Finite Group Databasebeta

← Group #312145

Character table — Group #312145

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-1-111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111111111-1-11-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-1111111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-11111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-200002222-2-20000222200-2-200220000000000-2-20000000-2000000000
χ18222222222-22-22-22-200002222-2-20000-2-2-2-200-2-200-2-200000000002200000002000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-200002222002200-2-20000000000-2-200000002000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-2002200220000000000220000000-2000000000
χ2122222222-22-22-22-2222220000-2-222220000-2-200220000000000-2-200000000-20000000000
χ2222222222-22-22-22-2222220000-2-2-2-2-2-20000-2-200-2-20000000000220000000020000000000
χ2322222222-22-22-22-22-2-2-2-20000-2-2222200002200-2-20000000000-2-20000000020000000000
χ2422222222-22-22-22-22-2-2-2-20000-2-2-2-2-2-2000022002200000000002200000000-20000000000
χ25222-2-2-2-222-2-222-2-222i2i−2i−2i0000-22000000002i−2i0000002i2i−2i−2i00000000000000002-20000000
χ26222-2-2-2-222-2-222-2-222i2i−2i−2i0000-22000000002i−2i000000−2i−2i2i2i0000000000000000-220000000
χ27222-2-2-2-222-2-222-2-22−2i−2i2i2i0000-2200000000−2i2i0000002i2i−2i−2i0000000000000000-220000000
χ28222-2-2-2-222-2-222-2-22−2i−2i2i2i0000-2200000000−2i2i000000−2i−2i2i2i00000000000000002-20000000
χ29222-2-2-2-22-222-2-222-200002i2i−2i−2i-2200000000002i−2i000000002i2i−2i−2i000000000000002-200000
χ30222-2-2-2-22-222-2-222-200002i2i−2i−2i-2200000000002i−2i00000000−2i−2i2i2i00000000000000-2200000
χ31222-2-2-2-22-222-2-222-20000−2i−2i2i2i-220000000000−2i2i000000002i2i−2i−2i00000000000000-2200000
χ32222-2-2-2-22-222-2-222-20000−2i−2i2i2i-220000000000−2i2i00000000−2i−2i2i2i000000000000002-200000
χ33222-2-2-2-22-2-222-2-2222i2i−2i−2i2i2i−2i−2i2-200000000−2i2i−2i2i000000000000000000002-200000000000
χ34222-2-2-2-22-2-222-2-2222i2i−2i−2i−2i−2i2i2i2-200000000−2i2i2i−2i00000000000000000000-2200000000000
χ35222-2-2-2-22-2-222-2-222−2i−2i2i2i2i2i−2i−2i2-2000000002i−2i−2i2i00000000000000000000-2200000000000
χ36222-2-2-2-22-2-222-2-222−2i−2i2i2i−2i−2i2i2i2-2000000002i−2i2i−2i000000000000000000002-200000000000
χ3722-22-2-22-2020-20-2022-22-20000002i2i−2i−2ii2i2−i2−i200002i−2i000000i2−i2i2−i200i2−i222−2−2000000002−2000
χ3822-22-2-22-2020-20-2022-22-20000002i2i−2i−2i−i2−i2i2i200002i−2i000000−i2i2−i2i200−i2i2−2−22200000000−22000
χ3922-22-2-22-2020-20-2022-22-2000000−2i−2i2i2ii2i2−i2−i20000−2i2i000000i2−i2i2−i200i2−i2−2−22200000000−22000
χ4022-22-2-22-2020-20-2022-22-2000000−2i−2i2i2i−i2−i2i2i20000−2i2i000000−i2i2−i2i200−i2i222−2−2000000002−2000
χ4122-22-2-22-2020-20-202-22-220000002i2i−2i−2ii2i2−i2−i20000−2i2i000000−i2i2−i2i200i2−i222−2−200000000−22000
χ4222-22-2-22-2020-20-202-22-220000002i2i−2i−2i−i2−i2i2i20000−2i2i000000i2−i2i2−i200−i2i2−2−222000000002−2000
χ4322-22-2-22-2020-20-202-22-22000000−2i−2i2i2ii2i2−i2−i200002i−2i000000−i2i2−i2i200i2−i2−2−222000000002−2000
χ4422-22-2-22-2020-20-202-22-22000000−2i−2i2i2i−i2−i2i2i200002i−2i000000i2−i2i2−i200−i2i222−2−200000000−22000
χ452-22-22-22-220-20-202000002-22-200i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i2i2−i20000i2−i2002−22−200000000002−20
χ462-22-22-22-220-20-202000002-22-200i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i2i2−i20000i2−i200−22−220000000000−220
χ472-22-22-22-220-20-202000002-22-200−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i2−i2i20000−i2i200−22−220000000000−220
χ482-22-22-22-220-20-202000002-22-200−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i2−i2i20000−i2i2002−22−200000000002−20
χ492-22-22-22-220-20-20200000-22-2200i2−i2i2−i22i−2i2i−2i000000−2i2i−i2i2−i2i20000i2−i2002−22−20000000000−220
χ502-22-22-22-220-20-20200000-22-2200i2−i2i2−i2−2i2i−2i2i0000002i−2i−i2i2−i2i20000i2−i200−22−2200000000002−20
χ512-22-22-22-220-20-20200000-22-2200−i2i2−i2i22i−2i2i−2i000000−2i2ii2−i2i2−i20000−i2i200−22−2200000000002−20
χ522-22-22-22-220-20-20200000-22-2200−i2i2−i2i2−2i2i−2i2i0000002i−2ii2−i2i2−i20000−i2i2002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-4-4444-4-444-4-4000000004-4000000000000000000000000000000000000000000000
χ5544-44-4-44-40-404040-4000000000000002i22i2−2i2−2i2000000000000000000−2i22i200000000000000000
χ5644-44-4-44-40-404040-400000000000000−2i2−2i22i22i20000000000000000002i2−2i200000000000000000
χ5744-4-444-4-404040-40-400000000000000000000000000000022−22−2222000000000000000000000
χ5844-4-444-4-404040-40-4000000000000000000000000000000−222222−22000000000000000000000
χ5944-4-444-4-40-40-404044i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6044-4-444-4-40-40-40404−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ614-444-44-4-44040-40-400000000000000000000000000022−22−22220000000000000000000000000
χ624-444-44-4-44040-40-4000000000000000000000000000−222222−220000000000000000000000000
χ634-444-44-4-4-40-40404000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ644-444-44-4-4-40-4040400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ654-44-44-44-4-404040-4000000000002i2−2i22i2−2i200000000000000000000−2i22i20000000000000000000
χ664-44-44-44-4-404040-400000000000−2i22i2−2i22i2000000000000000000002i2−2i20000000000000000000
χ674-4-4-4-444400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ684-4-4-4-444400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ694-4-4-4-4444000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ704-4-4-4-4444000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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