Finite Group Databasebeta

← Group #10852217

Character table — Group #10852217

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444466888888888888888888888888881212121616161616161624242424242424242424242448
order1222222222366622446666664422444444446666661212121212121212121244441212121212122244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-1-1-1-1-1-11
χ311111111111111111111111111-1-11111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-11111-1-11-1-11-1-11111-1
χ5111111111111111111111111-1-111111111111111111111111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1111111-1
χ7111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-11
χ911111111111111-1-1-1-111111111111-11-111-1-1-1-11111-1-11111-1-1-1-1111-1-1-111-1-111-11-1-11-111-1-1-1
χ1011111111111111-1-1-1-11111111111-11-11-1-111-1-11111-1-1-1-1-1-11111111-1-1-1-1-11111-1-11-1-11-1-111-1
χ1111111111111111-1-1-1-111111111-1-11-11-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-1-11-1-1-1111
χ1211111111111111-1-1-1-111111111-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-1111-1-11
χ1311111111111111-1-1-1-1111111-1-1111-11-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-11-1-1111
χ1411111111111111-1-1-1-1111111-1-111-11-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-111-111-1-11
χ1511111111111111-1-1-1-1111111-1-1-1-11-11-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-111111-111-1111-1-1-1
χ1611111111111111-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-11111-111-1-1-111-1
χ172222222222-1-1-1-12222-1-1-1-1-1-1002222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10002-1-1-1-1-1-10000000000000
χ182222222222-1-1-1-12222-1-1-1-1-1-10022-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110002-1-111110000000000000
χ192222222222-1-1-1-12222-1-1-1-1-1-100-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1000-21111110000000000000
χ202222222222-1-1-1-12222-1-1-1-1-1-100-2-2-2-2-2-22222-1-11111-1-111111111000-211-1-1-1-10000000000000
χ212222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-100222-22-222-2-211-1-1-1-111-1-1-1-11111000-211-1-1110000000000000
χ222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-10022-22-22-2-22211-1-1-1-1111111-1-1-1-1000-21111-1-10000000000000
χ232222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-100-2-22-22-2-2-22211111111-1-1-1-111110002-1-111-1-10000000000000
χ242222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-100-2-2-22-2222-2-2111111111111-1-1-1-10002-1-1-1-1110000000000000
χ2522222-2-2-2-22222222-2-22-2-22-2-2220000000000220000-2-2000000002-2-2000000000-20020000000
χ2622222-2-2-2-22222222-2-22-2-22-2-2-2-20000000000220000-2-200000000-222000000000200-20000000
χ2722222-2-2-2-222222-2-2222-2-22-2-2220000000000-2-2000022000000002-2-2000000000200-20000000
χ2822222-2-2-2-222222-2-2222-2-22-2-2-2-20000000000-2-200002200000000-222000000000-20020000000
χ292222-22-22-2-222220000-22-2-22-22200020-2000000000000000022-2-2-22-200000000000200-200000
χ302222-22-22-2-222220000-22-2-22-222000-2020000000000000000-2-222-22-200000000000-200200000
χ312222-22-22-2-222220000-22-2-22-2-2-200020-2000000000000000022-2-22-2200000000000-200200000
χ322222-22-22-2-222220000-22-2-22-2-2-2000-2020000000000000000-2-2222-2200000000000200-200000
χ332222-2-22-22-222220000-2-22-2-22220020-2000000000000022-2-20000-2-220000000000200-2000000
χ342222-2-22-22-222220000-2-22-2-222200-2020000000000000-2-2220000-2-220000000000-2002000000
χ352222-2-22-22-222220000-2-22-2-22-2-20020-2000000000000022-2-2000022-20000000000-2002000000
χ362222-2-22-22-222220000-2-22-2-22-2-200-2020000000000000-2-222000022-20000000000200-2000000
χ3722-2-2-222-2-2222-2-22-22-2-2-2-22220000000000002-200002-2000000000000000000000000002i−2i2i−2i0
