Finite Group Databasebeta

← Group #248709

Character table — Group #248709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122224444444444488888888888888816161616161616161616161616161616163232
order12222244224444444442222244444444442444444444444888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-11-1-11-1111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1
χ411111111111111111111-1-1-1-11-1-1111-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-111
χ5111111111111111-1-111-11111-11111-111-1-11-1-1-1-11-1-1-111-1-111-1-11-1
χ6111111111111111-1-111-11111-11111-111-1-1-1-111-1-1-1-1-1-1-111-1-111-11
χ7111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-11111-1-1-11
χ8111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-111-1-111-1-111111-1-1-1-1111-1
χ911111111111-1-1-1-11111111111-1-1-1-11-1-1-1-11-111-1111-11111-1-1-1-1-1-1
χ1011111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ1111111111111-1-1-1-111111-1-1-1-1111-1-1111111-111-11-1-11-1-1-1-1-1-1-1-111
χ1211111111111-1-1-1-111111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1111111111-1-1
χ1311111111111-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-1-1-111-11
χ1411111111111-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-111-11111-1-1-11-1-11111-1-11-1
χ1511111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-1-111-1-1111-1
χ1611111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-111-1-1-11111-111-111-1-111-1-1-11
χ1722222222-2-22222222-2-220000-200-2-2-200000-200200000000000000
χ1822222222-2-222222-2-2-2-2-20000200-2-2200000200-200000000000000
χ1922222222-2-22-2-2-2-222-2-220000-20022-200000200-200000000000000
χ2022222222-2-22-2-2-2-2-2-2-2-2-2000020022200000-200200000000000000
χ21222222-2-222-2000022-2-2-222-2-220000-200000000002-200000000000
χ22222222-2-222-2000022-2-2-2-2-22220000-20000000000-2200000000000
χ23222222-2-222-20000-2-2-2-2222-2-2-2000020000000000-2200000000000
χ24222222-2-222-20000-2-2-2-22-2-222-20000200000000002-200000000000
χ25222222-2-2-2-2-200002222-20000-222002-2-22200000000-20000000000
χ26222222-2-2-2-2-200002222-20000-2-2-200222-2-20000000020000000000
χ27222222-2-2-2-2-20000-2-2222000022200-2-2-2-2-20000000020000000000
χ28222222-2-2-2-2-20000-2-222200002-2-200-2222200000000-20000000000
χ292222-2-2222-2-222-2-2002-2000000002-200000002-2000000000002-200
χ302222-2-2222-2-222-2-2002-2000000002-20000000-2200000000000-2200
χ312222-2-2222-2-2-2-222002-200000000-2200000002-200000000000-2200
χ322222-2-2222-2-2-2-222002-200000000-220000000-22000000000002-200
χ332222-2-222-22-222-2-200-2200000000-220000020000-200000002-20000
χ342222-2-222-22-222-2-200-2200000000-2200000-2000020000000-220000
χ352222-2-222-22-2-2-22200-22000000002-20000020000-20000000-220000
χ362222-2-222-22-2-2-22200-22000000002-200000-20000200000002-20000
χ374444-4-4-4-44-44000000-440000000000000000000000000000000000
χ384444-4-4-4-4-4440000004-40000000000000000000000000000000000
χ3944-4-4004-4000004i−4i000002-22-202i−2i0002i−2i000000000000000000000
χ4044-4-4004-4000004i−4i00000-22-220−2i2i000−2i2i000000000000000000000
χ4144-4-4004-400000−4i4i000002-22-20−2i2i000−2i2i000000000000000000000
χ4244-4-4004-400000−4i4i00000-22-2202i−2i0002i−2i000000000000000000000
χ4344-4-400-440004i−4i00000002-2-2202i−2i000−2i2i000000000000000000000
χ4444-4-400-440004i−4i0000000-222-20−2i2i0002i−2i000000000000000000000
χ4544-4-400-44000−4i4i00000002-2-220−2i2i0002i−2i000000000000000000000
χ4644-4-400-44000−4i4i0000000-222-202i−2i000−2i2i000000000000000000000
χ474-4-444-40000000004i−4i000000000000000000000000002-22i−2i000000
χ484-4-444-40000000004i−4i00000000000000000000000000-22−2i2i000000
χ494-4-444-4000000000−4i4i000000000000000000000000002-2−2i2i000000
χ504-4-444-4000000000−4i4i00000000000000000000000000-222i−2i000000
χ518-88-800000000000000000000000000004i−4i0000000000000000000
χ528-88-80000000000000000000000000000−4i4i0000000000000000000
χ538-8-88-8800000000000000000000000000000000000000000000000

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