Finite Group Databasebeta

← Group #103483

Character table — Group #103483

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222444444444488888888816161616161616161616161616161616161616163232
order12222222444422444444444888888884444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ922222222222222-2-22-2-2-22-2-200000000000022-2-200000000000000
χ1022222222222222-2-22-2-2-22-2-2000000000000-2-22200000000000000
χ11222222222222-2-222-2-222-2-2-2000000000000000022-2-20000000000
χ12222222222222-2-222-2-222-2-2-20000000000000000-2-2220000000000
χ13222222222222-2-2-2-2-22-2-2-22200000000000000000000000000002-2
χ14222222222222-2-2-2-2-22-2-2-2220000000000000000000000000000-22
χ1522222222-2-2-2-22222-2-2-2-2-2-222i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ1622222222-2-2-2-22222-2-2-2-2-2-22−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ1722222222-2-2-2-222-2-2-2222-22-20000000000000000000022-2-2000000
χ1822222222-2-2-2-222-2-2-2222-22-200000000000000000000-2-222000000
χ1922222222-2-2-2-2-2-22222-2-222-20000000022-2-2000000000000000000
χ2022222222-2-2-2-2-2-22222-2-222-200000000-2-222000000000000000000
χ2122222222-2-2-2-2-2-2-2-22-2222-2200000000000000000000000022-2-200
χ2222222222-2-2-2-2-2-2-2-22-2222-22000000000000000000000000-2-22200
χ232-2-2222-2-222-2-22-200-2000200i2i2−i2−i2i2i2−i2−i200002-2000000i2−i2i2−i2000000
χ242-2-2222-2-222-2-22-200-2000200i2i2−i2−i2i2i2−i2−i20000-22000000−i2i2−i2i2000000
χ252-2-2222-2-222-2-22-200-2000200−i2−i2i2i2−i2−i2i2i200002-2000000−i2i2−i2i2000000
χ262-2-2222-2-222-2-22-200-2000200−i2−i2i2i2−i2−i2i2i20000-22000000i2−i2i2−i2000000
χ272-2-2222-2-2-2-2222-2002000-20022−2−2−2−2220000002i−2i0000i2−i2−i2i2000000
χ282-2-2222-2-2-2-2222-2002000-20022−2−2−2−222000000−2i2i0000−i2i2i2−i2000000
χ292-2-2222-2-2-2-2222-2002000-200−2−22222−2−20000002i−2i0000−i2i2i2−i2000000
χ302-2-2222-2-2-2-2222-2002000-200−2−22222−2−2000000−2i2i0000i2−i2−i2i2000000
χ314444-4-4-4-40000004-4000000000000000000000000022−220000000000
χ324444-4-4-4-40000004-40000000000000000000000000−22220000000000
χ334444-4-4-4-4000000-440000000000000000000000022−22000000000000
χ344444-4-4-4-4000000-4400000000000000000000000−2222000000000000
χ3544-4-44-44-40000000004000-402-22-22-22-20000000000000000000000
χ3644-4-44-44-40000000004000-40-22-22-22-220000000000000000000000
χ3744-4-44-44-4000000000-4000402i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ3844-4-44-44-4000000000-400040−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ3944-4-4-44-444-44-4000000000000000000000000000000000002i−2i2i−2i00
χ4044-4-4-44-444-44-400000000000000000000000000000000000−2i2i−2i2i00
χ4144-4-4-44-44-44-44000000000000000000000000000000000002i−2i−2i2i00
χ4244-4-4-44-44-44-4400000000000000000000000000000000000−2i2i2i−2i00
χ434-44-44-4-4400000000004i−4i0002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ444-44-44-4-4400000000004i−4i000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ454-44-44-4-440000000000−4i4i0002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ464-44-44-4-440000000000−4i4i000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ474-44-4-444-44-4-4400000000000000000002i−2i2i−2i000000000000000000
χ484-44-4-444-44-4-440000000000000000000−2i2i−2i2i000000000000000000
χ494-44-4-444-4-444-400000000000000000002i−2i−2i2i000000000000000000
χ504-44-4-444-4-444-40000000000000000000−2i2i2i−2i000000000000000000
χ514-4-4444-4-444-4-4-44004000-400000000000000000000000000000000
χ524-4-4444-4-4-4-444-4400-4000400000000000000000000000000000000
χ538-8-88-8-888000000000000000000000000000000000000000000000

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