Finite Group Databasebeta

← Group #288699

Character table — Group #288699

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222222444448888888888816161616161616161616161616161616161616163232
order12222244444444488888888888882244444488888888888824
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1111-111-11-1-11-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-11-1-1-11-1-1-11111-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1
χ51111111111111111111-1-11-1-11111-11-1-1-11111-111-11-1-1-1-111-1-1
χ61111111111111111111-1-11-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ71111111111111111111-1-11-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1
χ81111111111111111111-1-11-1-1-1-1-1-11-1111-1-1-11-1-1-1-11-1-1-1-11111
χ9111111111111111-1-1-1-111-1-1-11111-1111-11-1-11-1-1-11111-1-1-1-11-1
χ10111111111111111-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1111-1-1-11111-11
χ11111111111111111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-1-111111-1
χ12111111111111111-1-1-1-111-1-1-1-1-1-1-11-1-1-11-1111-1111111-1-1-1-1-11
χ13111111111111111-1-1-1-1-1-1-111111111-1-111-1-111-1-1-11-1-111-1-1-11
χ14111111111111111-1-1-1-1-1-1-11111111-1-1-11-1-1-1-1111-1-111-1-1111-1
χ15111111111111111-1-1-1-1-1-1-111-1-1-1-1-1111-1111-11-1-1-1-111-1-111-11
χ16111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-11-1-111-1-11-1
χ17222222-22222-2-2-2-222-2-2222-2-20000000000000200-2000000000
χ18222222-22222-2-2-2-222-2-2-2-22220000000000000-2002000000000
χ19222222-22222-2-2-2-2-2-22222-2220000000000000-200-2000000000
χ20222222-22222-2-2-2-2-2-222-2-2-2-2-200000000000002002000000000
χ21222222-2-2-2-2-2-22-220000000002i2i−2i−2i00000000002i−2i0000002-200
χ22222222-2-2-2-2-2-22-220000000002i2i−2i−2i0000000000−2i2i000000-2200
χ23222222-2-2-2-2-2-22-22000000000−2i−2i2i2i00000000002i−2i000000-2200
χ24222222-2-2-2-2-2-22-22000000000−2i−2i2i2i0000000000−2i2i0000002-200
χ252222-2-222-22-22-2-22222-200-2000000202-2-200000000000000000
χ262222-2-222-22-22-2-22222-200-2000000-20-22200000000000000000
χ272222-2-222-22-22-2-22-2-2-2200200000020-22-200000000000000000
χ282222-2-222-22-22-2-22-2-2-22002000000-202-2200000000000000000
χ292222-2-22-22-2222-2-20000000002-22-202000-20020000-200000000
χ302222-2-22-22-2222-2-20000000002-22-20-2000200-20000200000000
χ312222-2-22-22-2222-2-2000000000-22-2202000-200-20000200000000
χ322222-2-22-22-2222-2-2000000000-22-220-200020020000-200000000
χ332222-2-2-22-22-2-222-222-2200-2002i−2i−2i2i0000002i−2i00000000000000
χ342222-2-2-22-22-2-222-222-2200-200−2i2i2i−2i000000−2i2i00000000000000
χ352222-2-2-22-22-2-222-2-2-22-2002002i−2i−2i2i000000−2i2i00000000000000
χ362222-2-2-22-22-2-222-2-2-22-200200−2i2i2i−2i0000002i−2i00000000000000
χ374444444-4-4-4-44-44-400000000000000000000000000000000000
χ384444-4-4-4-44-44-4-44400000000000000000000000000000000000
χ394-4-444-4044-4-400000000000000000000000000000002i2−2i2000000
χ404-4-444-4044-4-40000000000000000000000000000000−2i22i2000000
χ414-4-444-40-4-444000000000004-400000000000000000000000000
χ424-4-444-40-4-44400000000000-4400000000000000000000000000
χ434-4-44-4404-4-4400000000000000000000000000000000022−220000
χ444-4-44-4404-4-44000000000000000000000000000000000−22220000
χ454-4-44-440-444-4000000004-400000000000000000000000000000
χ464-4-44-440-444-400000000-4400000000000000000000000000000
χ4788-8-8000000000004i2−4i2000000000000000000000000000000000
χ4888-8-800000000000−4i24i2000000000000000000000000000000000
χ498-88-80080000-800000000000000000000000000000000000000
χ508-88-800-80000800000000000000000000000000000000000000

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