Finite Group Databasebeta

← Group #10827636

Character table — Group #10827636

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order1222222222222236662244446666666666446612121212121212122222222244441212121212121212224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11-11-111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-11-11-1-111-1-1-1-1
χ711111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-1111111
χ811111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-11111
χ911111-1-1-1-1111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-1-1-11111-1-1
χ1011111-1-1-1-1111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-1111-1-111-1-1
χ1111111-1-1-1-1111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-11-1111-1-1-1-111
χ1211111-1-1-1-1111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1111-11-1-1-111-1-111
χ1311111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-1-1-111
χ1411111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-111
χ1511111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111-1-1-1-1111111-1-1
χ1611111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-11111-1-1-1-111-1-1
χ1722222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1000000000000
χ1822222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-211111111000000000000
χ1922222222222222-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-1111111110000000022-2-2-1-1-1-11111000000000000
χ2022222222222222-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-11111111100000000-2-2221111-1-1-1-1000000000000
χ21222222222-2-2-2-222222-2-222-2-2222222-2-2-2-22-2-2-222-2-222-2-200000000000000000000000000000000
χ22222222222-2-2-2-222222-2-2-2-222222222-2-2-2-2-22-2-2-2-222-2-22200000000000000000000000000000000
χ23222222222-2-2-2-22-1-1-1-1-2-222-2-2-1-1-1-1-1-111112-211-1-111-1-1110000000000003−33−33−33−3000000000000
χ24222222222-2-2-2-22-1-1-1-1-2-222-2-2-1-1-1-1-1-111112-211-1-111-1-111000000000000−33−33−33−33000000000000
χ25222222222-2-2-2-22-1-1-1-1-2-2-2-222-1-1-1-1-1-11111-221111-1-111-1-10000000000003−33−3−33−33000000000000
χ26222222222-2-2-2-22-1-1-1-1-2-2-2-222-1-1-1-1-1-11111-221111-1-111-1-1000000000000−33−333−33−3000000000000
χ2722222-2-2-2-222222-1-1-1-1-2-22222-1-11111-1-1-1-1-2-211-1-1-1-11111000000002-22-2-1-111-1-111000000000000
χ2822222-2-2-2-222222-1-1-1-1-2-22222-1-11111-1-1-1-1-2-211-1-1-1-1111100000000-22-2211-1-111-1-1000000000000
χ2922222-2-2-2-222222-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-122111111-1-1-1-1000000002-2-22-1-11111-1-1000000000000
χ3022222-2-2-2-222222-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-122111111-1-1-1-100000000-222-211-1-1-1-111000000000000
χ3122222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-222222-2-2-2-22200000000000000000000000000000000
χ3222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-22-222-2-22222-2-200000000000000000000000000000000
χ3322222-2-2-2-2-2-2-2-22-1-1-1-12222-2-2-1-111111111-22-1-1-1-11111-1-10000000000003−3−333−3−33000000000000
χ3422222-2-2-2-2-2-2-2-22-1-1-1-12222-2-2-1-111111111-22-1-1-1-11111-1-1000000000000−333−3−333−3000000000000
χ3522222-2-2-2-2-2-2-2-22-1-1-1-122-2-222-1-1111111112-2-1-111-1-1-1-1110000000000003−3−33−333−3000000000000
χ3622222-2-2-2-2-2-2-2-22-1-1-1-122-2-222-1-1111111112-2-1-111-1-1-1-111000000000000−333−33−3−33000000000000
χ372222-222-2-222-2-2-222222-20000-2-222-2-222-2-2002-2000000000000000000000000000020-202-2000000
χ382222-222-2-222-2-2-222222-20000-2-222-2-222-2-2002-20000000000000000000000000000-2020-22000000
χ392222-222-2-2-2-222-22222-220000-2-222-2-2-2-22200-220000000000000000000000000000020-2002-20000
χ402222-222-2-2-2-222-22222-220000-2-222-2-2-2-22200-2200000000000000000000000000000-20200-220000
