Finite Group Databasebeta

← Group #244899

Character table — Group #244899

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1
χ911111111111111111-1-1-1-1111111111111111-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-2-200002222-222220000-2-200220000-2-2000000000000-2000000000000
χ18222222222-22-22-22-2-200002222-2-2-2-2-20000-2-200-2-20000220000000000002000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2222200002200-2-20000-2-20000000000002000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2-2-20000220022000022000000000000-2000000000000
χ2122222222-22-22-22-22-222220000-200002222002200-2-2-2-200000000000000000-2000000000
χ2222222222-22-22-22-22-222220000-20000-2-2-2-200-2-200-2-222000000000000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-20000222200-2-20022-2-2000000000000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-20000-2-2-2-2002200222200000000000000000-2000000000
χ25222-2-2-2-220-202020-202i2i−2i−2i00000i2i2−i2−i22i2i−2i−2i002-2000000i2−i222−2−2000022−2−200000000i2−i2000
χ26222-2-2-2-220-202020-202i2i−2i−2i00000i2i2−i2−i2−2i−2i2i2i00-22000000i2−i222−2−20000−2−22200000000−i2i2000
χ27222-2-2-2-220-202020-202i2i−2i−2i00000−i2−i2i2i22i2i−2i−2i002-2000000−i2i2−2−2220000−2−22200000000−i2i2000
χ28222-2-2-2-220-202020-202i2i−2i−2i00000−i2−i2i2i2−2i−2i2i2i00-22000000−i2i2−2−222000022−2−200000000i2−i2000
χ29222-2-2-2-220-202020-20−2i−2i2i2i00000i2i2−i2−i22i2i−2i−2i00-22000000i2−i2−2−222000022−2−200000000−i2i2000
χ30222-2-2-2-220-202020-20−2i−2i2i2i00000i2i2−i2−i2−2i−2i2i2i002-2000000i2−i2−2−2220000−2−22200000000i2−i2000
χ31222-2-2-2-220-202020-20−2i−2i2i2i00000−i2−i2i2i22i2i−2i−2i00-22000000−i2i222−2−20000−2−22200000000i2−i2000
χ32222-2-2-2-220-202020-20−2i−2i2i2i00000−i2−i2i2i2−2i−2i2i2i002-2000000−i2i222−2−2000022−2−200000000−i2i2000
χ3322-2-22-22-220-20-2020000002i2i−2i−2i02i−2i2i−2ii2−i2i2−i200002-200i2−i200000022−2−22−22−20000000000i2−i20
χ3422-2-22-22-220-20-2020000002i2i−2i−2i02i−2i2i−2i−i2i2−i2i200002-200−i2i2000000−2−222−22−220000000000−i2i20
χ3522-2-22-22-220-20-2020000002i2i−2i−2i0−2i2i−2i2ii2−i2i2−i20000-2200i2−i200000022−2−2−22−220000000000−i2i20
χ3622-2-22-22-220-20-2020000002i2i−2i−2i0−2i2i−2i2i−i2i2−i2i20000-2200−i2i2000000−2−2222−22−20000000000i2−i20
χ3722-2-22-22-220-20-202000000−2i−2i2i2i02i−2i2i−2ii2−i2i2−i20000-2200i2−i2000000−2−2222−22−20000000000−i2i20
χ3822-2-22-22-220-20-202000000−2i−2i2i2i02i−2i2i−2i−i2i2−i2i20000-2200−i2i200000022−2−2−22−220000000000i2−i20
χ3922-2-22-22-220-20-202000000−2i−2i2i2i0−2i2i−2i2ii2−i2i2−i200002-200i2−i2000000−2−222−22−220000000000i2−i20
χ4022-2-22-22-220-20-202000000−2i−2i2i2i0−2i2i−2i2i−i2i2−i2i200002-200−i2i200000022−2−22−22−20000000000−i2i20
χ412-2-2-2-22222-2-222-2-22-22-22-200002000000000000002-2000000002-22-200000000002-200000
χ422-2-2-2-22222-2-222-2-22-22-22-200002000000000000002-200000000-22-220000000000-2200000
χ432-2-2-2-22222-2-222-2-22-2-22-220000200000000000000-22000000002-22-20000000000-2200000
χ442-2-2-2-22222-2-222-2-22-2-22-220000200000000000000-2200000000-22-2200000000002-200000
χ452-2-2-2-2222-222-2-222-2-200002-22-22000000002-200000000002-22-20000000000002-20000000
χ462-2-2-2-2222-222-2-222-2-200002-22-22000000002-20000000000-22-22000000000000-220000000
χ472-2-2-2-2222-222-2-222-2-20000-22-22200000000-2200000000002-22-2000000000000-220000000
χ482-2-2-2-2222-222-2-222-2-20000-22-22200000000-220000000000-22-220000000000002-20000000
χ492-2-2-2-2222-2-222-2-22222-22-22-22-2-200000000-220000-22000000000000000002-20000000000
χ502-2-2-2-2222-2-222-2-22222-22-2-22-22-2000000002-20000-2200000000000000000-220000000000
χ512-2-2-2-2222-2-222-2-2222-22-222-22-2-200000000-2200002-200000000000000000-220000000000
χ522-2-2-2-2222-2-222-2-2222-22-22-22-22-2000000002-200002-2000000000000000002-20000000000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-4-44040-40-40400000000002i22i2−2i2−2i200000000000000−2i22i20000000000000000000000000
χ55444-4-4-4-44040-40-4040000000000−2i2−2i22i22i2000000000000002i2−2i20000000000000000000000000
χ5644-44-44-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5744-44-44-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ5844-44-44-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ5944-44-44-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ6044-4-44-44-4-404040-40000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ6144-4-44-44-4-404040-4000000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ624-444-4-44-44040-40-40000000000000000000000000000000000022−22−222200000000000000000
χ634-444-4-44-44040-40-400000000000000000000000000000000000−222222−2200000000000000000
χ644-444-4-44-4-40-404040000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ654-444-4-44-4-40-40404000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ664-4-444-4-4404040-40-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ674-4-444-4-4404040-40-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ684-4-444-4-440-40-4040400000000000000000000000000000022−22−2222000000000000000000000
χ694-4-444-4-440-40-40404000000000000000000000000000000−222222−22000000000000000000000
χ704-4-4-4-444444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ718-88-888-8-8000000000000000000000000000000000000000000000000000000000000000

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