Finite Group Databasebeta

← Group #10827363

Character table — Group #10827363

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212444422444448812121212242424242424242422224444888846612121212121222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-1-11
χ61111111111111111111111-1-1-1-111111111-1-111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-111111
χ911111111111111111111-1-111111111111111-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-111-1-111-1-1-1-1-111-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1111-1-1111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111-1-111111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-111-1-1-1-111-1-11-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2222200-200000022-2-200000000-2-2220000000000000000000-200000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-200-200000022-2-20000000022-2-20000000000000000000200000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222002000000-2-22200000000-2-2-2-20000000000000000000200000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000-2-2220000000022220000000000000000000-200000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000222-2-2-2-2-2-2-1-1-1-1111111110000000000002-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-222222-2-2-1-1-1-111111111000000000000-21111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-222-2-2-2-21111-1-1-1-11111000000000000-2-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2-2-222-2-21111-1-1-1-11111000000000000211-1-111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2222211111111-1-1-1-1000000000000-2-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222-2-22211111111-1-1-1-1000000000000211-1-1-1-11100000000
χ2922-22-2-2-22222-2-22-2-222-2-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i000000002i2i−2i−2i00000000000000002-2000
χ3022-22-2-2-22222-2-22-2-222-2-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i00000000−2i−2i2i2i0000000000000000-22000
χ3122-22-2-2-22222-2-22-2-222-2-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i000000002i2i−2i−2i0000000000000000-22000
χ3222-22-2-2-22222-2-22-2-222-2-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i00000000−2i−2i2i2i00000000000000002-2000
χ3322-2-222-2-22000022-2-2-22-22i−2i2−22−200002i2i−2i−2i0000000−i2i22i−2i002−22−2−i2−i2i2i2002-20000−i2−i2i2i2000000000000002−20
χ3422-2-222-2-22000022-2-2-22-22i−2i2−22−20000−2i−2i2i2i0000000−i2i22i−2i002−22−2−i2−i2i2i200-220000i2i2−i2−i200000000000000−220
χ3522-2-222-2-22000022-2-2-22-22i−2i−22−2200002i2i−2i−2i0000000i2−i22i−2i00−22−22i2i2−i2−i2002-20000i2i2−i2−i200000000000000−220
χ3622-2-222-2-22000022-2-2-22-22i−2i−22−220000−2i−2i2i2i0000000i2−i22i−2i00−22−22i2i2−i2−i200-220000−i2−i2i2i2000000000000002−20
χ3722-2-222-2-22000022-2-2-22-2−2i2i2−22−200002i2i−2i−2i0000000i2−i2−2i2i002−22−2i2i2−i2−i200-220000−i2−i2i2i200000000000000−220
χ3822-2-222-2-22000022-2-2-22-2−2i2i2−22−20000−2i−2i2i2i0000000i2−i2−2i2i002−22−2i2i2−i2−i2002-20000i2i2−i2−i2000000000000002−20
χ3922-2-222-2-22000022-2-2-22-2−2i2i−22−2200002i2i−2i−2i0000000−i2i2−2i2i00−22−22−i2−i2i2i200-220000i2i2−i2−i2000000000000002−20
χ4022-2-222-2-22000022-2-2-22-2−2i2i−22−220000−2i−2i2i2i0000000−i2i2−2i2i00−22−22−i2−i2i2i2002-20000−i2−i2i2i200000000000000−220
χ412-22-2-22-2222-22-2-2222-2-2-200000022-2-200002-2000000000000000000000002i−2i2i−2i2i−2i2i−2i02-200000000000000
χ422-22-2-22-2222-22-2-2222-2-2-200000022-2-200002-200000000000000000000000−2i2i−2i2i−2i2i−2i2i02-200000000000000
χ432-22-2-22-2222-22-2-2222-2-2-200000022-2-20000-22000000000000000000000002i−2i2i−2i−2i2i−2i2i0-2200000000000000
χ442-22-2-22-2222-22-2-2222-2-2-200000022-2-20000-2200000000000000000000000−2i2i−2i2i2i−2i2i−2i0-2200000000000000
χ452-2-2-22-22222-2-22-2-2-22-2220000002-2-222-22-20002-200000000000000002-2002-2-220000000002-20000000000
χ462-2-2-22-22222-2-22-2-2-22-2220000002-2-222-22-2000-2200000000000000002-200-222-2000000000-220000000000
