Finite Group Databasebeta

← Group #23739

Character table — Group #23739

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222222444488888888888811112222224444888888888888
order1244222444888824444488888822442224448888244444888888
χ11111111111111111111111111111111111111111111111111111
χ21111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111
χ311111111111111-1-111-1-111-1-1-1-111111111111111-1-111-1-111-1-1-1-1
χ411111111111111-1-1-1-111-1-111-1-111111111111111-1-1-1-111-1-111-1-1
χ51111111111-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1
χ71111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111
χ81111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111
χ922222-2-2-2-22000000000000002-222222-2-2-2-22000000000000002-2
χ1022222-2-2-2-2200000000000000-2222222-2-2-2-2200000000000000-22
χ112222-22-22-2-2000000002-20000002222-22-22-2-2000000002-2000000
χ122222-22-22-2-200000000-220000002222-22-22-2-200000000-22000000
χ132222-2-22-22-20000002-2000000002222-2-22-22-20000002-200000000
χ142222-2-22-22-2000000-22000000002222-2-22-22-2000000-2200000000
χ1522-2-2222-2-2-22i2i−2i−2i00000000000022-2-2222-2-2-22i2i−2i−2i000000000000
χ1622-2-2222-2-2-2−2i−2i2i2i00000000000022-2-2222-2-2-2−2i−2i2i2i000000000000
χ1722-2-22-2-222-200002-2000000000022-2-22-2-222-200002-20000000000
χ1822-2-22-2-222-20000-22000000000022-2-22-2-222-20000-220000000000
χ1922-2-2-22-2-2220000000000002i−2i0022-2-2-22-2-2220000000000002i−2i00
χ2022-2-2-22-2-222000000000000−2i2i0022-2-2-22-2-222000000000000−2i2i00
χ2122-2-2-2-222-2200000000002i−2i000022-2-2-2-222-2200000000002i−2i0000
χ2222-2-2-2-222-220000000000−2i2i000022-2-2-2-222-220000000000−2i2i0000
χ234-44i−4i0000002ζ−2ζ2ζ3−2ζ30000000000004-44i−4i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ244-44i−4i000000−2ζ2ζ−2ζ32ζ30000000000004-44i−4i000000−2ζ2ζ−2ζ32ζ3000000000000
χ254-4−4i4i0000002ζ3−2ζ32ζ−2ζ0000000000004-4−4i4i0000002ζ3−2ζ32ζ−2ζ000000000000
χ264-4−4i4i000000−2ζ32ζ3−2ζ2ζ0000000000004-4−4i4i000000−2ζ32ζ3−2ζ2ζ000000000000
χ2711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ281111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ2911111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ3011111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ311111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ321111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ331111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ341111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ3522222-2-2-2-22000000000000002-2-2-2-2-2-22222-200000000000000-22
χ3622222-2-2-2-2200000000000000-22-2-2-2-2-22222-2000000000000002-2
χ372222-22-22-2-2000000002-2000000-2-2-2-22-22-22200000000-22000000
χ382222-22-22-2-200000000-22000000-2-2-2-22-22-222000000002-2000000
χ392222-2-22-22-20000002-200000000-2-2-2-222-22-22000000-2200000000
χ402222-2-22-22-2000000-2200000000-2-2-2-222-22-220000002-200000000
χ4122-2-2222-2-2-22i2i−2i−2i000000000000-2-222-2-2-2222−2i−2i2i2i000000000000
χ4222-2-2222-2-2-2−2i−2i2i2i000000000000-2-222-2-2-22222i2i−2i−2i000000000000
χ4322-2-22-2-222-200002-20000000000-2-222-222-2-220000-220000000000
χ4422-2-22-2-222-20000-220000000000-2-222-222-2-2200002-20000000000
χ4522-2-2-22-2-2220000000000002i−2i00-2-2222-222-2-2000000000000−2i2i00
χ4622-2-2-22-2-222000000000000−2i2i00-2-2222-222-2-20000000000002i−2i00
χ4722-2-2-2-222-2200000000002i−2i0000-2-22222-2-22-20000000000−2i2i0000
χ4822-2-2-2-222-220000000000−2i2i0000-2-22222-2-22-200000000002i−2i0000
χ494-44i−4i0000002ζ−2ζ2ζ3−2ζ3000000000000-44−4i4i000000−2ζ2ζ−2ζ32ζ3000000000000
χ504-44i−4i000000−2ζ2ζ−2ζ32ζ3000000000000-44−4i4i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ514-4−4i4i0000002ζ3−2ζ32ζ−2ζ000000000000-444i−4i000000−2ζ32ζ3−2ζ2ζ000000000000
χ524-4−4i4i000000−2ζ32ζ3−2ζ2ζ000000000000-444i−4i0000002ζ3−2ζ32ζ−2ζ000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.