Finite Group Databasebeta

← Group #312088

Character table — Group #312088

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-111111111-1-11-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-11-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-11
χ17222222222-22-22-22-20000-22222-20000222200-2-2002200-2-2000000000000000-2000000000
χ18222222222-22-22-22-20000-22222-20000-2-2-2-200-2-200-2-200220000000000000002000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-200002222002200-2-200-2-20000000000000002000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000000-2000000000
χ2122222222-22-22-22-222222-20000-222220000-2-2002200-2-20000000000000000-20000000000
χ2222222222-22-22-22-222222-20000-2-2-2-2-20000-2-200-2-20022000000000000000020000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-2222200002200-2-200-2-2000000000000000020000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-2000022002200220000000000000000-20000000000
χ25222-2-2-22-22-2-222-2-222i2i−2i−2i-200002000000002i−2i00000000002i2i−2i−2i000000002-200000000000
χ26222-2-2-22-22-2-222-2-222i2i−2i−2i-200002000000002i−2i0000000000−2i−2i2i2i00000000-2200000000000
χ27222-2-2-22-22-2-222-2-22−2i−2i2i2i-20000200000000−2i2i00000000002i2i−2i−2i00000000-2200000000000
χ28222-2-2-22-22-2-222-2-22−2i−2i2i2i-20000200000000−2i2i0000000000−2i−2i2i2i000000002-200000000000
χ29222-2-2-22-2-222-2-222-20000-22i2i−2i−2i200000000002i−2i0000000000002i2i−2i−2i00000000002-200000
χ30222-2-2-22-2-222-2-222-20000-22i2i−2i−2i200000000002i−2i000000000000−2i−2i2i2i0000000000-2200000
χ31222-2-2-22-2-222-2-222-20000-2−2i−2i2i2i20000000000−2i2i0000000000002i2i−2i−2i0000000000-2200000
χ32222-2-2-22-2-222-2-222-20000-2−2i−2i2i2i20000000000−2i2i000000000000−2i−2i2i2i00000000002-200000
χ33222-2-2-22-2-2-222-2-2222i2i−2i−2i22i2i−2i−2i-200000000−2i2i−2i2i0000000000000000000000002-20000000
χ34222-2-2-22-2-2-222-2-2222i2i−2i−2i2−2i−2i2i2i-200000000−2i2i2i−2i000000000000000000000000-220000000
χ35222-2-2-22-2-2-222-2-222−2i−2i2i2i22i2i−2i−2i-2000000002i−2i−2i2i000000000000000000000000-220000000
χ36222-2-2-22-2-2-222-2-222−2i−2i2i2i2−2i−2i2i2i-2000000002i−2i2i−2i0000000000000000000000002-20000000
χ3722-22-2-2-2220-20-2020000002-22-20i2i2−i2−i222-2-20000002-2i2−i200i2−i2i2−i20000i2i2−i2−i20000000000i2−i20
χ3822-22-2-2-2220-20-2020000002-22-20i2i2−i2−i2-2-222000000-22i2−i200i2−i2i2−i20000−i2−i2i2i20000000000−i2i20
χ3922-22-2-2-2220-20-2020000002-22-20−i2−i2i2i222-2-20000002-2−i2i200−i2i2−i2i20000−i2−i2i2i20000000000−i2i20
χ4022-22-2-2-2220-20-2020000002-22-20−i2−i2i2i2-2-222000000-22−i2i200−i2i2−i2i20000i2i2−i2−i20000000000i2−i20
χ4122-22-2-2-2220-20-202000000-22-220i2i2−i2−i222-2-2000000-22i2−i200−i2i2−i2i20000i2i2−i2−i20000000000−i2i20
χ4222-22-2-2-2220-20-202000000-22-220i2i2−i2−i2-2-2220000002-2i2−i200−i2i2−i2i20000−i2−i2i2i20000000000i2−i20
χ4322-22-2-2-2220-20-202000000-22-220−i2−i2i2i222-2-2000000-22−i2i200i2−i2i2−i20000−i2−i2i2i20000000000i2−i20
χ4422-22-2-2-2220-20-202000000-22-220−i2−i2i2i2-2-2220000002-2−i2i200i2−i2i2−i20000i2i2−i2−i20000000000−i2i20
χ452-22-2-22-2202020-20-22i−2i2i−2i0000002i−2i2i−2i2−22−200002-200002−20000i2−i2i2−i2i2−i2i2−i2000000002−2000
χ462-22-2-22-2202020-20-22i−2i2i−2i0000002i−2i2i−2i−22−2200002-20000−220000−i2i2−i2i2−i2i2−i2i200000000−22000
χ472-22-2-22-2202020-20-22i−2i2i−2i000000−2i2i−2i2i2−22−20000-2200002−20000i2−i2i2−i2−i2i2−i2i200000000−22000
χ482-22-2-22-2202020-20-22i−2i2i−2i000000−2i2i−2i2i−22−220000-220000−220000−i2i2−i2i2i2−i2i2−i2000000002−2000
χ492-22-2-22-2202020-20-2−2i2i−2i2i0000002i−2i2i−2i2−22−20000-2200002−20000−i2i2−i2i2i2−i2i2−i200000000−22000
χ502-22-2-22-2202020-20-2−2i2i−2i2i0000002i−2i2i−2i−22−220000-220000−220000i2−i2i2−i2−i2i2−i2i2000000002−2000
χ512-22-2-22-2202020-20-2−2i2i−2i2i000000−2i2i−2i2i2−22−200002-200002−20000−i2i2−i2i2−i2i2−i2i2000000002−2000
χ522-22-2-22-2202020-20-2−2i2i−2i2i000000−2i2i−2i2i−22−2200002-20000−220000i2−i2i2−i2i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ5544-44-4-4-44-404040-4000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ5644-44-4-4-44-404040-400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ5744-4-444-4-44040-40-4000000000000000000000000000000022−22−2222000000000000000000000
χ5844-4-444-4-44040-40-40000000000000000000000000000000−222222−22000000000000000000000
χ5944-4-444-4-4-40-404040000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6044-4-444-4-4-40-40404000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ614-4444-4-4-4040-40-404000000000000000000000000000000000022−22−222200000000000000000
χ624-4444-4-4-4040-40-4040000000000000000000000000000000000−222222−2200000000000000000
χ634-4444-4-4-40-404040-44-4-44000000000000000000000000000000000000000000000000000
χ644-4444-4-4-40-404040-4-444-4000000000000000000000000000000000000000000000000000
χ654-44-4-44-440-40-404040000000000000022−2222−220000000000−22220000000000000000000000000
χ664-44-4-44-440-40-4040400000000000000−2222−2222000000000022−220000000000000000000000000
χ674-4-4-44-44400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ684-4-4-44-44400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ694-4-4-44-444000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ704-4-4-44-444000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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