Finite Group Databasebeta

← Group #10823687

Character table — Group #10823687

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222233334444444444666666888888888888888812121212161616161616161616161616242424242424242424242424
order1222222222366644442222666666444444224444444444666644446612121212121212121212244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11-1-1-111-1-1-1-1111111111-1-1-11-111-1-1-1-1-1-11-11-111-1-1-1-1
χ31111111111111111111111111111111111-11-11-1-1-1-111-1-111111111-11-1-1-11-1-111-1-1-1-1-11-11-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-11111111111111-11-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-1-1-11111-1-11-11-1-1-11111
χ7111111111111111111-1-1-1-1111111111111-11-11-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1-11-1111-1-111
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-1-1-11-1-1-11-111-1-1-1-111-11-11-1-11111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-1-1-11-1-1-11-1-111-1-1111-11-111-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-111111-1-1-11-1-1-1111111-11-1111-1-1-1-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-11-1-1-1111-1-111111-11-1-1-111-1-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111
χ172222222222-1-1-1-100002222-1-1-1-1-1-1000000222222222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222222-1-1-1-100002222-1-1-1-1-1-10000002-22-2-2-222-2-2-2-2-1-1-1-10000-1111-11-1-11111000000000000
χ192222222222-1-1-1-100002222-1-1-1-1-1-1000000-22-22-2-2-2-222-2-2-1-1-1-100001-1111-111-1-111000000000000
χ202222222222-1-1-1-100002222-1-1-1-1-1-1000000-2-2-2-222-2-2-2-222-1-1-1-1000011-1-1111111-1-1000000000000
χ212222222222-1-1-1-10000-2-2-2-2-1-1-1-1-1-1000000222222-2-2-2-2-2-211110000-1-1-1-1-1-1111111000000000000
χ222222222222-1-1-1-10000-2-2-2-2-1-1-1-1-1-10000002-22-2-2-2-2-2222211110000-1111-1111-1-1-1-1000000000000
χ232222222222-1-1-1-10000-2-2-2-2-1-1-1-1-1-1000000-22-22-2-222-2-222111100001-1111-1-1-111-1-1000000000000
χ242222222222-1-1-1-10000-2-2-2-2-1-1-1-1-1-1000000-2-2-2-2222222-2-21111000011-1-111-1-1-1-111000000000000
χ2522222-2-22-2-22222222200002-2-22-2-222-2-2-2-200002-200000000000000002-200000000-220000000000
χ2622222-2-22-2-22222222200002-2-22-2-222-2-2-2-20000-220000000000000000-22000000002-20000000000
χ2722222-2-22-2-22222-2-2-2-200002-2-22-2-2-2-2222200002-200000000000000002-2000000002-20000000000
χ2822222-2-22-2-22222-2-2-2-200002-2-22-2-2-2-222220000-220000000000000000-2200000000-220000000000
χ292222-22-2-22-2222222220000-22-2-22-2-2-222-2-2020-2000000000000000002000-2000000000-202000000
χ302222-22-2-22-2222222220000-22-2-22-2-2-222-2-20-20200000000000000000-2000200000000020-2000000
χ312222-22-2-22-22222-2-2-2-20000-22-2-22-222-2-222020-2000000000000000002000-200000000020-2000000
χ322222-22-2-22-22222-2-2-2-20000-22-2-22-222-2-2220-20200000000000000000-20002000000000-202000000
χ332222-2-22-2-22222222220000-2-22-2-22-2-2-2-22220-2000000000000000002000-2000000000-2020000000
χ342222-2-22-2-22222222220000-2-22-2-22-2-2-2-222-20200000000000000000-2000200000000020-20000000
χ352222-2-22-2-222222-2-2-2-20000-2-22-2-222222-2-220-2000000000000000002000-200000000020-20000000
χ362222-2-22-2-222222-2-2-2-20000-2-22-2-222222-2-2-20200000000000000000-20002000000000-2020000000
χ3722-2-222-2-2-222-2-222i2i−2i−2i0000-2-2222-22i−2i2i−2i2i−2i000000002-20000000000000000002-200000000002i−2i00
χ3822-2-222-2-2-222-2-222i2i−2i−2i0000-2-2222-22i−2i2i−2i2i−2i00000000-22000000000000000000-220000000000−2i2i00
χ3922-2-222-2-2-222-2-22−2i−2i2i2i0000-2-2222-2−2i2i−2i2i−2i2i000000002-20000000000000000002-20000000000−2i2i00
χ4022-2-222-2-2-222-2-22−2i−2i2i2i0000-2-2222-2−2i2i−2i2i−2i2i00000000-22000000000000000000-2200000000002i−2i00
χ4122-2-22-22-22-22-2-222i2i−2i−2i0000-22-22-222i−2i−2i2i−2i2i0000002-20000000000000000002-200000000002i−2i0000
