Finite Group Databasebeta

← Group #309542

Character table — Group #309542

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-11-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ1722222222222-2-2-2-220000-22222-200002222002200-2-200-2-20000000000000-200000000000
χ1822222222222-2-2-2-220000-22222-20000-2-2-2-200-2-200-2-200220000000000000200000000000
χ1922222222222-2-2-2-220000-2-2-2-2-2-20000222200-2-2002200-2-20000000000000200000000000
χ2022222222222-2-2-2-220000-2-2-2-2-2-20000-2-2-2-20022002200220000000000000-200000000000
χ2122222222-2-2-22222-22222-20000-2222200002200-2-200-2-200000000000000-2000000000000
χ2222222222-2-2-22222-22222-20000-2-2-2-2-20000-2-200-2-20022000000000000002000000000000
χ2322222222-2-2-22222-2-2-2-2-2-20000-222220000-2-2002200-2-2000000000000002000000000000
χ2422222222-2-2-22222-2-2-2-2-2-20000-2-2-2-2-20000220022002200000000000000-2000000000000
χ25222-22-2-2-2-22-200002000002i2i−2i−2i022−2−222-2-2002i−2i00002−200i2i2−i2−i2000022−2−200000000i2−i2000
χ26222-22-2-2-2-22-200002000002i2i−2i−2i022−2−2-2-22200−2i2i00002−200i2i2−i2−i20000−2−22200000000−i2i2000
χ27222-22-2-2-2-22-200002000002i2i−2i−2i0−2−22222-2-2002i−2i0000−2200−i2−i2i2i20000−2−22200000000−i2i2000
χ28222-22-2-2-2-22-200002000002i2i−2i−2i0−2−222-2-22200−2i2i0000−2200−i2−i2i2i2000022−2−200000000i2−i2000
χ29222-22-2-2-2-22-20000200000−2i−2i2i2i022−2−222-2-200−2i2i00002−200−i2−i2i2i2000022−2−200000000−i2i2000
χ30222-22-2-2-2-22-20000200000−2i−2i2i2i022−2−2-2-222002i−2i00002−200−i2−i2i2i20000−2−22200000000i2−i2000
χ31222-22-2-2-2-22-20000200000−2i−2i2i2i0−2−22222-2-200−2i2i0000−2200i2i2−i2−i20000−2−22200000000i2−i2000
χ32222-22-2-2-2-22-20000200000−2i−2i2i2i0−2−222-2-222002i−2i0000−2200i2i2−i2−i2000022−2−200000000−i2i2000
χ3322-22-2-2-220002-22-2022-2-20000002i−2i2i−2ii2−i2i2−i22i−2i00000000i2−i20000i2i2−i2−i22−22−200000000002−20
χ3422-22-2-2-220002-22-2022-2-20000002i−2i2i−2i−i2i2−i2i22i−2i00000000−i2i20000−i2−i2i2i2−22−220000000000−220
χ3522-22-2-2-220002-22-2022-2-2000000−2i2i−2i2ii2−i2i2−i2−2i2i00000000i2−i20000i2i2−i2−i2−22−220000000000−220
χ3622-22-2-2-220002-22-2022-2-2000000−2i2i−2i2i−i2i2−i2i2−2i2i00000000−i2i20000−i2−i2i2i22−22−200000000002−20
χ3722-22-2-2-220002-22-20-2-2220000002i−2i2i−2ii2−i2i2−i2−2i2i00000000i2−i20000−i2−i2i2i22−22−20000000000−220
χ3822-22-2-2-220002-22-20-2-2220000002i−2i2i−2i−i2i2−i2i2−2i2i00000000−i2i20000i2i2−i2−i2−22−2200000000002−20
χ3922-22-2-2-220002-22-20-2-222000000−2i2i−2i2ii2−i2i2−i22i−2i00000000i2−i20000−i2−i2i2i2−22−2200000000002−20
χ4022-22-2-2-220002-22-20-2-222000000−2i2i−2i2i−i2i2−i2i22i−2i00000000−i2i20000i2i2−i2−i22−22−20000000000−220
χ412-222-22-2-22-2-222-2-220000-22i−2i2i−2i2000000000000002i−2i000000002-22-200000000002i−2i00000
χ422-222-22-2-22-2-222-2-220000-22i−2i2i−2i2000000000000002i−2i00000000-22-220000000000−2i2i00000
χ432-222-22-2-22-2-222-2-220000-2−2i2i−2i2i200000000000000−2i2i000000002-22-20000000000−2i2i00000
χ442-222-22-2-22-2-222-2-220000-2−2i2i−2i2i200000000000000−2i2i00000000-22-2200000000002i−2i00000
χ452-222-22-2-22-2-2-2-22222i−2i2i−2i22i−2i2i−2i-20000000000002i−2i−2i2i0000000000000000002-2000000000
χ462-222-22-2-22-2-2-2-22222i−2i2i−2i2−2i2i−2i2i-20000000000002i−2i2i−2i000000000000000000-22000000000
χ472-222-22-2-22-2-2-2-2222−2i2i−2i2i22i−2i2i−2i-2000000000000−2i2i−2i2i000000000000000000-22000000000
χ482-222-22-2-22-2-2-2-2222−2i2i−2i2i2−2i2i−2i2i-2000000000000−2i2i2i−2i0000000000000000002-2000000000
χ492-222-22-2-2-222-2-222-22i−2i2i−2i-200002000000000000−2i2i0000002-22-20000000000002i−2i0000000
χ502-222-22-2-2-222-2-222-22i−2i2i−2i-200002000000000000−2i2i000000-22-22000000000000−2i2i0000000
χ512-222-22-2-2-222-2-222-2−2i2i−2i2i-2000020000000000002i−2i0000002-22-2000000000000−2i2i0000000
χ522-222-22-2-2-222-2-222-2−2i2i−2i2i-2000020000000000002i−2i000000-22-220000000000002i−2i0000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-44-440000-400000000002222−22−22000000000000−2222000000000000000000000000000
χ55444-44-4-4-44-440000-40000000000−22−22222200000000000022−22000000000000000000000000000
χ5644-44-4-4-44000-44-440000000000000002i2−2i22i2−2i20000000000−2i22i20000000000000000000000000
χ5744-44-4-4-44000-44-44000000000000000−2i22i2−2i22i200000000002i2−2i20000000000000000000000000
χ5844-4-4-444-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ5944-4-4-444-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ6044-4-4-444-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ6144-4-4-444-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ624-444-44-4-4-44444-4-4-4000040000-4000000000000000000000000000000000000000000000
χ634-44-4-4-44444-40000-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ644-44-4-4-44444-40000-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ654-44-4-4-444-4-4400004000004-4-440000000000000000000000000000000000000000000000
χ664-44-4-4-444-4-440000400000-444-40000000000000000000000000000000000000000000000
χ674-4-444-44-40004-4-44000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-444-44-40004-4-4400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-444-44-4000-444-404i−4i−4i4i000000000000000000000000000000000000000000000000000
χ704-4-444-44-4000-444-40−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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