Finite Group Databasebeta

← Group #312153

Character table — Group #312153

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
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
χ511111111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-11-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-11-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1111-1-111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-111111-1-1111-1-1-1-1-1-11
χ17222222222-22-22-22-222220000-2-20000222222-2-20000-2-200000000000000000-2000000000
χ18222222222-22-22-22-222220000-2-20000-2-2-2-2-2-2-2-2000022000000000000000002000000000
χ19222222222-22-22-22-2-2-2-2-20000-2-200002222-2-2220000-2-2000000000000000002000000000
χ20222222222-22-22-22-2-2-2-2-20000-2-20000-2-2-2-2222200002200000000000000000-2000000000
χ2122222222-22-22-22-2200002222-2-2222200000000-2-2220000000000-2-20000-2000000000000
χ2222222222-22-22-22-2200002222-2-2-2-2-2-200000000-2-2-2-200000000002200002000000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-222220000000022-2-20000000000-2-200002000000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-2-2-2-2-20000000022220000000000220000-2000000000000
χ25222-2-2-22-2-20-2020202i2i−2i−2i00000022−2−222-2-22i−2i00000000i2i2−i2−i200002−222−2−200000000i2−i2000
χ26222-2-2-22-2-20-2020202i2i−2i−2i00000022−2−2-2-222−2i2i00000000i2i2−i2−i200002−2−2−22200000000−i2i2000
χ27222-2-2-22-2-20-2020202i2i−2i−2i000000−2−22222-2-22i−2i00000000−i2−i2i2i20000−22−2−22200000000−i2i2000
χ28222-2-2-22-2-20-2020202i2i−2i−2i000000−2−222-2-222−2i2i00000000−i2−i2i2i20000−2222−2−200000000i2−i2000
χ29222-2-2-22-2-20-202020−2i−2i2i2i00000022−2−222-2-2−2i2i00000000−i2−i2i2i200002−222−2−200000000−i2i2000
χ30222-2-2-22-2-20-202020−2i−2i2i2i00000022−2−2-2-2222i−2i00000000−i2−i2i2i200002−2−2−22200000000i2−i2000
χ31222-2-2-22-2-20-202020−2i−2i2i2i000000−2−22222-2-2−2i2i00000000i2i2−i2−i20000−22−2−22200000000i2−i2000
χ32222-2-2-22-2-20-202020−2i−2i2i2i000000−2−222-2-2222i−2i00000000i2i2−i2−i20000−2222−2−200000000−i2i2000
χ3322-2-2-22-222-2-222-2-2200002i2i−2i−2i-220000000000002i−2i00002i−2i2i−2i000000000002-20000000000
χ3422-2-2-22-222-2-222-2-2200002i2i−2i−2i-220000000000002i−2i0000−2i2i−2i2i00000000000-220000000000
χ3522-2-2-22-222-2-222-2-220000−2i−2i2i2i-22000000000000−2i2i00002i−2i2i−2i00000000000-220000000000
χ3622-2-2-22-222-2-222-2-220000−2i−2i2i2i-22000000000000−2i2i0000−2i2i−2i2i000000000002-20000000000
χ3722-2-2-22-22-222-2-222-22i−2i2i−2i0000-2200000000002i−2i00000000002i2i−2i−2i0000000000002-200000
χ3822-2-2-22-22-222-2-222-22i−2i2i−2i0000-2200000000002i−2i0000000000−2i−2i2i2i000000000000-2200000
χ3922-2-2-22-22-222-2-222-2−2i2i−2i2i0000-220000000000−2i2i00000000002i2i−2i−2i000000000000-2200000
χ4022-2-2-22-22-222-2-222-2−2i2i−2i2i0000-220000000000−2i2i0000000000−2i−2i2i2i0000000000002-200000
χ4122-2-2-22-22-2-222-2-2222i−2i2i−2i2i2i−2i−2i2-20000000000−2i2i−2i2i00000000000000000000002-20000000
χ4222-2-2-22-22-2-222-2-2222i−2i2i−2i−2i−2i2i2i2-20000000000−2i2i2i−2i0000000000000000000000-220000000
χ4322-2-2-22-22-2-222-2-222−2i2i−2i2i2i2i−2i−2i2-200000000002i−2i−2i2i0000000000000000000000-220000000
χ4422-2-2-22-22-2-222-2-222−2i2i−2i2i−2i−2i2i2i2-200000000002i−2i2i−2i00000000000000000000002-20000000
χ452-222-22-2-20-20-2020200002-22-2002i−2i2i−2i2−22−20000002i−2i2−200002−22−200i2−i2i2−i20000000000i2−i20
χ462-222-22-2-20-20-2020200002-22-2002i−2i2i−2i−22−220000002i−2i−220000−22−2200−i2i2−i2i20000000000−i2i20
χ472-222-22-2-20-20-2020200002-22-200−2i2i−2i2i2−22−2000000−2i2i2−200002−22−200−i2i2−i2i20000000000−i2i20
χ482-222-22-2-20-20-2020200002-22-200−2i2i−2i2i−22−22000000−2i2i−220000−22−2200i2−i2i2−i20000000000i2−i20
χ492-222-22-2-20-20-202020000-22-22002i−2i2i−2i2−22−2000000−2i2i2−20000−22−2200i2−i2i2−i20000000000−i2i20
χ502-222-22-2-20-20-202020000-22-22002i−2i2i−2i−22−22000000−2i2i−2200002−22−200−i2i2−i2i20000000000i2−i20
χ512-222-22-2-20-20-202020000-22-2200−2i2i−2i2i2−22−20000002i−2i2−20000−22−2200−i2i2−i2i20000000000i2−i20
χ522-222-22-2-20-20-202020000-22-2200−2i2i−2i2i−22−220000002i−2i−2200002−22−200i2−i2i2−i20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-44040-40-4000000000002222−22−220000000000000000000000−222200000000000000000
χ55444-4-4-44-44040-40-400000000000−22−222222000000000000000000000022−2200000000000000000
χ5644-444-4-4-440-40-40404-4-44000000000000000000000000000000000000000000000000000
χ5744-444-4-4-440-40-4040-444-4000000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-404040-40000000000000000000000000000022−22−222200000000000000000000000
χ5944-444-4-4-4-404040-400000000000000000000000000000−222222−2200000000000000000000000
χ6044-4-4-44-4444-4-444-4-4000000004-4000000000000000000000000000000000000000000000
χ614-444-44-4-404040-40-40000000000000022−2222−2200000000−2222000000000000000000000000000
χ624-444-44-4-404040-40-400000000000000−2222−22220000000022−22000000000000000000000000000
χ634-44-44-4-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ644-44-44-4-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ654-44-44-4-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ664-44-44-4-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ674-4-4-4444-4040-40-40400004i−4i−4i4i00000000000000000000000000000000000000000000000
χ684-4-4-4444-4040-40-4040000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ694-4-4-4444-40-404040-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ704-4-4-4444-40-404040-400000000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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