Finite Group Databasebeta

← Group #306449

Character table — Group #306449

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888882444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-11-1-1111111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-11111-11-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-111-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-22222-20000-22222000000-2-22200000000-2-200000000-2000000000000
χ18222222222-22-22-22-22222-20000-2-2-2-2-2000000-2-2-2-20000000022000000002000000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-2222200000022-2-200000000-2-2000000002000000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-2-2-2-2-20000002222000000002200000000-2000000000000
χ2122222222-22-22-22-220000-22222-200002222-2-2000022-2-2000000000000000-200000000000
χ2222222222-22-22-22-220000-22222-20000-2-2-2-2-2-20000-2-222000000000000000200000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-200002222220000-2-2-2-2000000000000000200000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-20000-2-2-2-22200002222000000000000000-200000000000
χ25222-2-22-2-22-2-222-2-220000-22i2i−2i−2i2000000002i−2i0000000000000022-2-200000000002i−2i00000
χ26222-2-22-2-22-2-222-2-220000-22i2i−2i−2i2000000002i−2i00000000000000-2-2220000000000−2i2i00000
χ27222-2-22-2-22-2-222-2-220000-2−2i−2i2i2i200000000−2i2i0000000000000022-2-20000000000−2i2i00000
χ28222-2-22-2-22-2-222-2-220000-2−2i−2i2i2i200000000−2i2i00000000000000-2-22200000000002i−2i00000
χ29222-2-22-2-2-222-2-222-222-2-2-20000200000000002-20000002i2i−2i−2i000000000000002i−2i0000000
χ30222-2-22-2-2-222-2-222-222-2-2-20000200000000002-2000000−2i−2i2i2i00000000000000−2i2i0000000
χ31222-2-22-2-2-222-2-222-2-2-222-2000020000000000-220000002i2i−2i−2i00000000000000−2i2i0000000
χ32222-2-22-2-2-222-2-222-2-2-222-2000020000000000-22000000−2i−2i2i2i000000000000002i−2i0000000
χ33222-2-22-2-2-2-222-2-22222-2-222i2i−2i−2i-200000000−2i2i-2200000000000000000000002i−2i000000000
χ34222-2-22-2-2-2-222-2-22222-2-22−2i−2i2i2i-2000000002i−2i-220000000000000000000000−2i2i000000000
χ35222-2-22-2-2-2-222-2-222-2-22222i2i−2i−2i-200000000−2i2i2-20000000000000000000000−2i2i000000000
χ36222-2-22-2-2-2-222-2-222-2-2222−2i−2i2i2i-2000000002i−2i2-200000000000000000000002i−2i000000000
χ3722-22-2-22-220-20-20202-22-20000002i2i−2i−2ii2i2−i2−i200002i−2i00i2−i2000000i2−i2i2−i222−2−2000000002−2000
χ3822-22-2-22-220-20-20202-22-20000002i2i−2i−2i−i2−i2i2i200002i−2i00−i2i2000000−i2i2−i2i2−2−22200000000−22000
χ3922-22-2-22-220-20-20202-22-2000000−2i−2i2i2ii2i2−i2−i20000−2i2i00i2−i2000000i2−i2i2−i2−2−22200000000−22000
χ4022-22-2-22-220-20-20202-22-2000000−2i−2i2i2i−i2−i2i2i20000−2i2i00−i2i2000000−i2i2−i2i222−2−2000000002−2000
χ4122-22-2-22-220-20-2020-22-220000002i2i−2i−2ii2i2−i2−i20000−2i2i00i2−i2000000−i2i2−i2i222−2−200000000−22000
χ4222-22-2-22-220-20-2020-22-220000002i2i−2i−2i−i2−i2i2i20000−2i2i00−i2i2000000i2−i2i2−i2−2−222000000002−2000
χ4322-22-2-22-220-20-2020-22-22000000−2i−2i2i2ii2i2−i2−i200002i−2i00i2−i2000000−i2i2−i2i2−2−222000000002−2000
χ4422-22-2-22-220-20-2020-22-22000000−2i−2i2i2i−i2−i2i2i200002i−2i00−i2i2000000i2−i2i2−i222−2−200000000−22000
χ452-2-2-2-22220-20-20202000002-22-202−22−22-22-20000002-2002−22−22−200002−22−200000000002−20
χ462-2-2-2-22220-20-20202000002-22-202−22−2-22-22000000-22002−22−22−20000−22−220000000000−220
χ472-2-2-2-22220-20-20202000002-22-20−22−222-22-20000002-200−22−22−220000−22−220000000000−220
χ482-2-2-2-22220-20-20202000002-22-20−22−22-22-22000000-2200−22−22−2200002−22−200000000002−20
χ492-2-2-2-22220-20-2020200000-22-2202−22−22-22-2000000-2200−22−222−200002−22−20000000000−220
χ502-2-2-2-22220-20-2020200000-22-2202−22−2-22-220000002-200−22−222−20000−22−2200000000002−20
χ512-2-2-2-22220-20-2020200000-22-220−22−222-22-2000000-22002−22−2−220000−22−2200000000002−20
χ522-2-2-2-22220-20-2020200000-22-220−22−22-22-220000002-2002−22−2−2200002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-44-4-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ5544-44-4-44-4-404040-40000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ5644-44-4-44-4-404040-4000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ5744-4-44-4-444040-40-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5844-4-44-4-444040-40-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5944-4-44-4-44-40-4040404-4-44000000000000000000000000000000000000000000000000000
χ6044-4-44-4-44-40-404040-444-4000000000000000000000000000000000000000000000000000
χ614-44-44-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ624-44-44-44-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ634-44-44-44-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ644-44-44-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ654-4-4444-4-4040-40-404000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-4-4444-4-4040-40-40400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-4444-4-40-404040-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ684-4-4444-4-40-404040-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ694-4-4-4-444404040-40-4000000000022−2222−22000000000000000000−2222000000000000000000000
χ704-4-4-4-444404040-40-40000000000−2222−222200000000000000000022−22000000000000000000000
χ718-888-8-8-88000000000000000000000000000000000000000000000000000000000000000

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