χ472-2-2-22-22222-2-22-2-2-22-2220000002-2-22-22-220002-20000000000000000-2200-222-20000000002-20000000000
χ482-2-2-22-22222-2-22-2-2-22-2220000002-2-22-22-22000-220000000000000000-22002-2-22000000000-220000000000
χ492-2-2-22-2222-222-2-2-2-22-222000000-222-22-22-2000002-200000000000000-22000000000000000002-22-2000000
χ502-2-2-22-2222-222-2-2-2-22-222000000-222-22-22-200000-2200000000000000-2200000000000000000-22-22000000
χ512-2-2-22-2222-222-2-2-2-22-222000000-222-2-22-22000002-2000000000000002-2000000000000000002-2-22000000
χ522-2-2-22-2222-222-2-2-2-22-222000000-222-2-22-2200000-22000000000000002-200000000000000000-222-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-24400002222000000-4000000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000400000022-2-20000000000000000000000000000000000000
χ55444-4-4-44-4400004-44-4-4-4400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ56444-4-4-44-4400004-44-4-4-44002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ57444-4-4-44-4-20000-22-2222-200−2i22i22i2−2i2000000000000000000023−23i2−i2−i2i2i6−i6i6−i600000000000000000000000000000
χ58444-4-4-44-4-20000-22-2222-200−2i22i22i2−2i20000000000000000000−2323i2−i2−i2i2−i6i6−i6i600000000000000000000000000000
χ59444-4-4-44-4-20000-22-2222-2002i2−2i2−2i22i2000000000000000000023−23−i2i2i2−i2−i6i6−i6i600000000000000000000000000000
χ60444-4-4-44-4-20000-22-2222-2002i2−2i2−2i22i20000000000000000000−2323−i2i2i2−i2i6−i6i6−i600000000000000000000000000000
χ6144-44-4-4-444-4-4444-4-444-4-4000000-44-44000000000000000000000000000000000000000000000000000000
χ6244-44-4-4-44-244-4-4-222-2-222004i4i−4i−4i-22-2200000000000000000−2i−2i2i2i000000000000000000000000000000000
χ6344-44-4-4-44-244-4-4-222-2-22200−4i−4i4i4i-22-22000000000000000002i2i−2i−2i000000000000000000000000000000000
χ6444-44-4-4-44-2-4-444-222-2-2220000002-22-200000000000000000000023−23−232300000000000000000000000000000
χ6544-44-4-4-44-2-4-444-222-2-2220000002-22-2000000000000000000000−232323−2300000000000000000000000000000
χ6644-4-444-4-4-20000-2-2222-224i−4i22−2222−22000000000000000−2i22i2−2i2i00−22−22i2i2−i2−i200000000000000000000000000000
χ6744-4-444-4-4-20000-2-2222-224i−4i−2222−22220000000000000002i2−2i2−2i2i002−22−2−i2−i2i2i200000000000000000000000000000
χ6844-4-444-4-4-20000-2-2222-22−4i4i22−2222−220000000000000002i2−2i22i−2i00−22−22−i2−i2i2i200000000000000000000000000000
χ6944-4-444-4-4-20000-2-2222-22−4i4i−2222−2222000000000000000−2i22i22i−2i002−22−2i2i2−i2−i200000000000000000000000000000
χ704-4444-4-4-440000-4-44-444-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ714-4444-4-4-440000-4-44-444-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ724-44-4-44-444-44-44-4444-4-4-4000000-4-444000000000000000000000000000000000000000000000000000000
χ734-44-4-44-44-24-44-42-2-2-2222000000-2-22200004-400000000000000000000000000000000-2200000000000000
χ744-44-4-44-44-24-44-42-2-2-2222000000-2-2220000-44000000000000000000000000000000002-200000000000000
χ754-44-4-44-44-2-44-442-2-2-222200000022-2-2000000000000000000000000000000000000000023−23000000000000
χ764-44-4-44-44-2-44-442-2-2-222200000022-2-20000000000000000000000000000000000000000−2323000000000000
χ774-4-44-444-440000-44-4-44-44000000000000000000000000000000000000000000022−22−222200000000000000000
χ784-4-44-444-440000-44-4-44-440000000000000000000000000000000000000000000−222222−2200000000000000000
χ794-4-4-44-444-24-4-44222-22-2-2000000-222-200000004-4000000000000000000000000000000000-220000000000
χ804-4-4-44-444-24-4-44222-22-2-2000000-222-20000000-440000000000000000000000000000000002-20000000000
χ814-4-4-44-444-2-444-4222-22-2-20000002-2-220000000004-4000000000000000000000000000000000-2200000000
χ824-4-4-44-444-2-444-4222-22-2-20000002-2-22000000000-440000000000000000000000000000000002-200000000
χ838-8888-8-8-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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