Finite Group Databasebeta

← Group #273241

Character table — Group #273241

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222444444444888888888888888888161616161616161616161616161616163232
order12222244444444444244444444444448888444444888888888848
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-111-11-1-11-1-1-1-1-1-1-1-1111-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-111
χ511111111111111111-11-1-11-11111111111-1-11-11-1-1-11-1-111-1-1-1-1-11-1
χ611111111111111111-11-1-11-111111111-1-1-1-1-1-1-11-11-111-1-111-1-1-1-11
χ711111111111111111-11-1-11-1-1-1-1-1-1-1-1-111111-11-1-1-11-1-1-1-111111-11
χ811111111111111111-11-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11111-1-11111-1
χ9111111111-1-11-1-11111-111-111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ10111111111-1-11-1-11111-111-111111-1-1-1-1-1-1111-111-11-1-1-1-1-1-1-11-1-111
χ11111111111-1-11-1-11111-111-11-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-11111
χ12111111111-1-11-1-11111-111-11-1-1-1-11111-1-1-1-11-111-11-1-1-11111-111-1-1
χ13111111111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1-11-11111-1-111-1-1-111-11
χ14111111111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-11-1-111-1-111-1111-1
χ15111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-111111111-11-11111-1-1-1-1111-1-11-1
χ16111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111111-11-1-11111-1-11-1-1-11
χ1722222222-2222-2-2-2-2-20200-2000000000220020-2000-200000000000
χ1822222222-2222-2-2-2-2-20200-2000000000-2-200-202000200000000000
χ1922222222-2-2-2222-2-2-20-20020000000002200-202000-200000000000
χ2022222222-2-2-2222-2-2-20-2002000000000-2-20020-2000200000000000
χ21222222-2-2-200-200-222202-20-222-2-2000000220000000000000-20000
χ22222222-2-2-200-200-222202-20-2-2-222000000-2-2000000000000020000
χ23222222-2-2-200-200-222-20-220222-2-2000000-2-2000000000000020000
χ24222222-2-2-200-200-222-20-2202-2-222000000220000000000000-20000
χ252222-2-222222-222-2-220-200-2000000000000000020-202-2000000000
χ262222-2-222222-222-2-220-200-20000000000000000-2020-22000000000
χ272222-2-2222-2-2-2-2-2-2-2202002000000000000000020-20-22000000000
χ282222-2-2222-2-2-2-2-2-2-22020020000000000000000-20202-2000000000
χ292222-2-222-222-2-2-222-22-2-2-2220000000000000200-20000000000000
χ302222-2-222-222-2-2-222-2-2-2222-20000000000000-20020000000000000
χ312222-2-222-2-2-2-22222-222-2-2-220000000000000-20020000000000000
χ322222-2-222-2-2-2-22222-2-2222-2-20000000000000200-20000000000000
χ332222-2-2-2-2200200-22-220-220-200002i2i−2i−2i0000000000000000002i−2i00
χ342222-2-2-2-2200200-22-220-220-20000−2i−2i2i2i000000000000000000−2i2i00
χ352222-2-2-2-2200200-22-2-202-20200002i2i−2i−2i000000000000000000−2i2i00
χ362222-2-2-2-2200200-22-2-202-2020000−2i−2i2i2i0000000000000000002i−2i00
χ37444444-4-4400-4004-4-4000000000000000000000000000000000000
χ384444-4-4-4-4-4004004-44000000000000000000000000000000000000
χ3944-4-44-4000000000000000000000000022−2222−22000000000002-200000
χ4044-4-44-4000000000000000000000000022−22−222200000000000-2200000
χ4144-4-44-40000000000000000000000000−222222−2200000000000-2200000
χ4244-4-44-40000000000000000000000000−2222−2222000000000002-200000
χ434-4-44004-400004-40000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ444-4-44004-400004-4000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ454-4-44004-40000-440000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ464-4-44004-40000-44000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ474-4-4400-4404i−4i0000000000002i−2i−2i2i2-2-220000000000000000000000
χ484-4-4400-4404i−4i000000000000−2i2i2i−2i-222-20000000000000000000000
χ494-4-4400-440−4i4i0000000000002i−2i−2i2i-222-20000000000000000000000
χ504-4-4400-440−4i4i000000000000−2i2i2i−2i2-2-220000000000000000000000
χ5188-8-8-8800000000000000000000000000000000000000000000000
χ528-88-8000000000000000000000000000000000000000022−220000000
χ538-88-80000000000000000000000000000000000000000−22220000000

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