Finite Group Databasebeta

← Group #268457

Character table — Group #268457

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444224444444444488888888888888888888888844444424
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111
χ511111111111111111111111111-1-111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ611111111111111111111111111-1-111-1-111-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-11-11-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1111-1
χ1011111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-111-11
χ1111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11
χ1211111111111-1-1-1-111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ1311111111111-1-1-1-111111-1-1-1-111-1-11111-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1
χ1411111111111-1-1-1-111111-1-1-1-111-1-11111-1-11111-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-11
χ1511111111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-11
χ1611111111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11111-1
χ17222222222222222-2-2-2-2222-2-2-2-2220022000000-2000000000000000000000000-20-200000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-200-2-2000000-200000000000000000000000020200000
χ1922222222222-2-2-2-2-2-2-2-22-2-222-2-22200-2-2000000200000000000000000000000020-200000
χ2022222222222-2-2-2-2-2-2-2-22-2-222-2-2-2-200220000002000000000000000000000000-20200000
χ2122222222-2-2-222222222-2-2-222-2-2002200220000-20000000000000000000000000-20-20000
χ2222222222-2-2-222222222-2-2-222-2-200-2-200-2-20000-200000000000000000000000002020000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-2220000000022-2-2200000000000000000000000000002-200
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-22200000000-2-22220000000000000000000000000000-2200
χ2522222222-2-2-2-2-2-2-22222-222-2-2-2-2002200-2-2000020000000000000000000000000-2020000
χ2622222222-2-2-2-2-2-2-22222-222-2-2-2-200-2-2002200002000000000000000000000000020-20000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000022-2-2-20000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-2-222-200000000000000000000000000002-200
χ29222-2-22-2-22-2-222-2-2000022-200002-2002-20000000i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i200000000
χ30222-2-22-2-22-2-222-2-2000022-200002-2002-20000000−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i200000000
χ31222-2-22-2-22-2-222-2-2000022-20000-2200-220000000i2i2−i2−i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i200000000
χ32222-2-22-2-22-2-222-2-2000022-20000-2200-220000000−i2−i2i2i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i200000000
χ33222-2-22-2-22-2-2-2-22200002-2200002-200-220000000i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2−i2−i2i2i200000000
χ34222-2-22-2-22-2-2-2-22200002-2200002-200-220000000−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2i2i2−i2−i200000000
χ35222-2-22-2-22-2-2-2-22200002-220000-22002-20000000i2i2−i2−i2−i2−i2i2i200000000−i2−i2i2i2i2i2−i2−i200000000
χ36222-2-22-2-22-2-2-2-22200002-220000-22002-20000000−i2−i2i2i2i2i2−i2−i200000000i2i2−i2−i2−i2−i2i2i200000000
χ3722-22-2-2-220002i−2i2i−2i2-22-20002i−2i00002-2002i−2i000000000000022−2−2i2i2−i2−i22−22−2i2−i2i2−i200000000
χ3822-22-2-2-220002i−2i2i−2i2-22-20002i−2i00002-2002i−2i0000000000000−2−222−i2−i2i2i2−22−22−i2i2−i2i200000000
χ3922-22-2-2-220002i−2i2i−2i2-22-20002i−2i0000-2200−2i2i000000000000022−2−2i2i2−i2−i2−22−22−i2i2−i2i200000000
χ4022-22-2-2-220002i−2i2i−2i2-22-20002i−2i0000-2200−2i2i0000000000000−2−222−i2−i2i2i22−22−2i2−i2i2−i200000000
χ4122-22-2-2-22000−2i2i−2i2i2-22-2000−2i2i00002-200−2i2i000000000000022−2−2−i2−i2i2i22−22−2−i2i2−i2i200000000
χ4222-22-2-2-22000−2i2i−2i2i2-22-2000−2i2i00002-200−2i2i0000000000000−2−222i2i2−i2−i2−22−22i2−i2i2−i200000000
χ4322-22-2-2-22000−2i2i−2i2i2-22-2000−2i2i0000-22002i−2i000000000000022−2−2−i2−i2i2i2−22−22i2−i2i2−i200000000
χ4422-22-2-2-22000−2i2i−2i2i2-22-2000−2i2i0000-22002i−2i0000000000000−2−222i2i2−i2−i22−22−2−i2i2−i2i200000000
χ452-22-2-2-22222-2000022-2-2-200002-2000000002-22-202i−2i2i−2i000000002i−2i2i−2i0000000000000000
χ462-22-2-2-22222-2000022-2-2-200002-2000000002-22-20−2i2i−2i2i00000000−2i2i−2i2i0000000000000000
χ472-22-2-2-22222-2000022-2-2-200002-200000000-22-2202i−2i2i−2i00000000−2i2i−2i2i0000000000000000
χ482-22-2-2-22222-2000022-2-2-200002-200000000-22-220−2i2i−2i2i000000002i−2i2i−2i0000000000000000
χ492-22-2-2-222-2-220000-2-222200002-2000000002-2-22000002-22-22-22-200000000000000000000
χ502-22-2-2-222-2-220000-2-222200002-2000000002-2-2200000-22-22-22-2200000000000000000000
χ512-22-2-2-222-2-220000-2-222200002-200000000-222-2000002-22-2-22-2200000000000000000000
χ522-22-2-2-222-2-220000-2-222200002-200000000-222-200000-22-222-22-200000000000000000000
χ53444-4-44-4-4-44444-4-40000-4-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-444-4-4440000-44-40000000000000000000000000000000000000000000000000
χ5544-44-4-4-440004i−4i4i−4i-44-44000−4i4i00000000000000000000000000000000000000000000000
χ5644-44-4-4-44000−4i4i−4i4i-44-440004i−4i00000000000000000000000000000000000000000000000
χ5744-4-44-44-40004i−4i−4i4i00000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ5844-4-44-44-40004i−4i−4i4i0000000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ5944-4-44-44-4000−4i4i4i−4i00000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ6044-4-44-44-4000−4i4i4i−4i0000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ614-4444-4-4-44-4400000000-4000000000000000000022−22−22220000000000000000000000000000
χ624-4444-4-4-44-4400000000-40000000000000000000−222222−220000000000000000000000000000
χ634-4444-4-4-4-44-4000000004000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ644-4444-4-4-4-44-400000000400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ654-44-4-4-44444-40000-4-444-40000-44000000000000000000000000000000000000000000000
χ664-44-4-4-444-4-44000044-4-440000-44000000000000000000000000000000000000000000000
χ674-4-4-444-4400000004-4-440000000000000000000000000000000022−22−22220000000000000000
χ684-4-4-444-4400000004-4-4400000000000000000000000000000000−222222−220000000000000000
χ694-4-4-444-440000000-444-4000000000000000000000000000022−22−222200000000000000000000
χ704-4-4-444-440000000-444-40000000000000000000000000000−222222−2200000000000000000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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