Finite Group Databasebeta

← Group #296767

Character table — Group #296767

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444444444444422444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-11111-1-11-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-111-11
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1111-1
χ172222222222-2-222-2-2222222-2-2-2-222-2-22200-2-200-2-20000000000000000000000000000
χ182222222222-2-222-2-22222-2-22222-2-2-2-2-2-2002200-2-20000000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-222-2-2-2-222-2-2-2-2002200220000000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22200-2-200220000000000000000000000000000
χ2122222222-2-222-2-222000022-2-222-2-2-2-200220022000000000000000000-2-20000000000
χ2222222222-2-222-2-222000022-2-222-2-2-2-200-2-200-2-2000000000000000000220000000000
χ2322222222-2-222-2-2220000-2-222-2-222-2-2002200-2-2000000000000000000-220000000000
χ2422222222-2-222-2-2220000-2-222-2-222-2-200-2-200220000000000000000002-20000000000
χ2522222222-2-2-2-2-2-2-2-200002222-2-2-2-22200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-200002222-2-2-2-2220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2-2-222222200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2-2-22222220000000000000000000000000000-222-2000000
χ29222-22-2-2-2-2-22-2222-22i2i−2i−2i000000002-2000000002i−2i00002i2i−2i−2i000022-2-2000000000000
χ30222-22-2-2-2-2-22-2222-22i2i−2i−2i000000002-2000000002i−2i0000−2i−2i2i2i0000-2-222000000000000
χ31222-22-2-2-2-2-22-2222-2−2i−2i2i2i000000002-200000000−2i2i00002i2i−2i−2i0000-2-222000000000000
χ32222-22-2-2-2-2-22-2222-2−2i−2i2i2i000000002-200000000−2i2i0000−2i−2i2i2i000022-2-2000000000000
χ33222-22-2-2-2-2-2-2222-222i2i−2i−2i00000000-2200000000−2i2i2i2i−2i−2i000022-2-20000000000000000
χ34222-22-2-2-2-2-2-2222-222i2i−2i−2i00000000-2200000000−2i2i−2i−2i2i2i0000-2-2220000000000000000
χ35222-22-2-2-2-2-2-2222-22−2i−2i2i2i00000000-22000000002i−2i2i2i−2i−2i0000-2-2220000000000000000
χ36222-22-2-2-2-2-2-2222-22−2i−2i2i2i00000000-22000000002i−2i−2i−2i2i2i000022-2-20000000000000000
χ3722-22-2-2-222-2002-2002-22-2002i−2i2i−2i000000002i−2i0000i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ3822-22-2-2-222-2002-2002-22-2002i−2i2i−2i000000002i−2i0000−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ3922-22-2-2-222-2002-2002-22-200−2i2i−2i2i00000000−2i2i0000i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ4022-22-2-2-222-2002-2002-22-200−2i2i−2i2i00000000−2i2i0000−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ4122-22-2-2-222-2002-200-22-22002i−2i2i−2i00000000−2i2i0000i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ4222-22-2-2-222-2002-200-22-22002i−2i2i−2i00000000−2i2i0000−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ4322-22-2-2-222-2002-200-22-2200−2i2i−2i2i000000002i−2i0000i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ4422-22-2-2-222-2002-200-22-2200−2i2i−2i2i000000002i−2i0000−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ4522-2-2-222-2-22002-2002i−2i−2i2i2i−2i00002i−2i002-2000000002−2−22i2−i2−i2i2−i2i2i2−i22−2−22000000000000
χ4622-2-2-222-2-22002-2002i−2i−2i2i2i−2i00002i−2i002-200000000−222−2−i2i2i2−i2i2−i2−i2i2−222−2000000000000
χ4722-2-2-222-2-22002-2002i−2i−2i2i−2i2i0000−2i2i00-22000000002−2−22−i2i2i2−i2−i2i2i2−i2−222−2000000000000
χ4822-2-2-222-2-22002-2002i−2i−2i2i−2i2i0000−2i2i00-2200000000−222−2i2−i2−i2i2i2−i2−i2i22−2−22000000000000
χ4922-2-2-222-2-22002-200−2i2i2i−2i2i−2i00002i−2i00-22000000002−2−22i2−i2−i2i2i2−i2−i2i2−222−2000000000000
χ5022-2-2-222-2-22002-200−2i2i2i−2i2i−2i00002i−2i00-2200000000−222−2−i2i2i2−i2−i2i2i2−i22−2−22000000000000
χ5122-2-2-222-2-22002-200−2i2i2i−2i−2i2i0000−2i2i002-2000000002−2−22−i2i2i2−i2i2−i2−i2i22−2−22000000000000
χ5222-2-2-222-2-22002-200−2i2i2i−2i−2i2i0000−2i2i002-200000000−222−2i2−i2−i2i2−i2i2i2−i2−222−2000000000000
χ53444-44-4-4-4444-4-4-44-4000000000000-4400000000000000000000000000000000000000
χ54444-44-4-4-444-44-4-4-440000000000004-400000000000000000000000000000000000000
χ5544-44-4-4-44-4400-44000000004i−4i−4i4i000000000000000000000000000000000000000000
χ5644-44-4-4-44-4400-4400000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5744-4-4-444-44-400-440000004i−4i0000−4i4i0000000000000000000000000000000000000000
χ5844-4-4-444-44-400-44000000−4i4i00004i−4i0000000000000000000000000000000000000000
χ594-4-444-44-4004-400-440000000000000000000000000000000000000000000000002i2−2i200
χ604-4-444-44-4004-400-44000000000000000000000000000000000000000000000000−2i22i200
χ614-4-444-44-400-44004-400000000000000000000000000000000000000000000002i2−2i20000
χ624-4-444-44-400-44004-40000000000000000000000000000000000000000000000−2i22i20000
χ634-4-4-444-44004400-4-400000000000000004i−4i0000000000000000000000000000000000
χ644-4-4-444-44004400-4-40000000000000000−4i4i0000000000000000000000000000000000
χ654-4-4-444-4400-4-40044000000000000000000004-4000000000000000000000000000000
χ664-4-4-444-4400-4-4004400000000000000000000-44000000000000000000000000000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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