Finite Group Databasebeta

← Group #349257

Character table — Group #349257

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222444444444444444444448888888888888888888816161616161616161616161616161616
order12222222222222224444444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1
χ10111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ11111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-22222-2-20000-2-200000000-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-22222-2-2-2-2-2-20000-2-2000000002200000000000000000000
χ19222222222222-2-2-2-22222-2-22222-2-2-2-2-2-200002200000000-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000022000000002200000000000000000000
χ2122222222-2-2-2-2000000002-222-2-222-2-22-200220022-2-200000000-2-20000000000000000
χ2222222222-2-2-2-2000000002-222-2-222-2-22-200-2-200-2-22200000000220000000000000000
χ2322222222-2-2-2-2000000002-2-2-222-2-2222-2002200-2-22200000000-2-20000000000000000
χ2422222222-2-2-2-2000000002-2-2-222-2-2222-200-2-20022-2-200000000220000000000000000
χ2522222222-2-2-2-200000000-2222-2-2-2-222-22220000000022-2-200-2-2000000000000000000
χ2622222222-2-2-2-200000000-2222-2-2-2-222-22-2-200000000-2-2220022000000000000000000
χ2722222222-2-2-2-200000000-22-2-22222-2-2-222200000000-2-22200-2-2000000000000000000
χ2822222222-2-2-2-200000000-22-2-22222-2-2-22-2-20000000022-2-20022000000000000000000
χ29222-2-2-2-222-2-2222-2-222-2-20000002-22-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ30222-2-2-2-222-2-2222-2-222-2-20000002-22-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ31222-2-2-2-222-2-2222-2-2-2-222000000-22-22000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ32222-2-2-2-222-2-2222-2-2-2-222000000-22-22000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ33222-2-2-2-222-2-22-2-22222-2-2000000-22-22000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ34222-2-2-2-222-2-22-2-22222-2-2000000-22-22000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ35222-2-2-2-222-2-22-2-222-2-2220000002-22-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ36222-2-2-2-222-2-22-2-222-2-2220000002-22-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3722-2-222-2-222-2-22-22-200002200000000-2-200002-22-22-22-22-20000000000000000000000
χ3822-2-222-2-222-2-22-22-200002200000000-2-200002-2-22-22-22-220000000000000000000000
χ3922-2-222-2-222-2-22-22-20000-2-200000000222i−2i2i−2i-2200000000002i−2i2i−2i0000000000000000
χ4022-2-222-2-222-2-22-22-20000-2-20000000022−2i2i−2i2i-220000000000−2i2i−2i2i0000000000000000
χ4122-2-222-2-222-2-2-22-2200002200000000-2-20000-222-22-2-22-220000000000000000000000
χ4222-2-222-2-222-2-2-22-2200002200000000-2-20000-22-22-222-22-20000000000000000000000
χ4322-2-222-2-222-2-2-22-220000-2-200000000222i−2i−2i2i2-200000000002i−2i−2i2i0000000000000000
χ4422-2-222-2-222-2-2-22-220000-2-20000000022−2i2i2i−2i2-20000000000−2i2i2i−2i0000000000000000
χ4522-2-222-2-2-2-22200002i−2i2i−2i2-200000000-222i−2i00002-2-2200002i−2i−2i2i000000000000000000
χ4622-2-222-2-2-2-22200002i−2i2i−2i2-200000000-22−2i2i0000-222-200002i−2i2i−2i000000000000000000
χ4722-2-222-2-2-2-22200002i−2i2i−2i-22000000002-2002i−2i000000-222-2−2i2i00−2i2i0000000000000000
χ4822-2-222-2-2-2-22200002i−2i2i−2i-22000000002-200−2i2i0000002-2-22−2i2i002i−2i0000000000000000
χ4922-2-222-2-2-2-2220000−2i2i−2i2i2-200000000-222i−2i0000-222-20000−2i2i−2i2i000000000000000000
χ5022-2-222-2-2-2-2220000−2i2i−2i2i2-200000000-22−2i2i00002-2-220000−2i2i2i−2i000000000000000000
χ5122-2-222-2-2-2-2220000−2i2i−2i2i-22000000002-2002i−2i0000002-2-222i−2i00−2i2i0000000000000000
χ5222-2-222-2-2-2-2220000−2i2i−2i2i-22000000002-200−2i2i000000-222-22i−2i002i−2i0000000000000000
χ53444-4-4-4-44-444-4000000000000004-4-4400000000000000000000000000000000000000
χ54444-4-4-4-44-444-400000000000000-444-400000000000000000000000000000000000000
χ5544-44-4-44-44-44-44-4-440000000000000000000000000000000000000000000000000000
χ5644-44-4-44-44-44-4-444-40000000000000000000000000000000000000000000000000000
χ5744-44-4-44-4-44-4400004i−4i−4i4i000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-44-440000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ594-44-44-44-400000000000000004-40000000000000000000000000000002i−2i2i−2i00000000
χ604-44-44-44-400000000000000004-4000000000000000000000000000000−2i2i−2i2i00000000
χ614-44-44-44-40000000000000000-440000000000000000000000000000002i−2i−2i2i00000000
χ624-44-44-44-40000000000000000-44000000000000000000000000000000−2i2i2i−2i00000000
χ634-4-4-4-4444000000000000004-400000000000000000000000000002-22-2000000000000
χ644-4-4-4-4444000000000000004-40000000000000000000000000000-22-22000000000000
χ654-4-4-4-444400000000000000-4400000000000000000000000000002-2-22000000000000
χ664-4-4-4-444400000000000000-440000000000000000000000000000-222-2000000000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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