Finite Group Databasebeta

← Group #296296

Character table — Group #296296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11111
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1
χ9111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-11-11-111-1-1
χ10111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-11-11-1-111
χ11111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-1-1111-11-1-1-111
χ12111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-11-1111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-11-1-11-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-111-111-111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-11-1-11-1-1111-1-1111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-111-111-1-1-111-1-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-2000022-2-222-2-200000000000000000000002-2000000-22000000
χ2222222222-2-2-2-22222-2-2000022-2-222-2-20000000000000000000000-220000002-2000000
χ2322222222-2-2-2-22222-2-20000-2-222-2-2220000000000000000000000002-2000000-220000
χ2422222222-2-2-2-22222-2-20000-2-222-2-222000000000000000000000000-220000002-20000
χ2522222222-2-2-2-2-2-2-2-222000022-2-2-2-22200000000000000000000000022000000-2-20000
χ2622222222-2-2-2-2-2-2-2-222000022-2-2-2-222000000000000000000000000-2-2000000220000
χ2722222222-2-2-2-2-2-2-2-2220000-2-22222-2-2000000000000000000000022000000-2-2000000
χ2822222222-2-2-2-2-2-2-2-2220000-2-22222-2-20000000000000000000000-2-200000022000000
χ29222-2-2-22-22-2-220000002i2i−2i−2i00002-22-2002i−2i0000002i2i−2i−2i000022-2-20000000000000000
χ30222-2-2-22-22-2-220000002i2i−2i−2i00002-22-2002i−2i000000−2i−2i2i2i0000-2-2220000000000000000
χ31222-2-2-22-22-2-220000002i2i−2i−2i0000-22-2200−2i2i002i2i−2i−2i000022-2-200000000000000000000
χ32222-2-2-22-22-2-220000002i2i−2i−2i0000-22-2200−2i2i00−2i−2i2i2i0000-2-22200000000000000000000
χ33222-2-2-22-22-2-22000000−2i−2i2i2i00002-22-200−2i2i0000002i2i−2i−2i0000-2-2220000000000000000
χ34222-2-2-22-22-2-22000000−2i−2i2i2i00002-22-200−2i2i000000−2i−2i2i2i000022-2-20000000000000000
χ35222-2-2-22-22-2-22000000−2i−2i2i2i0000-22-22002i−2i002i2i−2i−2i0000-2-22200000000000000000000
χ36222-2-2-22-22-2-22000000−2i−2i2i2i0000-22-22002i−2i00−2i−2i2i2i000022-2-200000000000000000000
χ3722-22-2-2-22-22-220000002i−2i2i−2i2-22-2000000002i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-22-2-2-22-22-220000002i−2i2i−2i2-22-2000000002i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-22-2-2-22-22-220000002i−2i2i−2i-22-2200000000−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ4022-22-2-2-22-22-220000002i−2i2i−2i-22-2200000000−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4122-22-2-2-22-22-22000000−2i2i−2i2i2-22-200000000−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4222-22-2-2-22-22-22000000−2i2i−2i2i2-22-200000000−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4322-22-2-2-22-22-22000000−2i2i−2i2i-22-22000000002i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ4422-22-2-2-22-22-22000000−2i2i−2i2i-22-22000000002i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4522-2-222-2-2-2-22222-2-22-22-2-22000000002-20000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ4622-2-222-2-2-2-22222-2-22-22-2-22000000002-20000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ4722-2-222-2-2-2-22222-2-22-2-222-200000000-220000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ4822-2-222-2-2-2-22222-2-22-2-222-200000000-220000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ4922-2-222-2-2-2-222-2-222-222-2-2200000000-220000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5022-2-222-2-2-2-222-2-222-222-2-2200000000-220000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5122-2-222-2-2-2-222-2-222-22-222-2000000002-20000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5222-2-222-2-2-2-222-2-222-22-222-2000000002-20000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ53444-4-4-44-4-444-4000000000000004-4-4400000000000000000000000000000000000000
χ54444-4-4-44-4-444-400000000000000-444-400000000000000000000000000000000000000
χ5544-44-4-4-444-44-400000000004-4-44000000000000000000000000000000000000000000
χ5644-44-4-4-444-44-40000000000-444-4000000000000000000000000000000000000000000
χ5744-4-444-4-444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ5844-4-444-4-444-4-4-4-4444-400000000000000000000000000000000000000000000000000
χ594-44-44-4-4400004i−4i4i−4i0000000000000000000000000000000000000000000000002-22i−2i
χ604-44-44-4-4400004i−4i4i−4i000000000000000000000000000000000000000000000000-22−2i2i
χ614-44-44-4-440000−4i4i−4i4i0000000000000000000000000000000000000000000000002-2−2i2i
χ624-44-44-4-440000−4i4i−4i4i000000000000000000000000000000000000000000000000-222i−2i
χ634-4-444-44-400004i−4i−4i4i00000000000000000000000000000000000000002-22i−2i00000000
χ644-4-444-44-400004i−4i−4i4i0000000000000000000000000000000000000000-22−2i2i00000000
χ654-4-444-44-40000−4i4i4i−4i00000000000000000000000000000000000000002-2−2i2i00000000
χ664-4-444-44-40000−4i4i4i−4i0000000000000000000000000000000000000000-222i−2i00000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8-8888000000000000000000000000000000000000000000000000000000000000

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