Finite Group Databasebeta

← Group #10824894

Character table — Group #10824894

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222233334444444444666666888888888888888812121212161616161616161616161616242424242424242424242424
order12222234444666444466888812121212444444444444888888242424248888121212121212242424242424222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-111
χ711111111111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-11111-1-1-1-111
χ811111111111111111111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1111111-1-1
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
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111-1-111-1-11111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ1311111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111111-1-11-1-111-1-1-1-1-1-11111-1-111
χ1411111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-111-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11111-1-1
χ1611111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-111-11111-1-11111-1-1-1-1-1-111
χ172222222-2-2-2-22222222220000-2-2-2-222-2-2-2-20000002i−2i0000000000000000002i−2i00000000002i−2i0000
χ182222222-2-2-2-22222222220000-2-2-2-222-2-2-2-2000000−2i2i000000000000000000−2i2i0000000000−2i2i0000
χ192222222-2-2-2-2222-2-2-2-2220000-2-2-2-2-2-222220000002i−2i0000000000000000002i−2i0000000000−2i2i0000
χ202222222-2-2-2-2222-2-2-2-2220000-2-2-2-2-2-22222000000−2i2i000000000000000000−2i2i00000000002i−2i0000
χ21222222-12222-1-1-10000-1-12222-1-1-1-1000000222222222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-10000-1-12222-1-1-1-10000002222-2-2-2-2-2-2-2-2-1-1-1-100001-1-1-1-11111111000000000000
χ23222222-12222-1-1-10000-1-12222-1-1-1-1000000-2-2-2-22222-2-2-2-2-1-1-1-10000-11111-1-1-11111000000000000
χ24222222-12222-1-1-10000-1-12222-1-1-1-1000000-2-2-2-2-2-2-2-22222-1-1-1-1000011111111-1-1-1-1000000000000
χ25222222-12222-1-1-10000-1-1-2-2-2-2-1-1-1-100000022-2-222-2-222-2-211110000-1-1-111-111-1-111000000000000
χ26222222-12222-1-1-10000-1-1-2-2-2-2-1-1-1-100000022-2-2-2-222-2-222111100001-1-1111-1-111-1-1000000000000
χ27222222-12222-1-1-10000-1-1-2-2-2-2-1-1-1-1000000-2-22222-2-2-2-22211110000-111-1-1-11111-1-1000000000000
χ28222222-12222-1-1-10000-1-1-2-2-2-2-1-1-1-1000000-2-222-2-22222-2-211110000111-1-11-1-1-1-111000000000000
χ292222-2-222-22-22222222-2-200002-22-2-2-222-2-200002-200000000000000-200002000000002-200000000
χ302222-2-222-22-22222222-2-200002-22-2-2-222-2-20000-220000000000000020000-200000000-2200000000
χ312222-2-222-22-2222-2-2-2-2-2-200002-22-222-2-22200002-200000000000000-20000200000000-2200000000
χ322222-2-222-22-2222-2-2-2-2-2-200002-22-222-2-2220000-220000000000000020000-2000000002-200000000
χ332222-2-22-22-222222222-2-222-2-2-22-22-2-2-2-22200000000000022-2-222-2-2000000000000000000000000
χ342222-2-22-22-222222222-2-2-2-222-22-22-2-2-2-222000000000000-2-222-2-222000000000000000000000000
χ352222-2-22-22-22222-2-2-2-2-2-222-2-2-22-222222-2-200000000000022-2-2-2-222000000000000000000000000
χ362222-2-22-22-22222-2-2-2-2-2-2-2-222-22-222222-2-2000000000000-2-22222-2-2000000000000000000000000
χ3722-2-22-2222-2-2-22-22i2i−2i−2i2-20000-2-2222i−2i2i−2i2i−2i000000002-20000000000000000002-200000000002i−2i00
χ3822-2-22-2222-2-2-22-22i2i−2i−2i2-20000-2-2222i−2i2i−2i2i−2i00000000-22000000000000000000-220000000000−2i2i00
χ3922-2-22-2222-2-2-22-2−2i−2i2i2i2-20000-2-222−2i2i−2i2i−2i2i000000002-20000000000000000002-20000000000−2i2i00
χ4022-2-22-2222-2-2-22-2−2i−2i2i2i2-20000-2-222−2i2i−2i2i−2i2i00000000-22000000000000000000-2200000000002i−2i00
χ4122-2-22-22-2-222-22-22i2i−2i−2i2-2000022-2-22i−2i−2i2i−2i2i002-200000000000000000002-2000000000002i−2i000000
χ4222-2-22-22-2-222-22-22i2i−2i−2i2-2000022-2-22i−2i−2i2i−2i2i00-220000000000000000000-2200000000000−2i2i000000