χ4222-2-22-22-22-22-2-222i2i−2i−2i0000-22-22-222i−2i−2i2i−2i2i000000-22000000000000000000-220000000000−2i2i0000
χ4322-2-22-22-22-22-2-22−2i−2i2i2i0000-22-22-22−2i2i2i−2i2i−2i0000002-20000000000000000002-20000000000−2i2i0000
χ4422-2-22-22-22-22-2-22−2i−2i2i2i0000-22-22-22−2i2i2i−2i2i−2i000000-22000000000000000000-2200000000002i−2i0000
χ4522-2-2-2222-2-22-2-222i2i−2i−2i22-2-22-2-2-222−2i2i2i−2i−2i2i00000000000022-2-22i2i−2i−2i000000000000000000000000
χ4622-2-2-2222-2-22-2-222i2i−2i−2i-2-2222-2-2-222−2i2i2i−2i−2i2i000000000000-2-222−2i−2i2i2i000000000000000000000000
χ4722-2-2-2222-2-22-2-22−2i−2i2i2i22-2-22-2-2-2222i−2i−2i2i2i−2i00000000000022-2-2−2i−2i2i2i000000000000000000000000
χ4822-2-2-2222-2-22-2-22−2i−2i2i2i-2-2222-2-2-2222i−2i−2i2i2i−2i000000000000-2-2222i2i−2i−2i000000000000000000000000
χ4922-2-2-2-2-22222-2-222i2i−2i−2i0000222-2-2-2−2i2i−2i2i2i−2i00000000002i−2i0000000000000000002i−2i00000000002-2
χ5022-2-2-2-2-22222-2-222i2i−2i−2i0000222-2-2-2−2i2i−2i2i2i−2i0000000000−2i2i000000000000000000−2i2i0000000000-22
χ5122-2-2-2-2-22222-2-22−2i−2i2i2i0000222-2-2-22i−2i2i−2i−2i2i00000000002i−2i0000000000000000002i−2i0000000000-22
χ5222-2-2-2-2-22222-2-22−2i−2i2i2i0000222-2-2-22i−2i2i−2i−2i2i0000000000−2i2i000000000000000000−2i2i00000000002-2
χ5344444-4-44-4-4-2-2-2-200000000-222-22200000000004-40000000000000000-2200000000000000000000
χ5444444-4-44-4-4-2-2-2-200000000-222-2220000000000-4400000000000000002-200000000000000000000
χ554444-44-4-44-4-2-2-2-2000000002-222-22000000040-400000000000000000-20002000000000000000000
χ564444-44-4-44-4-2-2-2-2000000002-222-220000000-404000000000000000002000-2000000000000000000
χ574444-4-44-4-44-2-2-2-20000000022-222-200000040-400000000000000000-200020000000000000000000
χ584444-4-44-4-44-2-2-2-20000000022-222-2000000-404000000000000000002000-20000000000000000000
χ5944-4-444-4-4-44-222-20000000022-2-2-22000000000000004-4000000000000000000-2200000000000000
χ6044-4-444-4-4-44-222-20000000022-2-2-2200000000000000-440000000000000000002-200000000000000
χ6144-4-44-44-44-4-222-2000000002-22-22-20000000000004-4000000000000000000-220000000000000000
χ6244-4-44-44-44-4-222-2000000002-22-22-2000000000000-440000000000000000002-20000000000000000
χ6344-4-4-4444-4-4-222-2000044-4-4-2222-2-2000000000000000000-2-2220000000000000000000000000000
χ6444-4-4-4444-4-4-222-20000-4-444-2222-2-200000000000000000022-2-20000000000000000000000000000
χ6544-4-4-4-4-4444-222-200000000-2-2-222200000000000000004i−4i000000000000000000−2i2i000000000000
χ6644-4-4-4-4-4444-222-200000000-2-2-22220000000000000000−4i4i0000000000000000002i−2i000000000000
χ674-44-400000044-4-44i−4i4i−4i2-22-20000000000000000000000002-22-22i−2i2i−2i000000000000000000000000
χ684-44-400000044-4-44i−4i4i−4i-22-22000000000000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ694-44-400000044-4-4−4i4i−4i4i2-22-20000000000000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ704-44-400000044-4-4−4i4i−4i4i-22-22000000000000000000000000-22-222i−2i2i−2i000000000000000000000000
χ714-4-440000004-44-44-4-442-2-220000000000000000000000002-2-222-2-22000000000000000000000000
χ724-4-440000004-44-44-4-44-222-2000000000000000000000000-222-2-222-2000000000000000000000000
χ734-4-440000004-44-4-444-42-2-220000000000000000000000002-2-22-222-2000000000000000000000000
χ744-4-440000004-44-4-444-4-222-2000000000000000000000000-222-22-2-22000000000000000000000000
χ758-88-8000000-4-44400004-44-4000000000000000000000000-22-220000000000000000000000000000
χ768-88-8000000-4-4440000-44-440000000000000000000000002-22-20000000000000000000000000000
χ778-8-88000000-44-4400004-4-44000000000000000000000000-222-20000000000000000000000000000
χ788-8-88000000-44-440000-444-40000000000000000000000002-2-220000000000000000000000000000

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