Finite Group Databasebeta

← Group #251143

Character table — Group #251143

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444422444222244444888888224444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111-11-1-1-1-1-11-111-1-1-1-1-1-1
χ311111111111111111111-111-1-1-1-1-11111111-1-1-111-111-1-1-1-111-1-1-1-1
χ411111111111111111111-111-1-1-1-1-1-1-1-1-1111-11-1-1-11-1-1-11-1-1-1-11111
χ5111111111111111111-1-1111111-1-11111-1-1-11-11-1-1-111-1-1-1-1-1-1-1111
χ6111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-11-1-1111-1-1-1
χ7111111111111111111-1-1-111-1-1-1111111-1-1-1-11-1-1-11111111-1-11-1-1-1
χ8111111111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-11111-1111
χ9111111111111-1-1111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-111-1-111111-1
χ10111111111111-1-1111-1111-1-111111-1-1-1-1-1-11-11-1111111-1-1-1-1-1-1-1-11
χ11111111111111-1-1111-111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-1-1-11111-1-1-11
χ12111111111111-1-1111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-111-1111-1-1111-1
χ13111111111111-1-1111-1-1-11-1-1111-1-1111111-1-11-1111-1-1-1-111-1-1-111-1
χ14111111111111-1-1111-1-1-11-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-111-1111111-1-11
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-111-1-1-1-11-1-11
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-111-1111-1-11111-1-1-111-111-1
χ1722222222-222-200-2-2-20222002-2-2-2-2000000-2000000002000000000
χ1822222222-222-200-2-2-2022-200-22222000000-200000000-2000000000
χ1922222222-222-200-2-2-20-2-22002-2-222000000200000000-2000000000
χ2022222222-222-200-2-2-20-2-2-200-222-2-20000002000000002000000000
χ21222222-2-22-2-2222-22-22000-2-20000000000000002-200000002-20000
χ22222222-2-22-2-2222-22-22000-2-2000000000000000-220000000-220000
χ23222222-2-22-2-22-2-2-22-2-2000220000000000000002-20000000-220000
χ24222222-2-22-2-22-2-2-22-2-200022000000000000000-2200000002-20000
χ252222-2-22-222-2222-2-22-20002-200000000000002000-200020000-2000
χ262222-2-22-222-2222-2-22-20002-20000000000000-20002000-200002000
χ272222-2-22-222-22-2-2-2-222000-2200000000000002000-2000-200002000
χ282222-2-22-222-22-2-2-2-222000-220000000000000-2000200020000-2000
χ292222-2-2-222-222222-2-2-2002-22-22-200000000020-2000000000000000
χ302222-2-2-222-222222-2-2-200-2-222-22000000000-202000000000000000
χ312222-2-2-222-222-2-22-2-220022-2-22-2000000000-202000000000000000
χ322222-2-2-222-222-2-22-2-2200-22-22-2200000000020-2000000000000000
χ332222-2-2-22-2-22-200-222000200-2-220000002-2000000000002-2000000
χ342222-2-2-22-2-22-200-222000200-2-22000000-2200000000000-22000000
χ352222-2-2-22-2-22-200-222000-20022-20000002-200000000000-22000000
χ362222-2-2-22-2-22-200-222000-20022-2000000-22000000000002-2000000
χ37444444-4-4-4-4-4-4004-44000000000000000000000000000000000000
χ384444-4-44-4-44-4-40044-4000000000000000000000000000000000000
χ3944-4-44-4440-4-400000004-4000000000000000000000000000000000
χ4044-4-44-4440-4-40000000-44000000000000000000000000000000000
χ4144-4-44-4-4-4044000000000000000002i22i2−2i2−2i2000000000000000000000
χ4244-4-44-4-4-404400000000000000000−2i2−2i22i22i2000000000000000000000
χ4344-4-4-444-40-440000000000000000000000000000000000000002i2−2i20
χ4444-4-4-444-40-44000000000000000000000000000000000000000−2i22i20
χ4544-4-4-44-4404-40000000000000004i−4i0000000000000000000000000
χ4644-4-4-44-4404-4000000000000000−4i4i0000000000000000000000000
χ474-44-40000400-44-4000000000000002i−2i2i−2i0000000002i−2i0000000000
χ484-44-40000400-44-400000000000000−2i2i−2i2i000000000−2i2i0000000000
χ494-44-40000400-4-44000000000000002i−2i2i−2i000000000−2i2i0000000000
χ504-44-40000400-4-4400000000000000−2i2i−2i2i0000000002i−2i0000000000
χ518-88-80000-800800000000000000000000000000000000000000000
χ528-8-8800000000000000000000000022−22−2222000000000000000000000
χ538-8-88000000000000000000000000−222222−22000000000000000000000

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