Finite Group Databasebeta

← Group #502708

Character table — Group #502708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122224444444444488888888888888816161616161616161616161616161616163232
order12222244222244444442444444444444442244444444444888844
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11-1-1-1111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-111-1-1-1-111-1-1-11-1111-11-1-1-1-1-1-1-1-1-111
χ41111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11-111111111-1-1
χ5111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-11111-111111-1-1-1-1-1-1
χ6111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111
χ7111111111111-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-11111-1-1
χ8111111111111-1-1-1-11111-1-1-1-111-1-111-1-1111-11-1-1-1-1-1-11111-1-1-1-111
χ9111111-1-1111111111-11-1-1-111-1-1-1-11111-1-111-1-1-11-1-1111-1-111-1-11-1
χ10111111-1-1111111111-11-1-1-111-1-1-1-11111-1-11-1-111-1-1-11-1-111-1-111-11
χ11111111-1-1111111111-11-1-1-1-1-1-1-111-1-11111-111-1-111-1-1-1-111-1-1111-1
χ12111111-1-1111111111-11-1-1-1-1-1-1-111-1-11111-1-1111-11-1-111-1-111-1-1-11
χ13111111-1-11111-1-1-1-11-11-11111-1-1-1-1-1-1-1-111-111-1-11-11111-1-1-1-111-11
χ14111111-1-11111-1-1-1-11-11-11111-1-1-1-1-1-1-1-111-1-1111-1-111-1-11111-1-11-1
χ15111111-1-11111-1-1-1-11-11-111-1-1-1-11111-1-1-1-111-1-1-1111-1-1-11111-1-1-11
χ16111111-1-11111-1-1-1-11-11-111-1-1-1-11111-1-1-1-11-1-111-111-111-1-1-1-1111-1
χ17222222222-2-220000-22-2-200222-222000000000000-20-20000000000
χ18222222222-2-220000-22-2-200-2-22-2-2-20000000000002020000000000
χ1922222222-222-22222-22-2-22200-220000-2-2000000000-200000000000
χ2022222222-222-2-2-2-2-2-22-2-2-2-200-22000022000000000200000000000
χ2122222222-2-2-2-2000022220000-2-200220022-20-20000000000000000
χ2222222222-2-2-2-2000022220000-2-200-2-200-2-22020000000000000000
χ23222222-2-22-2-220000-2-2-220022-22-2-200000000000020-20000000000
χ24222222-2-22-2-220000-2-2-2200-2-2-2222000000000000-2020000000000
χ25222222-2-2-222-22222-2-2-22-2-2002-20000-2-2000000000200000000000
χ26222222-2-2-222-2-2-2-2-2-2-2-2222002-2000022000000000-200000000000
χ27222222-2-2-2-2-2-200002-22-2000022002200-2-2-2020000000000000000
χ28222222-2-2-2-2-2-200002-22-200002200-2-2002220-20000000000000000
χ292-2-222-20022-2-22i2i−2i−2i-202000000000002i−2i000000000002i−2i002-20000
χ302-2-222-20022-2-22i2i−2i−2i-202000000000002i−2i00000000000−2i2i00-220000
χ312-2-222-20022-2-2−2i−2i2i2i-20200000000000−2i2i000000000002i−2i00-220000
χ322-2-222-20022-2-2−2i−2i2i2i-20200000000000−2i2i00000000000−2i2i002-20000
χ332-2-222-200-22-222i2i−2i−2i20-200000000000−2i2i00000000000002-2002i−2i00
χ342-2-222-200-22-222i2i−2i−2i20-200000000000−2i2i0000000000000-2200−2i2i00
χ352-2-222-200-22-22−2i−2i2i2i20-2000000000002i−2i00000000000002-200−2i2i00
χ362-2-222-200-22-22−2i−2i2i2i20-2000000000002i−2i0000000000000-22002i−2i00
χ374444-4-444000000000-400000000000000000202-2-20000000000000
χ384444-4-444000000000-400000000000000000-20-2220000000000000
χ394444-4-4-4-400000000040000000000000000020-22-20000000000000
χ404444-4-4-4-4000000000400000000000000000-202-220000000000000
χ4144-4-4004i−4i00002-22-200002i−2i2-2002i−2i2-2002i−2i0000000000000000000
χ4244-4-4004i−4i00002-22-200002i−2i-2200−2i2i-2200−2i2i0000000000000000000
χ4344-4-4004i−4i0000-22-220000−2i2i2-2002i−2i-2200−2i2i0000000000000000000
χ4444-4-4004i−4i0000-22-220000−2i2i-2200−2i2i2-2002i−2i0000000000000000000
χ4544-4-400−4i4i00002-22-20000−2i2i2-200−2i2i2-200−2i2i0000000000000000000
χ4644-4-400−4i4i00002-22-20000−2i2i-22002i−2i-22002i−2i0000000000000000000
χ4744-4-400−4i4i0000-22-2200002i−2i2-200−2i2i-22002i−2i0000000000000000000
χ4844-4-400−4i4i0000-22-2200002i−2i-22002i−2i2-200−2i2i0000000000000000000
χ494-4-444-4004-44-4000040-40000000000000000000000000000000000
χ504-4-444-400-4-4440000-4040000000000000000000000000000000000
χ518-88-8000000004i−4i−4i4i0000000000000000000000000000000000000
χ528-88-800000000−4i4i4i−4i0000000000000000000000000000000000000
χ538-8-88-8800000000000000000000000000000000000000000000000

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