-2-22-22222-2-2-2-222-2-22-2200000000-2-22222-2-2-2-22200000000000000000000000000000000000000-22
χ372222-2-2-22-222-2-222-2-222-2-222-200000000-2-222-2-22222-2-20000000000000000000000000000000000002-200
χ382222-2-2-22-222-2-222-2-222-2-222-200000000-2-222-2-22222-2-2000000000000000000000000000000000000-2200
χ392-2-222-222-2-22000022-2-2-2-22002i2i−2i−2i00002-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000002−22−2−i2i2−i2i20000
χ402-2-222-222-2-22000022-2-2-2-22002i2i−2i−2i00002-22-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−22−22i2−i2i2−i20000
χ412-2-222-222-2-22000022-2-2-2-2200−2i−2i2i2i00002-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000002−22−2i2−i2i2−i20000
χ422-2-222-222-2-22000022-2-2-2-2200−2i−2i2i2i00002-22-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000−22−22−i2i2−i2i20000
χ432-2-222-2-2-22220000-2-2-2-222200000022-2-22-2-22000000000000000022-2-222-2-20000000000002−2−222−2−220000
χ442-2-222-2-2-22220000-2-2-2-222200000022-2-22-2-22000000000000000022-2-222-2-2000000000000−222−2−222−20000
χ452-2-222-2-2-22220000-2-2-2-2222000000-2-2222-2-220000000000000000-2-222-2-2220000000000002−2−22−222−20000
χ462-2-222-2-2-22220000-2-2-2-2222000000-2-2222-2-220000000000000000-2-222-2-222000000000000−222−22−2−220000
χ47444444-4-4-4-4-2444422-2-222-2-4-400000000-2-222-2-2-2-222220000000000000000000000000000000000000000
χ48444444-4-4-4-4-2-4-4-4-422-2-222-24400000000-2-2222222-2-2-2-20000000000000000000000000000000000000000
χ494444-4-4-44-44-244-4-422-2-222-2-440000000022-2-2-2-22222-2-20000000000000000000000000000000000000000
χ504444-4-4-44-44-2-4-44422-2-222-24-40000000022-2-222-2-2-2-2220000000000000000000000000000000000000000
χ5144-4-40000004004-4004-400-4002i−2i2i−2i2i−2i2i−2i0000004-400002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5244-4-40000004004-4004-400-400−2i2i−2i2i−2i2i−2i2i0000004-40000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5344-4-4000000400-44004-400-4002i−2i2i−2i−2i2i−2i2i000000-4400002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5444-4-4000000400-44004-400-400−2i2i−2i2i2i−2i2i−2i000000-440000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5544-4-4000000-2004-4−2i32i3-22−2i32i32002i−2i2i−2i2i−2i2i−2i000000-2200−2i32i32ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ5644-4-4000000-2004-4−2i32i3-22−2i32i3200−2i2i−2i2i−2i2i−2i2i000000-2200−2i32i3−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ5744-4-4000000-2004-42i3−2i3-222i3−2i32002i−2i2i−2i2i−2i2i−2i000000-22002i3−2i32ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ5844-4-4000000-2004-42i3−2i3-222i3−2i3200−2i2i−2i2i−2i2i−2i2i000000-22002i3−2i3−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ5944-4-4000000-200-44−2i32i3-22−2i32i32002i−2i2i−2i−2i2i−2i2i0000002-2002i3−2i32ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ6044-4-4000000-200-44−2i32i3-22−2i32i3200−2i2i−2i2i2i−2i2i−2i0000002-2002i3−2i3−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ6144-4-4000000-200-442i3−2i3-222i3−2i32002i−2i2i−2i−2i2i−2i2i0000002-200−2i32i32ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ6244-4-4000000-200-442i3−2i3-222i3−2i3200−2i2i−2i2i2i−2i2i−2i0000002-200−2i32i3−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ634-44-400000044i−4i0000-4400-4002-2-222i−2i−2i2i00004i−4i0000002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ644-44-400000044i−4i0000-4400-400-222-2−2i2i2i−2i00004i−4i000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ654-44-40000004−4i4i0000-4400-4002-2-22−2i2i2i−2i0000−4i4i0000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ664-44-40000004−4i4i0000-4400-400-222-22i−2i−2i2i0000−4i4i000000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ674-44-4000000-24i−4i00−2i32i32-22i3−2i32002-2-222i−2i−2i2i0000−2i2i0023−2300−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22000000000000000000000000
χ684-44-4000000-24i−4i00−2i32i32-22i3−2i3200-222-2−2i2i2i−2i0000−2i2i0023−23001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22000000000000000000000000
χ694-44-4000000-24i−4i002i3−2i32-2−2i32i32002-2-222i−2i−2i2i0000−2i2i00−232300−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14000000000000000000000000
χ704-44-4000000-24i−4i002i3−2i32-2−2i32i3200-222-2−2i2i2i−2i0000−2i2i00−2323001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14000000000000000000000000
χ714-44-4000000-2−4i4i00−2i32i32-22i3−2i32002-2-22−2i2i2i−2i00002i−2i00−232300−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22000000000000000000000000
χ724-44-4000000-2−4i4i00−2i32i32-22i3−2i3200-222-22i−2i−2i2i00002i−2i00−2323001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22000000000000000000000000
χ734-44-4000000-2−4i4i002i3−2i32-2−2i32i32002-2-22−2i2i2i−2i00002i−2i0023−2300−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14000000000000000000000000
χ744-44-4000000-2−4i4i002i3−2i32-2−2i32i3200-222-22i−2i−2i2i00002i−2i0023−23001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14000000000000000000000000
χ754-4-444-444-4-4-20000-2-22222-2004i4i−4i−4i0000-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ764-4-444-444-4-4-20000-2-22222-200−4i−4i4i4i0000-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ774-4-444-4-4-444-200002222-2-2-200000044-4-4-222-20000000000000000-2-222-2-222000000000000000000000000
χ784-4-444-4-4-444-200002222-2-2-2000000-4-444-222-2000000000000000022-2-222-2-2000000000000000000000000
χ794-4-44-444-4-444000044-4-4-4-440000000000-44-44000000000000000000000000000000000000000000000000
χ804-4-44-444-4-44-20000-2-22222-200000000002-22-2000000002323−23−23−23−23232300000000000000000000000000000000
χ814-4-44-444-4-44-20000-2-22222-200000000002-22-200000000−23−2323232323−23−2300000000000000000000000000000000
χ824-4-44-44-444-440000-4-4-4-44440000000000-444-4000000000000000000000000000000000000000000000000
χ834-4-44-44-444-4-200002222-2-2-200000000002-2-220000000000000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000
χ844-4-44-44-444-4-200002222-2-2-200000000002-2-2200000000000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000

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