Finite Group Databasebeta

← Group #10849271

Character table — Group #10849271

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212444422444448812121212242424242424242444444444888846612121212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ51111111111111111111111-1-1-1-11111111111-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1-1-1111-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-1-1111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-1-11111-1
χ911111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-111-1-11
χ1011111111111111111111-1-1111111111111-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-11111-1-111-1-1-1-1-1-1
χ1111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-111111-1-111-1
χ1211111111111111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ1311111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1-111-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-1-1-11111-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-11111-1-1-1-1-1-11-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1111111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222000000-200-2-22200000000-2-2220000000000000000000-200000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000-200-2-2220000000022-2-20000000000000000000200000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2222200000020022-2-200000000-2-2-2-20000000000000000000200000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200000020022-2-20000000022220000000000000000000-200000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-2-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022-2-2222-2-2-1-1-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-222-2-22-2-2-1-1-1-111111111000000000000211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-2-2-2-2-2-21111-1-1-1-111110000000000002-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-22222-2-2-21111-1-1-1-11111000000000000-211-1-1-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-100002222-2-2-22211111111-1-1-1-1000000000000-2-1-1-1-1111100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-2-222-22211111111-1-1-1-100000000000021111-1-1-1-100000000
χ2922-22-22-2-22-22-222-2-2-222-2000000-2-2220000002-20000000000000000000002i2i−2i−2i2i2i−2i−2i0002-2000000000000
χ3022-22-22-2-22-22-222-2-2-222-2000000-2-2220000002-2000000000000000000000−2i−2i2i2i−2i−2i2i2i0002-2000000000000
χ3122-22-22-2-22-22-222-2-2-222-2000000-2-222000000-220000000000000000000002i2i−2i−2i−2i−2i2i2i000-22000000000000
χ3222-22-22-2-22-22-222-2-2-222-2000000-2-222000000-22000000000000000000000−2i−2i2i2i2i2i−2i−2i000-22000000000000
χ332-222-2-2-2220000-22-222-2-22i−2i−i2−i2i2i200002i2i−2i−2i00000002−2002i−2i−i2−i2i2i222−2−2002-200002−22−200000000000000−i2i20
χ342-222-2-2-2220000-22-222-2-22i−2i−i2−i2i2i20000−2i−2i2i2i00000002−2002i−2i−i2−i2i2i222−2−200-220000−22−2200000000000000i2−i20
χ352-222-2-2-2220000-22-222-2-22i−2ii2i2−i2−i200002i2i−2i−2i0000000−22002i−2ii2i2−i2−i2−2−222002-20000−22−2200000000000000i2−i20
χ362-222-2-2-2220000-22-222-2-22i−2ii2i2−i2−i20000−2i−2i2i2i0000000−22002i−2ii2i2−i2−i2−2−22200-2200002−22−200000000000000−i2i20
χ372-222-2-2-2220000-22-222-2-2−2i2i−i2−i2i2i200002i2i−2i−2i0000000−2200−2i2i−i2−i2i2i2−2−22200-2200002−22−200000000000000i2−i20
χ382-222-2-2-2220000-22-222-2-2−2i2i−i2−i2i2i20000−2i−2i2i2i0000000−2200−2i2i−i2−i2i2i2−2−222002-20000−22−2200000000000000−i2i20
χ392-222-2-2-2220000-22-222-2-2−2i2ii2i2−i2−i200002i2i−2i−2i00000002−200−2i2ii2i2−i2−i222−2−200-220000−22−2200000000000000−i2i20
χ402-222-2-2-2220000-22-222-2-2−2i2ii2i2−i2−i20000−2i−2i2i2i00000002−200−2i2ii2i2−i2−i222−2−2002-200002−22−200000000000000i2−i20
χ412-22-222-2-22-2-222-222-2-22-2002i−2i2i−2i2-22-2000000000000000002i−2i2i−2i000000002i−2i2i−2i00000000000002-2000000
χ422-22-222-2-22-2-222-222-2-22-2002i−2i2i−2i2-22-2000000000000000002i−2i2i−2i00000000−2i2i−2i2i0000000000000-22000000
χ432-22-222-2-22-2-222-222-2-22-200−2i2i−2i2i2-22-200000000000000000−2i2i−2i2i000000002i−2i2i−2i0000000000000-22000000
