Finite Group Databasebeta

← Group #306545

Character table — Group #306545

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11-11111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-11111111111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-11-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111-111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111111111-1-11111-1-1-1-1-1-11
χ17222222222-22-22-22-20000-22222-2000022220000-2-222-2-20000000000000000-20000000000
χ18222222222-22-22-22-20000-22222-20000-2-2-2-20000-2-2-2-222000000000000000020000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-200002222000022-2-2-2-2000000000000000020000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-200002222220000000000000000-20000000000
χ2122222222-22-22-22-222222-20000-222220000-2-2220000000000-2-200000000000-2000000000
χ2222222222-22-22-22-222222-20000-2-2-2-2-20000-2-2-2-2000000000022000000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-22222000022-2-20000000000-2-2000000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-20000222200000000002200000000000-2000000000
χ25222-2-2-2-2220-20-20200000022-2-20i2i2−i2−i222-2-20000002-200i2i2−i2−i2i2−i20000i2i2−i2−i20000000000i2−i20
χ26222-2-2-2-2220-20-20200000022-2-20i2i2−i2−i2-2-222000000-2200i2i2−i2−i2i2−i20000−i2−i2i2i20000000000−i2i20
χ27222-2-2-2-2220-20-20200000022-2-20−i2−i2i2i222-2-20000002-200−i2−i2i2i2−i2i20000−i2−i2i2i20000000000−i2i20
χ28222-2-2-2-2220-20-20200000022-2-20−i2−i2i2i2-2-222000000-2200−i2−i2i2i2−i2i20000i2i2−i2−i20000000000i2−i20
χ29222-2-2-2-2220-20-202000000-2-2220i2i2−i2−i222-2-2000000-2200−i2−i2i2i2i2−i20000i2i2−i2−i20000000000−i2i20
χ30222-2-2-2-2220-20-202000000-2-2220i2i2−i2−i2-2-2220000002-200−i2−i2i2i2i2−i20000−i2−i2i2i20000000000i2−i20
χ31222-2-2-2-2220-20-202000000-2-2220−i2−i2i2i222-2-2000000-2200i2i2−i2−i2−i2i20000−i2−i2i2i20000000000i2−i20
χ32222-2-2-2-2220-20-202000000-2-2220−i2−i2i2i2-2-2220000002-200i2i2−i2−i2−i2i20000i2i2−i2−i20000000000−i2i20
χ3322-2-22-22-20-20-2020222-2-20000002i−2i2i−2i2−22−2002i−2i00002−200000022−2−2i2−i2i2−i200000000i2−i2000
χ3422-2-22-22-20-20-2020222-2-20000002i−2i2i−2i−22−22002i−2i0000−22000000−2−222−i2i2−i2i200000000−i2i2000
χ3522-2-22-22-20-20-2020222-2-2000000−2i2i−2i2i2−22−200−2i2i00002−200000022−2−2−i2i2−i2i200000000−i2i2000
χ3622-2-22-22-20-20-2020222-2-2000000−2i2i−2i2i−22−2200−2i2i0000−22000000−2−222i2−i2i2−i200000000i2−i2000
χ3722-2-22-22-20-20-20202-2-2220000002i−2i2i−2i2−22−200−2i2i00002−2000000−2−222i2−i2i2−i200000000−i2i2000
χ3822-2-22-22-20-20-20202-2-2220000002i−2i2i−2i−22−2200−2i2i0000−2200000022−2−2−i2i2−i2i200000000i2−i2000
χ3922-2-22-22-20-20-20202-2-222000000−2i2i−2i2i2−22−2002i−2i00002−2000000−2−222−i2i2−i2i200000000i2−i2000
χ4022-2-22-22-20-20-20202-2-222000000−2i2i−2i2i−22−22002i−2i0000−2200000022−2−2i2−i2i2−i200000000−i2i2000
χ412-222-2-22-22-2-222-2-222-22-2-200002000000002-2000000002i−2i2i−2i00000000002i−2i00000000000
χ422-222-2-22-22-2-222-2-222-22-2-200002000000002-200000000−2i2i−2i2i0000000000−2i2i00000000000
χ432-222-2-22-22-2-222-2-22-22-22-20000200000000-22000000002i−2i2i−2i0000000000−2i2i00000000000
χ442-222-2-22-22-2-222-2-22-22-22-20000200000000-2200000000−2i2i−2i2i00000000002i−2i00000000000
χ452-222-2-22-2-222-2-222-20000-22i−2i2i−2i20000000000002i−2i00000000002-22-200000000002i−2i00000
χ462-222-2-22-2-222-2-222-20000-22i−2i2i−2i20000000000002i−2i0000000000-22-220000000000−2i2i00000
χ472-222-2-22-2-222-2-222-20000-2−2i2i−2i2i2000000000000−2i2i00000000002-22-20000000000−2i2i00000
χ482-222-2-22-2-222-2-222-20000-2−2i2i−2i2i2000000000000−2i2i0000000000-22-2200000000002i−2i00000
χ492-222-2-22-2-2-222-2-2222-22-222i−2i2i−2i-200000000-2200−2i2i00000000000000000000002i−2i0000000
χ502-222-2-22-2-2-222-2-2222-22-22−2i2i−2i2i-200000000-22002i−2i0000000000000000000000−2i2i0000000
χ512-222-2-22-2-2-222-2-222-22-2222i−2i2i−2i-2000000002-200−2i2i0000000000000000000000−2i2i0000000
χ522-222-2-22-2-2-222-2-222-22-222−2i2i−2i2i-2000000002-2002i−2i00000000000000000000002i−2i0000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-44-404040-4000000000002i22i2−2i2−2i2000000000000000000−2i22i2000000000000000000000
χ55444-4-4-4-44-404040-400000000000−2i2−2i22i22i20000000000000000002i2−2i2000000000000000000000
χ5644-44-44-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5744-44-44-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ5844-44-44-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ5944-44-44-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ6044-4-44-44-404040-40-40000000000000022−2222−2200000000−2222000000000000000000000000000
χ6144-4-44-44-404040-40-400000000000000−2222−22220000000022−22000000000000000000000000000
χ624-444-4-44-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ634-44-444-4-44040-40-40000000000000000000000000000022−22−222200000000000000000000000
χ644-44-444-4-44040-40-400000000000000000000000000000−222222−2200000000000000000000000
χ654-44-444-4-4-40-404040000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-44-444-4-4-40-40404000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-4-4-4444040-40-4044-4-44000000000000000000000000000000000000000000000000000
χ684-4-4-4-4444040-40-404-444-4000000000000000000000000000000000000000000000000000
χ694-4-4-4-44440-404040-4000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-4-44440-404040-40000000000000000000000000000000000−222222−2200000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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