Finite Group Databasebeta

← Group #306497

Character table — Group #306497

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888882444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-111-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-111-1-111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
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
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
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
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
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
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-111-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1111111111-1-1111-1-1-1-1-1-11
χ17222222222-22-22-22-22222-20000-222220000-2-2220000000000-2-200000000-2000000000000
χ18222222222-22-22-22-22222-20000-2-2-2-2-20000-2-2-2-2000000000022000000002000000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-22222000022-2-20000000000-2-2000000002000000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-2-2-2-2-20000222200000000002200000000-2000000000000
χ2122222222-22-22-22-220000-22222-2000022220000-2-222-2-20000000000000000000-20000000
χ2222222222-22-22-22-220000-22222-20000-2-2-2-20000-2-2-2-222000000000000000000020000000
χ2322222222-22-22-22-220000-2-2-2-2-2-200002222000022-2-2-2-2000000000000000000020000000
χ2422222222-22-22-22-220000-2-2-2-2-2-20000-2-2-2-200002222220000000000000000000-20000000
χ25222-22-2-2-2-20-20202022-2-20000002i2i−2i−2i22−2−2002i−2i00002−200000022−2−2i2i2−i2−i200000000i2−i2000
χ26222-22-2-2-2-20-20202022-2-20000002i2i−2i−2i−2−222002i−2i0000−22000000−2−222−i2−i2i2i200000000−i2i2000
χ27222-22-2-2-2-20-20202022-2-2000000−2i−2i2i2i22−2−200−2i2i00002−200000022−2−2−i2−i2i2i200000000−i2i2000
χ28222-22-2-2-2-20-20202022-2-2000000−2i−2i2i2i−2−22200−2i2i0000−22000000−2−222i2i2−i2−i200000000i2−i2000
χ29222-22-2-2-2-20-202020-2-2220000002i2i−2i−2i22−2−200−2i2i00002−2000000−2−222i2i2−i2−i200000000−i2i2000
χ30222-22-2-2-2-20-202020-2-2220000002i2i−2i−2i−2−22200−2i2i0000−2200000022−2−2−i2−i2i2i200000000i2−i2000
χ31222-22-2-2-2-20-202020-2-222000000−2i−2i2i2i22−2−2002i−2i00002−2000000−2−222−i2−i2i2i200000000i2−i2000
χ32222-22-2-2-2-20-202020-2-222000000−2i−2i2i2i−2−222002i−2i0000−2200000022−2−2i2i2−i2−i200000000−i2i2000
χ3322-2-2-222-202020-20-2000002i2i−2i−2i02−22−22i−2i2i−2i0000002-200i2i2−i2−i22−20000i2−i2i2−i200000000002−20
χ3422-2-2-222-202020-20-2000002i2i−2i−2i02−22−2−2i2i−2i2i000000-2200i2i2−i2−i22−20000−i2i2−i2i20000000000−220
χ3522-2-2-222-202020-20-2000002i2i−2i−2i0−22−222i−2i2i−2i0000002-200−i2−i2i2i2−220000−i2i2−i2i20000000000−220
χ3622-2-2-222-202020-20-2000002i2i−2i−2i0−22−22−2i2i−2i2i000000-2200−i2−i2i2i2−220000i2−i2i2−i200000000002−20
χ3722-2-2-222-202020-20-200000−2i−2i2i2i02−22−22i−2i2i−2i000000-2200−i2−i2i2i22−20000i2−i2i2−i20000000000−220
χ3822-2-2-222-202020-20-200000−2i−2i2i2i02−22−2−2i2i−2i2i0000002-200−i2−i2i2i22−20000−i2i2−i2i200000000002−20
χ3922-2-2-222-202020-20-200000−2i−2i2i2i0−22−222i−2i2i−2i000000-2200i2i2−i2−i2−220000−i2i2−i2i200000000002−20
χ4022-2-2-222-202020-20-200000−2i−2i2i2i0−22−22−2i2i−2i2i0000002-200i2i2−i2−i2−220000i2−i2i2−i20000000000−220
χ412-222-22-2-22-2-222-2-220000-22i−2i2i−2i20000000000002i−2i00000000002-22-200000000002i−2i00000
χ422-222-22-2-22-2-222-2-220000-22i−2i2i−2i20000000000002i−2i0000000000-22-220000000000−2i2i00000
χ432-222-22-2-22-2-222-2-220000-2−2i2i−2i2i2000000000000−2i2i00000000002-22-20000000000−2i2i00000
χ442-222-22-2-22-2-222-2-220000-2−2i2i−2i2i2000000000000−2i2i0000000000-22-2200000000002i−2i00000
χ452-222-22-2-2-222-2-222-22-22-2-200002000000002-2000000002i−2i2i−2i000000000002i−2i0000000000
χ462-222-22-2-2-222-2-222-22-22-2-200002000000002-200000000−2i2i−2i2i00000000000−2i2i0000000000
χ472-222-22-2-2-222-2-222-2-22-22-20000200000000-22000000002i−2i2i−2i00000000000−2i2i0000000000
χ482-222-22-2-2-222-2-222-2-22-22-20000200000000-2200000000−2i2i−2i2i000000000002i−2i0000000000
χ492-222-22-2-2-2-222-2-2222-22-222i−2i2i−2i-200000000-2200−2i2i0000000000000000000002i−2i00000000
χ502-222-22-2-2-2-222-2-2222-22-22−2i2i−2i2i-200000000-22002i−2i000000000000000000000−2i2i00000000
χ512-222-22-2-2-2-222-2-222-22-2222i−2i2i−2i-2000000002-200−2i2i000000000000000000000−2i2i00000000
χ522-222-22-2-2-2-222-2-222-22-222−2i2i−2i2i-2000000002-2002i−2i0000000000000000000002i−2i00000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-44040-40-40000000000000002222−22−2200000000−2222000000000000000000000000000
χ55444-44-4-4-44040-40-4000000000000000−22−2222220000000022−22000000000000000000000000000
χ5644-44-4-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ5744-44-4-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ5844-44-4-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ5944-44-4-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ6044-4-4-444-40-40-40404000000000022−2222−22000000000000000000−2222000000000000000000000
χ6144-4-4-444-40-40-404040000000000−2222−222200000000000000000022−22000000000000000000000
χ624-444-44-4-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ634-44-4-4-44440-40-40404-4-44000000000000000000000000000000000000000000000000000
χ644-44-4-4-44440-40-4040-444-4000000000000000000000000000000000000000000000000000
χ654-44-4-4-444-404040-40000000000000000000000000000000000022−22−222200000000000000000
χ664-44-4-4-444-404040-400000000000000000000000000000000000−222222−2200000000000000000
χ674-4-4-444-44040-40-404000000000000000000000000000022−22−222200000000000000000000000
χ684-4-4-444-44040-40-4040000000000000000000000000000−222222−2200000000000000000000000
χ694-4-4-444-440-404040-4000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-444-440-404040-400000-444-40000000000000000000000000000000000000000000000
χ718-8-888-88-8000000000000000000000000000000000000000000000000000000000000000

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