χ442-22-222-2-22-2-222-222-2-22-200−2i2i−2i2i2-22-200000000000000000−2i2i−2i2i00000000−2i2i−2i2i00000000000002-2000000
χ452-2-2-2-222222-2-22-2-2-22-222000000-222-22-22-200002-20000000000000002-2002-2-220000000002-20000000000
χ462-2-2-2-222222-2-22-2-2-22-222000000-222-22-22-20000-220000000000000002-200-222-2000000000-220000000000
χ472-2-2-2-222222-2-22-2-2-22-222000000-222-2-22-2200002-2000000000000000-2200-222-20000000002-20000000000
χ482-2-2-2-222222-2-22-2-2-22-222000000-222-2-22-220000-22000000000000000-22002-2-22000000000-220000000000
χ492-2-2-2-22222-222-2-2-2-22-2220000002-2-222-22-22-20000000000000000000-22000000000002-20000000002-2000
χ502-2-2-2-22222-222-2-2-2-22-2220000002-2-222-22-2-220000000000000000000-2200000000000-22000000000-22000
χ512-2-2-2-22222-222-2-2-2-22-2220000002-2-22-22-222-200000000000000000002-2000000000002-2000000000-22000
χ522-2-2-2-22222-222-2-2-2-22-2220000002-2-22-22-22-2200000000000000000002-200000000000-220000000002-2000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000000000-40022-2-20000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022220000000000400-2-2220000000000000000000000000000000000000
χ55444-4-4-44-44000044-4-4-4-440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ56444-4-4-44-44000044-4-4-4-4400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ57444-4-4-44-4-20000-2-22222-20022−22−22220000000000000000023−2300−222−26−66−600000000000000000000000000000
χ58444-4-4-44-4-20000-2-22222-20022−22−222200000000000000000−232300−222−2−66−6600000000000000000000000000000
χ59444-4-4-44-4-20000-2-22222-200−222222−220000000000000000023−23002−2−22−66−6600000000000000000000000000000
χ60444-4-4-44-4-20000-2-22222-200−222222−2200000000000000000−2323002−2−226−66−600000000000000000000000000000
χ6144-44-44-4-444-44-44-4-4-444-400000044-4-4000000000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-24-44-4-2222-2-22000000-2-2220000000000000000000000000000000000000000000023−2300000000
χ6344-44-44-4-4-24-44-4-2222-2-22000000-2-22200000000000000000000000000000000000000000000−232300000000
χ6444-44-44-4-4-2-44-44-2222-2-2200000022-2-20000004-400000000000000000000000000000000-22000000000000
χ6544-44-44-4-4-2-44-44-2222-2-2200000022-2-2000000-44000000000000000000000000000000002-2000000000000
χ6644-4-44-4-44400004-444-4-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6744-4-44-4-44400004-444-4-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ684-444-4-4-44-200002-22-2-2224i−4i−2i2−2i22i22i200000000000000022−2200−2i2ii2i2−i2−i2−2−22200000000000000000000000000000
χ694-444-4-4-44-200002-22-2-2224i−4i2i22i2−2i2−2i2000000000000000−222200−2i2i−i2−i2i2i222−2−200000000000000000000000000000
χ704-444-4-4-44-200002-22-2-222−4i4i−2i2−2i22i22i2000000000000000−2222002i−2ii2i2−i2−i222−2−200000000000000000000000000000
χ714-444-4-4-44-200002-22-2-222−4i4i2i22i2−2i2−2i200000000000000022−22002i−2i−i2−i2i2i2−2−22200000000000000000000000000000
χ724-44-444-4-4444-4-4-444-4-44-4000000-44-44000000000000000000000000000000000000000000000000000000
χ734-44-444-4-4-244-4-42-2-222-220000002-22-200000000000000000000023−23−232300000000000000000000000000000
χ744-44-444-4-4-244-4-42-2-222-220000002-22-2000000000000000000000−232323−2300000000000000000000000000000
χ754-44-444-4-4-2-4-4442-2-222-22004i−4i4i−4i-22-2200000000000000000−2i2i−2i2i000000000000000000000000000000000
χ764-44-444-4-4-2-4-4442-2-222-2200−4i4i−4i4i-22-22000000000000000002i−2i2i−2i000000000000000000000000000000000
χ774-4-444-44-440000-4-44-44-440000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ784-4-444-44-440000-4-44-44-4400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ794-4-4-4-4444-24-4-44222-22-2-20000002-2-22000000004-400000000000000000000000000000000-220000000000
χ804-4-4-4-4444-24-4-44222-22-2-20000002-2-2200000000-44000000000000000000000000000000002-20000000000
χ814-4-4-4-4444-2-444-4222-22-2-2000000-222-200004-400000000000000000000000000000000-2200000000000000
χ824-4-4-4-4444-2-444-4222-22-2-2000000-222-20000-44000000000000000000000000000000002-200000000000000
χ8388-8-88-8-88-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).