Finite Group Databasebeta

← Group #306341

Character table — Group #306341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-11111111111-11-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-111-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-1-1-111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111111111-1-111-1-1-1-1-1-11
χ17222222222-22-22-22-22222-20000-2222200002200-2-200000000-2-2000000000-200000000000
χ18222222222-22-22-22-22222-20000-2-2-2-2-20000-2-200-2-20000000022000000000200000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-222220000-2-2002200000000-2-2000000000200000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-2-2-2-2-200002200220000000022000000000-200000000000
χ2122222222-22-22-22-220000-22222-20000222200-2-20022-2-200000000000000-2000000000000
χ2222222222-22-22-22-220000-22222-20000-2-2-2-200-2-200-2-222000000000000002000000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-200002222002200-2-2-2-2000000000000002000000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-20000-2-2-2-2002200222200000000000000-2000000000000
χ25222-2-2-2-22-202020-2022-2-200000022-2-2i2i2−i2−i22-2000000i2−i2000000i2i2−i2−i2i2i2−i2−i200000000i2−i2000
χ26222-2-2-2-22-202020-2022-2-200000022-2-2−i2−i2i2i22-2000000−i2i2000000−i2−i2i2i2−i2−i2i2i200000000−i2i2000
χ27222-2-2-2-22-202020-2022-2-2000000-2-222i2i2−i2−i2-22000000i2−i2000000i2i2−i2−i2−i2−i2i2i200000000−i2i2000
χ28222-2-2-2-22-202020-2022-2-2000000-2-222−i2−i2i2i2-22000000−i2i2000000−i2−i2i2i2i2i2−i2−i200000000i2−i2000
χ29222-2-2-2-22-202020-20-2-22200000022-2-2i2i2−i2−i2-22000000i2−i2000000−i2−i2i2i2i2i2−i2−i200000000−i2i2000
χ30222-2-2-2-22-202020-20-2-22200000022-2-2−i2−i2i2i2-22000000−i2i2000000i2i2−i2−i2−i2−i2i2i200000000i2−i2000
χ31222-2-2-2-22-202020-20-2-222000000-2-222i2i2−i2−i22-2000000i2−i2000000−i2−i2i2i2−i2−i2i2i200000000i2−i2000
χ32222-2-2-2-22-202020-20-2-222000000-2-222−i2−i2i2i22-2000000−i2i2000000i2i2−i2−i2i2i2−i2−i200000000−i2i2000
χ3322-2-222-2-22-2-222-2-220000-22i2i−2i−2i200000000002i−2i0000000000002-22-20000002i−2i000000000
χ3422-2-222-2-22-2-222-2-220000-22i2i−2i−2i200000000002i−2i000000000000-22-22000000−2i2i000000000
χ3522-2-222-2-22-2-222-2-220000-2−2i−2i2i2i20000000000−2i2i0000000000002-22-2000000−2i2i000000000
χ3622-2-222-2-22-2-222-2-220000-2−2i−2i2i2i20000000000−2i2i000000000000-22-220000002i−2i000000000
χ3722-2-222-2-2-222-2-222-22-22-2-2000020000000000002-200002i2i−2i−2i00000000000000002i−2i00000
χ3822-2-222-2-2-222-2-222-22-22-2-2000020000000000002-20000−2i−2i2i2i0000000000000000−2i2i00000
χ3922-2-222-2-2-222-2-222-2-22-22-200002000000000000-2200002i2i−2i−2i0000000000000000−2i2i00000
χ4022-2-222-2-2-222-2-222-2-22-22-200002000000000000-220000−2i−2i2i2i00000000000000002i−2i00000
χ4122-2-222-2-2-2-222-2-2222-22-222i2i−2i−2i-20000000000−2i2i-2200000000000000000000002i−2i0000000
χ4222-2-222-2-2-2-222-2-2222-22-22−2i−2i2i2i-200000000002i−2i-220000000000000000000000−2i2i0000000
χ4322-2-222-2-2-2-222-2-222-22-2222i2i−2i−2i-20000000000−2i2i2-20000000000000000000000−2i2i0000000
χ4422-2-222-2-2-2-222-2-222-22-222−2i−2i2i2i-200000000002i−2i2-200000000000000000000002i−2i0000000
χ452-2222-2-2-20-20-20202000002i−2i2i−2i02−22−22-22-20000002i−2i00i2−i2i2−i22−200002−22−20000000000i2−i20
χ462-2222-2-2-20-20-20202000002i−2i2i−2i02−22−2-22-22000000−2i2i00i2−i2i2−i22−20000−22−220000000000−i2i20
χ472-2222-2-2-20-20-20202000002i−2i2i−2i0−22−222-22-20000002i−2i00−i2i2−i2i2−220000−22−220000000000−i2i20
χ482-2222-2-2-20-20-20202000002i−2i2i−2i0−22−22-22-22000000−2i2i00−i2i2−i2i2−2200002−22−20000000000i2−i20
χ492-2222-2-2-20-20-2020200000−2i2i−2i2i02−22−22-22-2000000−2i2i00−i2i2−i2i22−200002−22−20000000000−i2i20
χ502-2222-2-2-20-20-2020200000−2i2i−2i2i02−22−2-22-220000002i−2i00−i2i2−i2i22−20000−22−220000000000i2−i20
χ512-2222-2-2-20-20-2020200000−2i2i−2i2i0−22−222-22-2000000−2i2i00i2−i2i2−i2−220000−22−220000000000i2−i20
χ522-2222-2-2-20-20-2020200000−2i2i−2i2i0−22−22-22-220000002i−2i00i2−i2i2−i2−2200002−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-4440-40-4040000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ55444-4-4-4-4440-40-404000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ5644-44-4-44-44040-40-404-4-44000000000000000000000000000000000000000000000000000
χ5744-44-4-44-44040-40-40-444-4000000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-40-40404000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5944-44-4-44-4-40-4040400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6044-4-444-4-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ614-4444-4-4-404040-40-4000000000022−2222−22000000000000000000−2222000000000000000000000
χ624-4444-4-4-404040-40-40000000000−2222−222200000000000000000022−22000000000000000000000
χ634-44-4-444-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ644-44-4-444-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ654-44-4-444-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ664-44-4-444-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ674-4-4-44-444040-40-404000004-4-440000000000000000000000000000000000000000000000
χ684-4-4-44-444040-40-40400000-444-40000000000000000000000000000000000000000000000
χ694-4-4-44-4440-404040-4000000000000000000000000000022−22−222200000000000000000000000
χ704-4-4-44-4440-404040-40000000000000000000000000000−222222−2200000000000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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