Finite Group Databasebeta

← Group #290652

Character table — Group #290652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244442222444444444444444488888888888888882444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-111-111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-11111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-11111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1111-1-111
χ11111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-1111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-111111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1-1-1-111
χ172222222222222222-2-2-2-22222-2-222-2-2-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ2122222222-2-2-2-2222222-2-200002-2-2-22-200000000000000000000002-202-200000000000
χ2222222222-2-2-2-2222222-2-200002-2-2-22-20000000000000000000000-220-2200000000000
χ2322222222-2-2-2-22222-2-2220000-22-2-2-220000000000000000000000002002-200-2000000
χ2422222222-2-2-2-22222-2-2220000-22-2-2-22000000000000000000000000-200-22002000000
χ2522222222-2-2-2-2-2-2-2-222-2-20000-2222-22000000000000000000000000200-2200-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-20000-2222-22000000000000000000000000-2002-2002000000
χ2722222222-2-2-2-2-2-2-2-2-2-22200002-2222-200000000000000000000002-20-2200000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22200002-2222-20000000000000000000000-2202-200000000000
χ29222-2-2-2-222-22-2000000002i2i−2i−2i2-200-222i−2i00002i2i−2i−2i000022-2-200000000000000000000
χ30222-2-2-2-222-22-2000000002i2i−2i−2i2-200-222i−2i0000−2i−2i2i2i0000-2-22200000000000000000000
χ31222-2-2-2-222-22-2000000002i2i−2i−2i-22002-2−2i2i0000000022-2-200002i2i−2i−2i0000000000000000
χ32222-2-2-2-222-22-2000000002i2i−2i−2i-22002-2−2i2i00000000-2-2220000−2i−2i2i2i0000000000000000
χ33222-2-2-2-222-22-200000000−2i−2i2i2i2-200-22−2i2i00002i2i−2i−2i0000-2-22200000000000000000000
χ34222-2-2-2-222-22-200000000−2i−2i2i2i2-200-22−2i2i0000−2i−2i2i2i000022-2-200000000000000000000
χ35222-2-2-2-222-22-200000000−2i−2i2i2i-22002-22i−2i0000000022-2-20000−2i−2i2i2i0000000000000000
χ36222-2-2-2-222-22-200000000−2i−2i2i2i-22002-22i−2i00000000-2-22200002i2i−2i−2i0000000000000000
χ3722-222-2-2-2-2-22200002-22-22i−2i2i−2i00000000002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ3822-222-2-2-2-2-22200002-22-22i−2i2i−2i00000000002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ3922-222-2-2-2-2-22200002-22-2−2i2i−2i2i0000000000−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ4022-222-2-2-2-2-22200002-22-2−2i2i−2i2i0000000000−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ4122-222-2-2-2-2-2220000-22-222i−2i2i−2i0000000000−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ4222-222-2-2-2-2-2220000-22-222i−2i2i−2i0000000000−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ4322-222-2-2-2-2-2220000-22-22−2i2i−2i2i00000000002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ4422-222-2-2-2-2-2220000-22-22−2i2i−2i2i00000000002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ4522-2-2-222-2-222-22i2i−2i−2i00002-2-22002i−2i00002i−2i002−2−22i2−i2−i2i22−2−22−i2i2i2−i20000000000000000
χ4622-2-2-222-2-222-22i2i−2i−2i00002-2-22002i−2i00002i−2i00−222−2−i2i2i2−i2−222−2i2−i2−i2i20000000000000000
χ4722-2-2-222-2-222-22i2i−2i−2i0000-222-2002i−2i0000−2i2i002−2−22i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ4822-2-2-222-2-222-22i2i−2i−2i0000-222-2002i−2i0000−2i2i00−222−2−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ4922-2-2-222-2-222-2−2i−2i2i2i00002-2-2200−2i2i0000−2i2i002−2−22−i2i2i2−i22−2−22i2−i2−i2i20000000000000000
χ5022-2-2-222-2-222-2−2i−2i2i2i00002-2-2200−2i2i0000−2i2i00−222−2i2−i2−i2i2−222−2−i2i2i2−i20000000000000000
χ5122-2-2-222-2-222-2−2i−2i2i2i0000-222-200−2i2i00002i−2i002−2−22−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ5222-2-2-222-2-222-2−2i−2i2i2i0000-222-200−2i2i00002i−2i00−222−2i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ53444-4-4-4-44-44-440000000000004400-4-400000000000000000000000000000000000000
χ54444-4-4-4-44-44-44000000000000-4-4004400000000000000000000000000000000000000
χ5544-444-4-4-444-4-400004-4-44000000000000000000000000000000000000000000000000
χ5644-444-4-4-444-4-40000-444-4000000000000000000000000000000000000000000000000
χ5744-4-4-444-44-4-444i4i−4i−4i0000000000−4i4i0000000000000000000000000000000000000000
χ5844-4-4-444-44-4-44−4i−4i4i4i00000000004i−4i0000000000000000000000000000000000000000
χ594-444-4-44-400004i−4i4i−4i0000000000000000000000000000000000000000000000002-22i−2i
χ604-444-4-44-400004i−4i4i−4i000000000000000000000000000000000000000000000000-22−2i2i
χ614-444-4-44-40000−4i4i−4i4i0000000000000000000000000000000000000000000000002-2−2i2i
χ624-444-4-44-40000−4i4i−4i4i000000000000000000000000000000000000000000000000-222i−2i
χ634-4-4-44-44400004-4-4400000000000000000000000000000000000000000002-202-20000
χ644-4-4-44-44400004-4-440000000000000000000000000000000000000000000-220-220000
χ654-4-4-44-4440000-444-400000000000000000000000000000000000000000002-20-220000
χ664-4-4-44-4440000-444-40000000000000000000000000000000000000000000-2202-20000
χ678-88-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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