Finite Group Databasebeta

← Group #251081

Character table — Group #251081

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444222224444888888222444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-111111-1-1-11-111-1-1-1-1-1-1
χ3111111111111111111111-1-1-11-1-1-1111111-1-11-111-111-1-1-1-111-1-1-1-1
χ4111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-11-11-1111-1-1-11-1-1-1-11111
χ51111111111111111111-1-111111-1-11111-1-1-11-11-1-1-111-1-1-1-1-1-1-1111
χ61111111111111111111-1-111111-1-1-1-1-1-11111-11-1-11-1-1-11-1-1111-1-1-1
χ71111111111111111111-1-1-1-1-11-1111111-1-11-1-1-1-1-11111111-1-11-1-1-1
χ81111111111111111111-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1-1-1-1-11-11111-1111
χ91111111111111-1-111-1-111111-11111111-1-1-1-11-1-1-1-1-1-111-1-111111-1
χ101111111111111-1-111-1-111111-1111-1-1-1-1111-11-1-1-11111-1-1-1-1-1-1-1-11
χ111111111111111-1-111-1-111-1-1-1-1-1-1-11111-1-11111-1-11-1-1-1-11111-1-1-11
χ121111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-111-1111-1-1111-1
χ131111111111111-1-111-1-1-1-1111-11-1-11111111-1-1-1111-1-1-1-111-1-1-111-1
χ141111111111111-1-111-1-1-1-1111-11-1-1-1-1-1-1-1-1-1-1-1-111-111-1111111-1-11
χ151111111111111-1-111-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-111-1-1-1-11-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11111111-1-1-111-111-1
χ172222222-222-22-200-2-200222-2-202-2-200000000-20000002000000000
χ182222222-222-22-200-2-20022-2220-22200000000-2000000-2000000000
χ192222222-222-22-200-2-200-2-22-2-20222000000002000000-2000000000
χ202222222-222-22-200-2-200-2-2-2220-2-2-20000000020000002000000000
χ21222222-22-2-22-2-222-22-2-200000200000002-200000000000002-20000
χ22222222-22-2-22-2-222-22-2-20000020000000-220000000000000-220000
χ23222222-22-2-22-2-2-2-2-222200000-200000002-20000000000000-220000
χ24222222-22-2-22-2-2-2-2-222200000-20000000-2200000000000002-20000
χ252222-2-222-222-2-2222-22-200000-2000000000200000-2000-200002000
χ262222-2-222-222-2-2222-22-200000-2000000000-200000200020000-2000
χ272222-2-222-222-2-2-2-22-2-22000002000000000200000-200020000-2000
χ282222-2-222-222-2-2-2-22-2-22000002000000000-2000002000-200002000
χ292222-2-2-222-222222-2-2-22002-22-2-200000000020-2000000000000000
χ302222-2-2-222-222222-2-2-2200-22-2-22000000000-202000000000000000
χ312222-2-2-222-2222-2-2-2-22-2002-222-2000000000-202000000000000000
χ322222-2-2-222-2222-2-2-2-22-200-22-22200000000020-2000000000000000
χ332222-2-2-2-22-2-22-20022000022-20-20000000000002-2000002-2000000
χ342222-2-2-2-22-2-22-20022000022-20-2000000000000-2200000-22000000
χ352222-2-2-2-22-2-22-200220000-2-22020000000000002-200000-22000000
χ362222-2-2-2-22-2-22-200220000-2-2202000000000000-22000002-2000000
χ37444444-4-4-4-4-4-44004-4000000000000000000000000000000000000
χ384444-4-44-4-44-4-4400-44000000000000000000000000000000000000
χ394-44-4000400-4004i−4i00000000000002i2i−2i−2i0000000002-20000000000
χ404-44-4000400-4004i−4i0000000000000−2i−2i2i2i000000000-220000000000
χ414-44-4000400-400−4i4i00000000000002i2i−2i−2i000000000-220000000000
χ424-44-4000400-400−4i4i0000000000000−2i−2i2i2i0000000002-20000000000
χ434-4-444-4404-40-4000000000000004i−4i0000000000000000000000000
χ444-4-444-4404-40-400000000000000−4i4i0000000000000000000000000
χ454-4-444-4-40-44040000000000000000000000000000000000000022−220
χ464-4-444-4-40-440400000000000000000000000000000000000000−22220
χ474-4-44-4440-4-404000000000000000022−2222−22000000000000000000000
χ484-4-44-4440-4-4040000000000000000−2222−2222000000000000000000000
χ494-4-44-44-40440-400000004-400000000000000000000000000000000
χ504-4-44-44-40440-40000000-4400000000000000000000000000000000
χ5188-8-80000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5288-8-8000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ538-88-8000-8008000000000000000000000000000000000000000000

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