Finite Group Databasebeta

← Group #103993

Character table — Group #103993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222444444444444444448888888888888888224444448888888824
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ9222222222222222222-2-2-2-2-2-2-200000000000000000000000022-2-2000000
χ10222222222222222222-2-2-2-2-2-2-2000000000000000000000000-2-222000000
χ112222222222-2-222-2-2-2-2222-22-2-2000000002222-2-2-2-2000000000000000000
χ122222222222-2-222-2-2-2-2222-22-2-200000000-2-2-2-22222000000000000000000
χ132222222222-2-222-2-2-2-2-2-2-22-222000000000000000000000000000022-2-200
χ142222222222-2-222-2-2-2-2-2-2-22-2220000000000000000000000000000-2-22200
χ1522222222-2-222-2-222-2-222-22-22-200000000000000000022-2-2000000000000
χ1622222222-2-222-2-222-2-222-22-22-2000000000000000000-2-222000000000000
χ1722222222-2-222-2-222-2-2-2-22-22-22000000000000000000000000000000002-2
χ1822222222-2-222-2-222-2-2-2-22-22-2200000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-2-2-22222-2-2-2-222i2i2i2i−2i−2i−2i−2i00000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-22222-2-2-2-22−2i−2i−2i−2i2i2i2i2i00000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-222-2-22222-20000000000000000220000-2-20000000000
χ2222222222-2-2-2-2-2-2-2-222-2-22222-20000000000000000-2-20000220000000000
χ23222-2-2-2-22222-2-2-22-22-200000000000000022−2−222−2−200000000002i−2ii2−i2i2−i200
χ24222-2-2-2-22222-2-2-22-22-200000000000000022−2−222−2−20000000000−2i2i−i2i2−i2i200
χ25222-2-2-2-22222-2-2-22-22-2000000000000000−2−222−2−22200000000002i−2i−i2i2−i2i200
χ26222-2-2-2-22222-2-2-22-22-2000000000000000−2−222−2−2220000000000−2i2ii2−i2i2−i200
χ27222-2-2-2-2222-22-2-2-22-2200000000000000022−2−2−2−222000000002i−2i00i2−i2−i2i200
χ28222-2-2-2-2222-22-2-2-22-2200000000000000022−2−2−2−22200000000−2i2i00−i2i2i2−i200
χ29222-2-2-2-2222-22-2-2-22-22000000000000000−2−22222−2−2000000002i−2i00−i2i2i2−i200
χ30222-2-2-2-2222-22-2-2-22-22000000000000000−2−22222−2−200000000−2i2i00i2−i2−i2i200
χ312-2-22-22-22002200-2-2002-2020-20i2i2−i2−i2i2i2−i2−i22−22−22−22−200002i−2i000000000000
χ322-2-22-22-22002200-2-2002-2020-20i2i2−i2−i2i2i2−i2−i2−22−22−22−220000−2i2i000000000000
χ332-2-22-22-22002200-2-2002-2020-20−i2−i2i2i2−i2−i2i2i22−22−22−22−20000−2i2i000000000000
χ342-2-22-22-22002200-2-2002-2020-20−i2−i2i2i2−i2−i2i2i2−22−22−22−2200002i−2i000000000000
χ352-2-22-22-2200-2-20022002-20-202022−2−2−2−2222−22−2−22−22002-200000000000000
χ362-2-22-22-2200-2-20022002-20-202022−2−2−2−222−22−222−22−200-2200000000000000
χ372-2-22-22-2200-2-20022002-20-2020−2−22222−2−22−22−2−22−2200-2200000000000000
χ382-2-22-22-2200-2-20022002-20-2020−2−22222−2−2−22−222−22−2002-200000000000000
χ39444-4-4-4-44-4-44-4444-4-4400000000000000000000000000000000000000000
χ40444-4-4-4-44-4-4-4444-444-400000000000000000000000000000000000000000
χ4144-444-4-4-400000000000040-4002-22-22-22-200000000000000000000000000
χ4244-444-4-4-400000000000040-400-22-22-22-2200000000000000000000000000
χ4344-444-4-4-4000000000000-404002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ4444-444-4-4-4000000000000-40400−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ454-444-4-44-44i−4i004i−4i000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000
χ464-444-4-44-44i−4i004i−4i00000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000
χ474-444-4-44-4−4i4i00−4i4i000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000
χ484-444-4-44-4−4i4i00−4i4i00000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000
χ494-44-444-4-44i−4i00−4i4i0000000000000000000000000002-200002i−2i0000000000
χ504-44-444-4-44i−4i00−4i4i000000000000000000000000000-220000−2i2i0000000000
χ514-44-444-4-4−4i4i004i−4i0000000000000000000000000002-20000−2i2i0000000000
χ524-44-444-4-4−4i4i004i−4i000000000000000000000000000-2200002i−2i0000000000
χ534-4-44-44-44004400-4-400-440-40400000000000000000000000000000000000
χ544-4-44-44-4400-4-4004400-44040-400000000000000000000000000000000000
χ554-4-4-44-444004-400-44000000000000000002-2-222-2-22000000000000000000
χ564-4-4-44-444004-400-4400000000000000000-222-2-222-2000000000000000000
χ574-4-4-44-44400-44004-4000000000000000002-2-22-222-2000000000000000000
χ584-4-4-44-44400-44004-400000000000000000-222-22-2-22000000000000000000
χ5988-8-8-888-8000000000000000000000000000000000000000000000000000

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