χ3822-2-2-222-2-2222-2-22-22-2-2-2-22220000000000002-200002-200000000000000000000000000−2i2i−2i2i0
χ3922-2-2-222-2-2222-2-2-22-22-2-2-2222000000000000-220000-22000000000000000000000000002i−2i−2i2i0
χ4022-2-2-222-2-2222-2-2-22-22-2-2-2222000000000000-220000-2200000000000000000000000000−2i2i2i−2i0
χ4122-2-2-2-2-222222-2-22-2-22-2222-2-2000000002i−2i2i−2i2-20000-22000000000000002i−2i2i−2i0000000000000
χ4222-2-2-2-2-222222-2-22-2-22-2222-2-200000000−2i2i−2i2i2-20000-2200000000000000−2i2i−2i2i0000000000000
χ4322-2-2-2-2-222222-2-2-222-2-2222-2-2000000002i−2i−2i2i-2200002-2000000000000002i−2i−2i2i0000000000000
χ4422-2-2-2-2-222222-2-2-222-2-2222-2-200000000−2i2i2i−2i-2200002-200000000000000−2i2i2i−2i0000000000000
χ4522-2-2-2-2-2222-1-1112-2-221-1-1-111000000002i−2i2i−2i-11−i3−i3i3i31-13−33−33−33−30000−i3i3−ii−ii0000000000000
χ4622-2-2-2-2-2222-1-1112-2-221-1-1-111000000002i−2i2i−2i-11i3i3−i3−i31-1−33−33−33−330000i3−i3−ii−ii0000000000000
χ4722-2-2-2-2-2222-1-1112-2-221-1-1-11100000000−2i2i−2i2i-11−i3−i3i3i31-1−33−33−33−330000−i3i3i−ii−i0000000000000
χ4822-2-2-2-2-2222-1-1112-2-221-1-1-11100000000−2i2i−2i2i-11i3i3−i3−i31-13−33−33−33−30000i3−i3i−ii−i0000000000000
χ4922-2-2-2-2-2222-1-111-222-21-1-1-111000000002i−2i−2i2i1-1−i3−i3i3i3-113−33−3−33−330000i3−i3−iii−i0000000000000
χ5022-2-2-2-2-2222-1-111-222-21-1-1-111000000002i−2i−2i2i1-1i3i3−i3−i3-11−33−333−33−30000−i3i3−iii−i0000000000000
χ5122-2-2-2-2-2222-1-111-222-21-1-1-11100000000−2i2i2i−2i1-1−i3−i3i3i3-11−33−333−33−30000i3−i3i−i−ii0000000000000
χ5222-2-2-2-2-2222-1-111-222-21-1-1-11100000000−2i2i2i−2i1-1i3i3−i3−i3-113−33−3−33−330000−i3i3i−i−ii0000000000000
χ5344444-4-4-4-44-2-2-2-244-4-4-222-222000000000000-2-20000220000000000000000000000000000000
χ5444444-4-4-4-44-2-2-2-2-4-444-222-222000000000000220000-2-20000000000000000000000000000000
χ554444-44-44-4-4-2-2-2-200002-222-220000040-40000000000000000-2-22200000000000000000000000
χ564444-44-44-4-4-2-2-2-200002-222-2200000-404000000000000000022-2-200000000000000000000000
χ574444-4-44-44-4-2-2-2-2000022-222-2000040-40000000000000-2-222000000000000000000000000000
χ584444-4-44-44-4-2-2-2-2000022-222-20000-404000000000000022-2-2000000000000000000000000000
χ5944-4-444-4-44-444-4-400004-44-44-4000000000000000000000000000000000000000000000000000
χ6044-4-444-4-44-4-2-2220000-22-22-220000000000000000000023−23−2323000000000000000000000000000
χ6144-4-444-4-44-4-2-2220000-22-22-2200000000000000000000−232323−23000000000000000000000000000
χ6244-4-44-444-4-444-4-4000044-4-4-44000000000000000000000000000000000000000000000000000
χ6344-4-44-444-4-4-2-2220000-2-2222-200000000000000000000000023−23−232300000000000000000000000
χ6444-4-44-444-4-4-2-2220000-2-2222-2000000000000000000000000−232323−2300000000000000000000000
χ6544-4-4-444-4-44-2-2224-44-4222-2-2-2000000000000-220000-220000000000000000000000000000000
χ6644-4-4-444-4-44-2-222-44-44222-2-2-20000000000002-200002-20000000000000000000000000000000
χ674-4-440000004-44-400000000004-42-200000000002-22-2000000000000000000002-200000000000
χ684-4-440000004-44-400000000004-4-220000000000-22-2200000000000000000000-2200000000000
χ694-4-440000004-44-40000000000-442-200000000002-22-200000000000000000000-2200000000000
χ704-4-440000004-44-40000000000-44-220000000000-22-22000000000000000000002-200000000000
χ718-88-80000008-8-880000000000000000000000000000000000000000000000000000000000000
χ728-88-8000000-444-4000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ738-88-8000000-444-40000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ748-8-88000000-44-440000000000004-40000000000-22-22000000000000000000000000000000000
χ758-8-88000000-44-44000000000000-4400000000002-22-2000000000000000000000000000000000

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