Finite Group Databasebeta

← Group #306811

Character table — Group #306811

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-1111-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-11111-1
χ91111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1111-1-111-1-11
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-111-1-111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-11111111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-1-1-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111-1-11-1-1-1-1-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1111-1-1-1111111-1-1-1
χ17222222222-22-22-22-20000-2-2222222-2-2-2-20000000000-2-2000000200000000000000
χ18222222222-22-22-22-20000-2-22222-2-222220000000000-2-2000000-200000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222-2-222000000000022000000-200000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-222-2-2000000000022000000200000000000000
χ2122222222-22-22-22-222222-2-20000000000-2-222-2-200000022000000000-2000000000
χ2222222222-22-22-22-222222-2-20000000000-2-2-2-222000000-2-20000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000000222222000000-2-2000000000-2000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000000022-2-2-2-2000000220000000002000000000
χ25222-2-2-22-22-2-222-2-222i2i−2i−2i-2200000000002i−2i00000000000000000000002i−2i00002-20
χ26222-2-2-22-22-2-222-2-222i2i−2i−2i-2200000000002i−2i0000000000000000000000−2i2i0000-220
χ27222-2-2-22-22-2-222-2-22−2i−2i2i2i-220000000000−2i2i00000000000000000000002i−2i0000-220
χ28222-2-2-22-22-2-222-2-22−2i−2i2i2i-220000000000−2i2i0000000000000000000000−2i2i00002-20
χ29222-2-2-22-2-222-2-222-20000-2200002-22-2000000002i2i−2i−2i000000000002i−2i0000000000
χ30222-2-2-22-2-222-2-222-20000-2200002-22-200000000−2i−2i2i2i00000000000−2i2i0000000000
χ31222-2-2-22-2-222-2-222-20000-220000-22-22000000002i2i−2i−2i00000000000−2i2i0000000000
χ32222-2-2-22-2-222-2-222-20000-220000-22-2200000000−2i−2i2i2i000000000002i−2i0000000000
χ33222-2-2-22-2-2-222-2-2222i2i−2i−2i2-200002-2-2200−2i2i000000000000000002i−2i000000000000
χ34222-2-2-22-2-2-222-2-2222i2i−2i−2i2-20000-222-200−2i2i00000000000000000−2i2i000000000000
χ35222-2-2-22-2-2-222-2-222−2i−2i2i2i2-200002-2-22002i−2i00000000000000000−2i2i000000000000
χ36222-2-2-22-2-2-222-2-222−2i−2i2i2i2-20000-222-2002i−2i000000000000000002i−2i000000000000
χ3722-22-2-2-220-202020-22i−2i2i−2i00i2i2−i2−i2000000002-2002−22−2i2−i22i−2i22−2−20000000000i2−i2000
χ3822-22-2-2-220-202020-22i−2i2i−2i00i2i2−i2−i200000000-22002−22−2i2−i2−2i2i−2−2220000000000−i2i2000
χ3922-22-2-2-220-202020-22i−2i2i−2i00−i2−i2i2i2000000002-200−22−22−i2i22i−2i−2−2220000000000−i2i2000
χ4022-22-2-2-220-202020-22i−2i2i−2i00−i2−i2i2i200000000-2200−22−22−i2i2−2i2i22−2−20000000000i2−i2000
χ4122-22-2-2-220-202020-2−2i2i−2i2i00i2i2−i2−i2000000002-200−22−22i2−i2−2i2i−2−2220000000000i2−i2000
χ4222-22-2-2-220-202020-2−2i2i−2i2i00i2i2−i2−i200000000-2200−22−22i2−i22i−2i22−2−20000000000−i2i2000
χ4322-22-2-2-220-202020-2−2i2i−2i2i00−i2−i2i2i2000000002-2002−22−2−i2i2−2i2i22−2−20000000000−i2i2000
χ4422-22-2-2-220-202020-2−2i2i−2i2i00−i2−i2i2i200000000-22002−22−2−i2i22i−2i−2−2220000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-44-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ4744-44-4-4-44040-40-4040000002i22i2−2i2−2i20000000000000000−2i22i2000000000000000000000
χ4844-44-4-4-44040-40-404000000−2i2−2i22i22i200000000000000002i2−2i2000000000000000000000
χ4944-4-444-4-404040-40-44-4-44000000000000000000000000000000000000000000000
χ5044-4-444-4-404040-40-4-444-4000000000000000000000000000000000000000000000
χ5144-4-444-4-40-40-4040400000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5244-4-444-4-40-40-404040000000000000000000000−2i22i22i2−2i200000000000000000000000
χ534-4444-4-4-44040-40-400000004-44-4000000000000000000000000000000000000000
χ544-4444-4-4-44040-40-40000000-44-44000000000000000000000000000000000000000
χ554-4444-4-4-4-40-4040400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ564-4444-4-4-4-40-404040000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ574-44-4-44-4440-40-40400000000000000000000000000000000000000000002i2−2i200000
χ584-44-4-44-4440-40-4040000000000000000000000000000000000000000000−2i22i200000
χ594-44-4-44-44-404040-40000000000000004i−4i000000000000000000000000000000000
χ604-44-4-44-44-404040-4000000000000000−4i4i000000000000000000000000000000000
χ614-4-44-444-4000000000000002i2−2i2−2i22i2000000000022−22000000002i−2i−2i2i000000000000000
χ624-4-44-444-4000000000000002i2−2i2−2i22i20000000000−222200000000−2i2i2i−2i000000000000000
χ634-4-44-444-400000000000000−2i22i22i2−2i2000000000022−2200000000−2i2i2i−2i000000000000000
χ644-4-44-444-400000000000000−2i22i22i2−2i20000000000−2222000000002i−2i−2i2i000000000000000
χ658-8-8-88-888000000000000000000000000000000000000000000000000000000000

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