χ4322-2-22-22-2-222-22-2−2i−2i2i2i2-2000022-2-2−2i2i2i−2i2i−2i002-200000000000000000002-200000000000−2i2i000000
χ4422-2-22-22-2-222-22-2−2i−2i2i2i2-2000022-2-2−2i2i2i−2i2i−2i00-220000000000000000000-22000000000002i−2i000000
χ4522-2-2-2222-2-22-22-22i2i−2i−2i-220000-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000002i−2i0000000002-20000000000
χ4622-2-2-2222-2-22-22-22i2i−2i−2i-220000-222-2−2i2i2i−2i−2i2i−2i2i0000000000000000000−2i2i000000000-220000000000
χ4722-2-2-2222-2-22-22-2−2i−2i2i2i-220000-222-22i−2i−2i2i2i−2i2i−2i00000000000000000002i−2i000000000-220000000000
χ4822-2-2-2222-2-22-22-2−2i−2i2i2i-220000-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000−2i2i0000000002-20000000000
χ4922-2-2-222-222-2-22-22i2i−2i−2i-2200002-2-22−2i2i−2i2i2i−2i00000000002i−2i0000000000000000002i−2i00000000002-2
χ5022-2-2-222-222-2-22-22i2i−2i−2i-2200002-2-22−2i2i−2i2i2i−2i0000000000−2i2i000000000000000000−2i2i0000000000-22
χ5122-2-2-222-222-2-22-2−2i−2i2i2i-2200002-2-222i−2i2i−2i−2i2i00000000002i−2i0000000000000000002i−2i0000000000-22
χ5222-2-2-222-222-2-22-2−2i−2i2i2i-2200002-2-222i−2i2i−2i−2i2i0000000000−2i2i000000000000000000−2i2i00000000002-2
χ53444444-2-4-4-4-4-2-2-20000-2-2000022220000000000004i−4i000000000000000000−2i2i0000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-200002222000000000000−4i4i0000000000000000002i−2i0000000000000000
χ554444-4-4-24-44-4-2-2-20000220000-22-2200000000004-40000000000000020000-2000000000000000000
χ564444-4-4-24-44-4-2-2-20000220000-22-220000000000-4400000000000000-200002000000000000000000
χ574444-4-4-2-44-44-2-2-200002244-4-42-22-2000000000000000000-2-2220000000000000000000000000000
χ584444-4-4-2-44-44-2-2-2000022-4-4442-22-200000000000000000022-2-20000000000000000000000000000
χ5944-4-44-4-244-4-42-220000-22000022-2-2000000000000004-4000000000000000000-2200000000000000
χ6044-4-44-4-244-4-42-220000-22000022-2-200000000000000-440000000000000000002-200000000000000
χ6144-4-44-4-2-4-4442-220000-220000-2-222000000004-40000000000000000000-220000000000000000000
χ6244-4-44-4-2-4-4442-220000-220000-2-22200000000-4400000000000000000002-20000000000000000000
χ6344-4-4-44-24-4-442-2200002-200002-2-220000004i−4i0000000000000000000−2i2i000000000000000000000
χ6444-4-4-44-24-4-442-2200002-200002-2-22000000−4i4i00000000000000000002i−2i000000000000000000000
χ6544-4-4-44-2-444-42-2200002-20000-222-200000000000000004i−4i000000000000000000−2i2i000000000000
χ6644-4-4-44-2-444-42-2200002-20000-222-20000000000000000−4i4i0000000000000000002i−2i000000000000
χ674-44-40040000-4-444-44-400002i2−2i20000000000000000000000002i2−2i2002i2−2i2000000000000000000000000
χ684-44-40040000-4-444-44-40000−2i22i2000000000000000000000000−2i22i200−2i22i2000000000000000000000000
χ694-44-40040000-4-44-44-4400002i2−2i20000000000000000000000002i2−2i200−2i22i2000000000000000000000000
χ704-44-40040000-4-44-44-440000−2i22i2000000000000000000000000−2i22i2002i2−2i2000000000000000000000000
χ714-4-4400400004-4-44i−4i−4i4i0022−2200000000000000000000000022−22002i2−2i200000000000000000000000000
χ724-4-4400400004-4-44i−4i−4i4i00−2222000000000000000000000000−222200−2i22i200000000000000000000000000
χ734-4-4400400004-4-4−4i4i4i−4i0022−2200000000000000000000000022−2200−2i22i200000000000000000000000000
χ744-4-4400400004-4-4−4i4i4i−4i00−2222000000000000000000000000−2222002i2−2i200000000000000000000000000
χ758-88-800-4000044-4000000004i2−4i2000000000000000000000000−2i22i20000000000000000000000000000
χ768-88-800-4000044-400000000−4i24i20000000000000000000000002i2−2i20000000000000000000000000000
χ778-8-8800-40000-44400000042−42000000000000000000000000−2222000000000000000000000000000000
χ788-8-8800-40000-444000000−424200000000000000000000000022−22000000000000000000000000000000

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