Finite Group Databasebeta

← Group #289297

Character table — Group #289297

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12224444448888244488888888888888888888888888822444488884488
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1111111111-11-1-1-111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-111-1-1
χ71111111111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1111111-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ91111111111-1-1-1-11111-1-1-1-11111-111111111-1-1-1-1-1-1-1-1-1-1111-11-1-1-11-11-11-1
χ101111111111-1-1-1-11111-1-1-1-11111-1111111-1-111-1-1-1-1-1-1-1-11-111-11-1-1-11-11-11
χ111111111111-1-1-1-11111-1-1-1-11111-111-1-1-1-111-1-1-1-1-1-11111-11-1-11-1111-1-11-11
χ121111111111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-111-1-1-1-11111-1-1-11-1111-111-11-1
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-11-11111-1-111-1
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11-1-11-111-111-1-11
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-111-11-1-11-11-1-11
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1-11-111-1
χ1722222222-2-22222-2-22-222-2-20000-200000022220000000000000000-2-20000
χ1822222222-2-22222-2-22-222-2-20000-2000000-2-2-2-20000000000000000220000
χ1922222222-2-2-2-2-2-2-2-22-2-2-2220000200000022-2-20000000000000000-220000
χ2022222222-2-2-2-2-2-2-2-22-2-2-22200002000000-2-22200000000000000002-20000
χ21222222-2-2222222-2-2-22-2-2220000-20000000000000000000202-2-200000000
χ22222222-2-2222222-2-2-22-2-2220000-20000000000000000000-20-22200000000
χ23222222-2-222-2-2-2-2-2-2-2222-2-200002000000000000000000020-2-2200000000
χ24222222-2-222-2-2-2-2-2-2-2222-2-2000020000000000000000000-2022-200000000
χ25222222-2-2-2-2222222-2-2-2-2-2-22i2i−2i−2i22i−2i000000002i2i−2i−2i000000000000000000
χ26222222-2-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i2−2i2i00000000−2i−2i2i2i000000000000000000
χ27222222-2-2-2-2-2-2-2-222-2-222222i2i−2i−2i-22i−2i00000000−2i−2i2i2i000000000000000000
χ28222222-2-2-2-2-2-2-2-222-2-22222−2i−2i2i2i-2−2i2i000000002i2i−2i−2i000000000000000000
χ292222-2-222220000-22-2-2000022220-2-222-2-200000000000020-200000000000
χ302222-2-222220000-22-2-2000022220-2-2-2-222000000000000-20200000000000
χ312222-2-222220000-22-2-20000-2-2-2-202222-2-2000000000000-20200000000000
χ322222-2-222220000-22-2-20000-2-2-2-2022-2-22200000000000020-200000000000
χ332222-2-2-2-2-2-20000-222200002i2i−2i−2i0−2i2i00000000000022-2-20000002i−2i000000
χ342222-2-2-2-2-2-20000-222200002i2i−2i−2i0−2i2i000000000000-2-222000000−2i2i000000
χ352222-2-2-2-2-2-20000-22220000−2i−2i2i2i02i−2i00000000000022-2-2000000−2i2i000000
χ362222-2-2-2-2-2-20000-22220000−2i−2i2i2i02i−2i000000000000-2-2220000002i−2i000000
χ374444-4-444-4-400004-4-4400000000000000000000000000000000000000000
χ384444-4-4-4-44400004-44-400000000000000000000000000000000000000000
χ3944-4-4-44000044-4-400000000000000000002i2−2i22i2−2i20000000000000000000000
χ4044-4-4-44000044-4-40000000000000000000−2i22i2−2i22i20000000000000000000000
χ4144-4-4-440000-4-44400000000000000000002i2−2i2−2i22i20000000000000000000000
χ4244-4-4-440000-4-4440000000000000000000−2i22i22i2−2i20000000000000000000000
χ434-44-400004-42i2−2i22i2−2i20000002i2−2i22i2−2i22i2−2i2000000000002-22-2000000000000000000
χ444-44-400004-42i2−2i22i2−2i20000002i2−2i2−2i22i2−2i22i200000000000-22-22000000000000000000
χ454-44-400004-4−2i22i2−2i22i2000000−2i22i22i2−2i22i2−2i200000000000-22-22000000000000000000
χ464-44-400004-4−2i22i2−2i22i2000000−2i22i2−2i22i2−2i22i2000000000002-22-2000000000000000000
χ474-44-40000-442i2−2i22i2−2i2000000−2i22i222−22−222200000000000−2i2i2i−2i000000000000000000
χ484-44-40000-442i2−2i22i2−2i2000000−2i22i2−222222−22000000000002i−2i−2i2i000000000000000000
χ494-44-40000-44−2i22i2−2i22i20000002i2−2i222−22−2222000000000002i−2i−2i2i000000000000000000
χ504-44-40000-44−2i22i2−2i22i20000002i2−2i2−222222−2200000000000−2i2i2i−2i000000000000000000
χ514-4-44004-4002i2−2i2−2i22i200002i2−2i200000000022−2200000000002i−2i2i−2i00000000000000
χ524-4-44004-4002i2−2i2−2i22i200002i2−2i2000000000−22220000000000−2i2i−2i2i00000000000000
χ534-4-44004-400−2i22i22i2−2i20000−2i22i200000000022−220000000000−2i2i−2i2i00000000000000
χ544-4-44004-400−2i22i22i2−2i20000−2i22i2000000000−222200000000002i−2i2i−2i00000000000000
χ554-4-4400-44002i2−2i2−2i22i20000−2i22i20000000000022−22000000002i−2i−2i2i00000000000000
χ564-4-4400-44002i2−2i2−2i22i20000−2i22i200000000000−222200000000−2i2i2i−2i00000000000000
χ574-4-4400-4400−2i22i22i2−2i200002i2−2i20000000000022−2200000000−2i2i2i−2i00000000000000
χ584-4-4400-4400−2i22i22i2−2i200002i2−2i200000000000−2222000000002i−2i−2i2i00000000000000
χ5988-8-88-800000000000000000000000000000000000000000000000000000

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