χ412222-2-2-22222-2-2-22222-220000-2-2-2-22222-2-200-22000000000000000000000000000020-20-22000000
χ422222-2-2-22222-2-2-22222-220000-2-2-2-22222-2-200-220000000000000000000000000000-20202-2000000
χ432222-2-2-222-2-222-222222-20000-2-2-2-222-2-222002-20000000000000000000000000000020-200-220000
χ442222-2-2-222-2-222-222222-20000-2-2-2-222-2-222002-200000000000000000000000000000-202002-20000
χ4522-2-2200002-22-2-222-2-2002i−2i2i−2i2-200002-22-200002i−2i2i−2i0000000022-2-200000000000000000000002i−2i
χ4622-2-2200002-22-2-222-2-2002i−2i2i−2i2-200002-22-200002i−2i2i−2i00000000-2-2220000000000000000000000−2i2i
χ4722-2-2200002-22-2-222-2-200−2i2i−2i2i2-200002-22-20000−2i2i−2i2i0000000022-2-20000000000000000000000−2i2i
χ4822-2-2200002-22-2-222-2-200−2i2i−2i2i2-200002-22-20000−2i2i−2i2i00000000-2-22200000000000000000000002i−2i
χ4922-2-220000-22-22-222-2-2002i−2i−2i2i2-20000-22-2200002i−2i−2i2i000022-2-20000000000000000000000002i−2i00
χ5022-2-220000-22-22-222-2-2002i−2i−2i2i2-20000-22-2200002i−2i−2i2i0000-2-222000000000000000000000000−2i2i00
χ5122-2-220000-22-22-222-2-200−2i2i2i−2i2-20000-22-220000−2i2i2i−2i000022-2-2000000000000000000000000−2i2i00
χ5222-2-220000-22-22-222-2-200−2i2i2i−2i2-20000-22-220000−2i2i2i−2i0000-2-2220000000000000000000000002i−2i00
χ534444-444-4-444-4-4-4-2-2-2-24-4000022-2-222-2-22200-220000000000000000000000000000000000000000
χ544444-444-4-4-4-444-4-2-2-2-2-44000022-2-22222-2-2002-20000000000000000000000000000000000000000
χ554444-4-4-44444-4-4-4-2-2-2-2-4400002222-2-2-2-222002-20000000000000000000000000000000000000000
χ564444-4-4-444-4-444-4-2-2-2-24-400002222-2-222-2-200-220000000000000000000000000000000000000000
χ5744-4-4400004-44-4-4-2-222004i−4i4i−4i-220000-22-220000−2i2i−2i2i000000000000000000000000000000000000
χ5844-4-4400004-44-4-4-2-22200−4i4i−4i4i-220000-22-2200002i−2i2i−2i000000000000000000000000000000000000
χ5944-4-440000-44-44-4-2-222004i−4i−4i4i-2200002-22-20000−2i2i2i−2i000000000000000000000000000000000000
χ6044-4-440000-44-44-4-2-22200−4i4i4i−4i-2200002-22-200002i−2i−2i2i000000000000000000000000000000000000
χ6144-4-4-400004-4-44444-4-4000000-4400004-4-4400000000000000000000000000000000000000000000
χ6244-4-4-400004-4-444-2-2220000002-20000-222-20000000023−2323−2300000000000000000000000000000000
χ6344-4-4-400004-4-444-2-2220000002-20000-222-200000000−2323−232300000000000000000000000000000000
χ6444-4-4-40000-444-4444-4-4000000-440000-444-400000000000000000000000000000000000000000000
χ6544-4-4-40000-444-44-2-2220000002-200002-2-220000000023−23−232300000000000000000000000000000000
χ6644-4-4-40000-444-44-2-2220000002-200002-2-2200000000−232323−2300000000000000000000000000000000
χ674-44-40004-4000004-44-400000000004-400000000000000002-22-22-22-2000000000000000000000000
χ684-44-40004-4000004-44-400000000004-40000000000000000-22-22-22-22000000000000000000000000
χ694-44-4000-44000004-44-40000000000-4400000000000000002-22-2-22-22000000000000000000000000
χ704-44-4000-44000004-44-40000000000-440000000000000000-22-222-22-2000000000000000000000000
χ714-4-4404-400000004-4-44000000004-40000000000000000002-2-222-2-22000000000000000000000000
χ724-4-4404-400000004-4-44000000004-4000000000000000000-222-2-222-2000000000000000000000000
χ734-4-440-4400000004-4-4400000000-440000000000000000002-2-22-222-2000000000000000000000000
χ744-4-440-4400000004-4-4400000000-44000000000000000000-222-22-2-22000000000000000000000000
χ758-88-80008-800000-44-440000000000-44000000000000000000000000000000000000000000000000
χ768-88-8000-8800000-44-4400000000004-4000000000000000000000000000000000000000000000000
χ778-8-8808-80000000-444-400000000-4400000000000000000000000000000000000000000000000000
χ788-8-880-880000000-444-4000000004-400000000000000000000000000000000000000000000000000

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