Finite Group Databasebeta

← Group #268404

Character table — Group #268404

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444222244444444488888888888888888888888824444444
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
χ3111111111111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ511111111111111111111111111-1-1-1-111-1-1111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ91111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-11-11-1
χ101111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1-11-1-11
χ111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11-11
χ121111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-111-1
χ131111111111111-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11-11
χ141111111111111-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-111-1
χ151111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-11-1
χ161111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1111-1-11
χ1722222222222-2-22222-2-2222-2-2-2-200002200-22200000000000000000000000000-2-2000000
χ1822222222222-2-22222-2-2222-2-2-2-20000-2-200-2-2-20000000000000000000000000022000000
χ1922222222222-2-2-2-2-2-2-2-22-2-222-2-2000022002-2-2000000000000000000000000002-2000000
χ2022222222222-2-2-2-2-2-2-2-22-2-222-2-20000-2-20022200000000000000000000000000-22000000
χ2122222222-2-2-222222222-2-2-222-2-200000022-200220000000000000000000000000000-2-200
χ2222222222-2-2-222222222-2-2-222-2-2000000-2-2-200-2-200000000000000000000000000002200
χ2322222222-2-2-222-2-2-2-222-222-2-2-2-200000022200-2-20000000000000000000000000000-2200
χ2422222222-2-2-222-2-2-2-222-222-2-2-2-2000000-2-22002200000000000000000000000000002-200
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22222-2-2000020000000000000000000000000000002-20000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-222-2-22200002000000000000000000000000000000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-20000-2000000000000000000000000000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2220000-20000000000000000000000000000002-20000
χ29222-22-2-2-22-2-20022-2-20022-2000000002i−2i0002i−2i0022−2−222−2−200000000i2i2−i2−i2i2i2−i2−i200000000
χ30222-22-2-2-22-2-20022-2-20022-2000000002i−2i0002i−2i00−2−222−2−22200000000−i2−i2i2i2−i2−i2i2i200000000
χ31222-22-2-2-22-2-20022-2-20022-200000000−2i2i000−2i2i0022−2−222−2−200000000−i2−i2i2i2−i2−i2i2i200000000
χ32222-22-2-2-22-2-20022-2-20022-200000000−2i2i000−2i2i00−2−222−2−22200000000i2i2−i2−i2i2i2−i2−i200000000
χ33222-22-2-2-22-2-200-2-222002-22000000002i−2i000−2i2i0022−2−2−2−22200000000i2i2−i2−i2−i2−i2i2i200000000
χ34222-22-2-2-22-2-200-2-222002-22000000002i−2i000−2i2i00−2−22222−2−200000000−i2−i2i2i2i2i2−i2−i200000000
χ35222-22-2-2-22-2-200-2-222002-2200000000−2i2i0002i−2i0022−2−2−2−22200000000−i2−i2i2i2i2i2−i2−i200000000
χ36222-22-2-2-22-2-200-2-222002-2200000000−2i2i0002i−2i00−2−22222−2−200000000i2i2−i2−i2−i2−i2i2i200000000
χ3722-2-2-222-20002-22i−2i2i−2i2-20002i−2i000000002i−2i0002-200000000i2i2−i2−i222−2−22−22−2i2−i2i2−i200000000
χ3822-2-2-222-20002-22i−2i2i−2i2-20002i−2i000000002i−2i0002-200000000−i2−i2i2i2−2−222−22−22−i2i2−i2i200000000
χ3922-2-2-222-20002-22i−2i2i−2i2-20002i−2i00000000−2i2i000-2200000000i2i2−i2−i222−2−2−22−22−i2i2−i2i200000000
χ4022-2-2-222-20002-22i−2i2i−2i2-20002i−2i00000000−2i2i000-2200000000−i2−i2i2i2−2−2222−22−2i2−i2i2−i200000000
χ4122-2-2-222-20002-2−2i2i−2i2i2-2000−2i2i000000002i−2i000-2200000000i2i2−i2−i2−2−2222−22−2−i2i2−i2i200000000
χ4222-2-2-222-20002-2−2i2i−2i2i2-2000−2i2i000000002i−2i000-2200000000−i2−i2i2i222−2−2−22−22i2−i2i2−i200000000
χ4322-2-2-222-20002-2−2i2i−2i2i2-2000−2i2i00000000−2i2i0002-200000000i2i2−i2−i2−2−222−22−22i2−i2i2−i200000000
χ4422-2-2-222-20002-2−2i2i−2i2i2-2000−2i2i00000000−2i2i0002-200000000−i2−i2i2i222−2−22−22−2−i2i2−i2i200000000
χ452-2-2-222-2222-2220000-2-2-200002-22-22-200000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ462-2-2-222-2222-2220000-2-2-200002-22-22-20000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ472-2-2-222-2222-2220000-2-2-200002-2-22-2200000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ482-2-2-222-2222-2220000-2-2-200002-2-22-220000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ492-2-2-222-22-2-22-2-2000022200002-22-2-220000000002-22-200002-22-200000000000000000000
χ502-2-2-222-22-2-22-2-2000022200002-22-2-22000000000-22-220000-22-2200000000000000000000
χ512-2-2-222-22-2-22-2-2000022200002-2-222-20000000002-22-20000-22-2200000000000000000000
χ522-2-2-222-22-2-22-2-2000022200002-2-222-2000000000-22-2200002-22-200000000000000000000
χ53444-44-4-4-4-4440044-4-400-4-440000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-44400-4-44400-44-40000000000000000000000000000000000000000000000000
χ5544-44-4-4-44000004i−4i−4i4i000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ5644-44-4-4-44000004i−4i−4i4i00000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ5744-44-4-4-4400000−4i4i4i−4i000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ5844-44-4-4-4400000−4i4i4i−4i00000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ5944-4-4-444-4000-444i−4i4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ6044-4-4-444-4000-44−4i4i−4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ614-444-44-4-40004-40000-44000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ624-444-44-4-40004-40000-4400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-444-44-4-4000-4400004-400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ644-444-44-4-4000-4400004-40000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ654-4-444-44-44-4400000000-4000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ664-4-444-44-44-4400000000-400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ674-4-444-44-4-44-4000000004000000000000000000022−22−22220000000000000000000000000000
χ684-4-444-44-4-44-40000000040000000000000000000−222222−220000000000000000000000000000
χ694-4-4-444-4444-4-4-4000044-40000-44000000000000000000000000000000000000000000000
χ704-4-4-444-44-4-44440000-4-440000-44000000000000000000000000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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