Finite Group Databasebeta

← Group #251155

Character table — Group #251155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444422444224444444888888444444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1111-1-1-1-1-11-111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111-1-11-1-1-1-1-111-1-1-1-1-1-1-1111
χ4111111111111111111111111-1-1-1-1-1-1-1-11-111-1-1111-1-1-11-1-1111-1-1-1
χ5111111111111111111-111-1-1-111-1-11111-11-1-11111-111-1-1-1-111-1-1-1-1
χ6111111111111111111-111-1-1-111-1-1-1-1-1-1-111-111-1-11-1-1-11-1-1-1-11111
χ7111111111111111111-111-1-1-1-1-1111111-1-11-1-1-1-1-11111111-1-11-1-1-1
χ8111111111111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-11111-1111
χ9111111111111-1-1111-11-1-111111111111-11-1-1-1-1-1-1-1-1-111-1-111111-1
χ10111111111111-1-1111-11-1-11111111-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-11
χ11111111111111-1-1111-11-1-1111-1-1-1-11111-1-11-111111-1-1-1-111-1-1-111-1
χ12111111111111-1-1111-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1111111-1-11
χ13111111111111-1-1111-1-1-1-1-1-1-111-1-111111111-1-1-1-11-1-1-1-11111-1-1-11
χ14111111111111-1-1111-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-111-111-1111-1-1111-1
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-11111111-1-111111-1-1-111-1-1-1-11-1-11
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-11111-1-1-111-111-1
χ1722222222-222-200-2-2-202002-2-222-2-200000-20000000002000000000
χ1822222222-222-200-2-2-202002-2-2-2-222000002000000000-2000000000
χ1922222222-222-200-2-2-20-200-222222200000-2000000000-2000000000
χ2022222222-222-200-2-2-20-200-222-2-2-2-20000020000000002000000000
χ21222222-2-22-2-2222-22-220-2-2000000000000000002-200000002-20000
χ22222222-2-22-2-2222-22-220-2-200000000000000000-220000000-220000
χ23222222-2-22-2-22-2-2-22-2-2022000000000000000002-20000000-220000
χ24222222-2-22-2-22-2-2-22-2-202200000000000000000-2200000002-20000
χ252222-2-22-222-2222-2-22-202-20000000000000200000-200020000-2000
χ262222-2-22-222-2222-2-22-202-20000000000000-2000002000-200002000
χ272222-2-22-222-22-2-2-2-2220-220000000000000200000-2000-200002000
χ282222-2-22-222-22-2-2-2-2220-220000000000000-200000200020000-2000
χ292222-2-2-222-222222-2-2-22-22-22-200000000200-200000000000000000
χ302222-2-2-222-222222-2-2-2-2-222-2200000000-200200000000000000000
χ312222-2-2-222-222-2-22-2-2222-2-22-200000000-200200000000000000000
χ322222-2-2-222-222-2-22-2-22-22-22-2200000000200-200000000000000000
χ332222-2-2-22-2-22-200-2220200-2-220000000000002-200000002-2000000
χ342222-2-2-22-2-22-200-2220200-2-22000000000000-220000000-22000000
χ352222-2-2-22-2-22-200-2220-20022-20000000000002-20000000-22000000
χ362222-2-2-22-2-22-200-2220-20022-2000000000000-2200000002-2000000
χ37444444-4-4-4-4-4-4004-44000000000000000000000000000000000000
χ384444-4-44-4-44-4-40044-4000000000000000000000000000000000000
χ3944-4-40000400-44-40000000000000022-2-20000000002-20000000000
χ4044-4-40000400-44-400000000000000-2-222000000000-220000000000
χ4144-4-40000400-4-440000000000000022-2-2000000000-220000000000
χ4244-4-40000400-4-4400000000000000-2-2220000000002-20000000000
χ434-44-44-44-40-440000000000000004-40000000000000000000000000
χ444-44-44-44-40-44000000000000000-440000000000000000000000000
χ454-44-44-4-4404-400000000000000000000000000000000000000022−220
χ464-44-44-4-4404-4000000000000000000000000000000000000000−22220
χ474-44-4-44440-4-40000000000000000022−2222−22000000000000000000000
χ484-44-4-44440-4-400000000000000000−2222−2222000000000000000000000
χ494-44-4-44-4-404400000000000004i−4i000000000000000000000000000
χ504-44-4-44-4-40440000000000000−4i4i000000000000000000000000000
χ5188-8-80000-800800000000000000000000000000000000000000000
χ528-8-8800000000000000000000000022−22−2222000000000000000000000
χ538-8-88000000000000000000000000−222222−22000000000000000000000

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