Finite Group Databasebeta

← Group #130310

Character table — Group #130310

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244444444444224444448888888844444444488888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-111-1-1-1-111111111-111-1-111-1-1-1-1-1-111-1-1
χ611111111111111111-1-111-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-111
χ711111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111
χ811111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1
χ9111111-1-111-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i-11-11-11-11-1ii−i−ii−ii−i
χ10111111-1-111-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i-1-11-11-11-11ii−i−i−ii−ii
χ11111111-1-111-1-1-1-1-1-1-11111-1-111−i−i−i−iiiii-11-11-11-11-1−i−iii−ii−ii
χ12111111-1-111-1-1-1-1-1-1-11111-1-111−i−i−i−iiiii-1-11-11-11-11−i−iiii−ii−i
χ13111111-1-111-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-1-111-1-11−i−iiii−i−ii
χ14111111-1-111-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-111-1-111-1−i−iii−iii−i
χ15111111-1-111-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-1-111-1-11ii−i−i−iii−i
χ16111111-1-111-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-111-1-111-1ii−i−ii−i−ii
χ172222222222-2-2222-2-222-2-2-2-2-2-20000000020000000000000000
χ182222222222-2-2222-2-2-2-2-2-2222200000000-20000000000000000
χ1922222222-2-22-22-2-22-2002-20000000000000002200-2-200000000
χ2022222222-2-22-22-2-22-2002-2000000000000000-2-2002200000000
χ2122222222-2-2-222-2-2-2200-2200000000000002200-2-20000000000
χ2222222222-2-2-222-2-2-2200-220000000000000-2-200220000000000
χ23222222-2-22222-2-2-22222-2-222-2-200000000-20000000000000000
χ24222222-2-22222-2-2-222-2-2-2-2-2-2220000000020000000000000000
χ25222222-2-2-2-22-2-2222-200-2200000000000002-200-220000000000
χ26222222-2-2-2-22-2-2222-200-220000000000000-22002-20000000000
χ27222222-2-2-2-2-22-222-22002-20000000000000002-200-2200000000
χ28222222-2-2-2-2-22-222-22002-2000000000000000-22002-200000000
χ2922-2-22-2002-222000-2-22-2002-20022−2−222−2−20000000002−22−20000
χ3022-2-22-2002-222000-2-22-2002-200−2−222−2−222000000000−22−220000
χ3122-2-22-2002-222000-2-2-2200-220022−2−222−2−2000000000−22−220000
χ3222-2-22-2002-222000-2-2-2200-2200−2−222−2−2220000000002−22−20000
χ3322-2-22-2002-2-2-2000222-200-2200i2i2−i2−i2−i2−i2i2i2000000000i2−i2−i2i20000
χ3422-2-22-2002-2-2-2000222-200-2200−i2−i2i2i2i2i2−i2−i2000000000−i2i2i2−i20000
χ3522-2-22-2002-2-2-200022-22002-200i2i2−i2−i2−i2−i2i2i2000000000−i2i2i2−i20000
χ3622-2-22-2002-2-2-200022-22002-200−i2−i2i2i2i2i2−i2−i2000000000i2−i2−i2i20000
χ374444-4-4440000-40000000000002-22-22-22-200000000000000000
χ384444-4-4440000-4000000000000-22-22-22-2200000000000000000
χ394444-4-4-4-4000040000000000002i−2i2i−2i−2i2i−2i2i00000000000000000
χ404444-4-4-4-400004000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000
χ4144-4-44-400-444-4000-44000000000000000000000000000000000
χ4244-4-44-400-44-440004-4000000000000000000000000000000000
χ4344-4-4-4400000004i−4i00000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000
χ4444-4-4-4400000004i−4i0000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000
χ4544-4-4-440000000−4i4i00000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000
χ4644-4-4-440000000−4i4i0000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000
χ478-88-800000000000000000004i−4i0000000000000000000000000
χ488-88-80000000000000000000−4i4i0000000000000000000000000
χ498-8-88008i−8i000000000000000000000000000000000000000000
χ508-8-8800−8i8i000000000000000000000000000000000000000000

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