Finite Group Databasebeta

← Group #104017

Character table — Group #104017

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222444444444444444448888888888888888444444448888888824
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111
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
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ92222222222222222-222-2-2-2-2-2-200000000000000000000000022-2-2000000
χ102222222222222222-222-2-2-2-2-2-2000000000000000000000000-2-222000000
χ112222222222-2-222-2-22-2-222-22-2-2000000002222-2-2-2-2000000000000000000
χ122222222222-2-222-2-22-2-222-22-2-200000000-2-2-2-22222000000000000000000
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
χ1522222222-2-222-2-2222-2-2-2-2-22-22000000000000000000000000000000002-2
χ1622222222-2-222-2-2222-2-2-2-2-22-2200000000000000000000000000000000-22
χ1722222222-2-222-2-222-2-2-2222-22-20000000000000000220000-2-20000000000
χ1822222222-2-222-2-222-2-2-2222-22-20000000000000000-2-20000220000000000
χ1922222222-2-2-2-2-2-2-2-2222-2-2222-200000000000000000022-2-2000000000000
χ2022222222-2-2-2-2-2-2-2-2222-2-2222-2000000000000000000-2-222000000000000
χ2122222222-2-2-2-2-2-2-2-2-22222-2-2-222i2i2i2i−2i−2i−2i−2i00000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-22222-2-2-22−2i−2i−2i−2i2i2i2i2i00000000000000000000000000
χ2322-2-22-2-22222-2-2-22-202-200000000000000i2i2−i2−i2i2i2−i2−i200000000002-2i2−i2i2−i200
χ2422-2-22-2-22222-2-2-22-202-200000000000000i2i2−i2−i2i2i2−i2−i20000000000-22−i2i2−i2i200
χ2522-2-22-2-22222-2-2-22-202-200000000000000−i2−i2i2i2−i2−i2i2i200000000002-2−i2i2−i2i200
χ2622-2-22-2-22222-2-2-22-202-200000000000000−i2−i2i2i2−i2−i2i2i20000000000-22i2−i2i2−i200
χ2722-2-22-2-2222-22-2-2-220-2200000000000000i2i2−i2−i2−i2−i2i2i2000000002-200i2−i2−i2i200
χ2822-2-22-2-2222-22-2-2-220-2200000000000000i2i2−i2−i2−i2−i2i2i200000000-2200−i2i2i2−i200
χ2922-2-22-2-2222-22-2-2-220-2200000000000000−i2−i2i2i2i2i2−i2−i2000000002-200−i2i2i2−i200
χ3022-2-22-2-2222-22-2-2-220-2200000000000000−i2−i2i2i2i2i2−i2−i200000000-2200i2−i2−i2i200
χ312-2-2-2-2222002200-2-20002-220-20i2i2−i2−i2i2i2−i2−i22−22−22−22−22i−2i0000000000000000
χ322-2-2-2-2222002200-2-20002-220-20i2i2−i2−i2i2i2−i2−i2−22−22−22−22−2i2i0000000000000000
χ332-2-2-2-2222002200-2-20002-220-20−i2−i2i2i2−i2−i2i2i22−22−22−22−2−2i2i0000000000000000
χ342-2-2-2-2222002200-2-20002-220-20−i2−i2i2i2−i2−i2i2i2−22−22−22−222i−2i0000000000000000
χ352-2-2-2-222200-2-200220002-2-202022−2−2−2−2222−22−2−22−220000002-20000000000
χ362-2-2-2-222200-2-200220002-2-202022−2−2−2−222−22−222−22−2000000-220000000000
χ372-2-2-2-222200-2-200220002-2-2020−2−22222−2−22−22−2−22−22000000-220000000000
χ382-2-2-2-222200-2-200220002-2-2020−2−22222−2−2−22−222−22−20000002-20000000000
χ39444-4-44-4-400000000400000-4002-22-22-22-200000000000000000000000000
χ40444-4-44-4-400000000400000-400-22-22-22-2200000000000000000000000000
χ41444-4-44-4-400000000-4000004002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ42444-4-44-4-400000000-400000400−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ4344-4-44-4-44-4-44-4444-40-440000000000000000000000000000000000000000
χ4444-4-44-4-44-4-4-4444-4404-40000000000000000000000000000000000000000
χ454-444-4-4-44004-400-44000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ464-444-4-4-44004-400-4400000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ474-444-4-4-4400-44004-4000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ484-444-4-4-4400-44004-400000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ494-44-44-44-44i−4i004i−4i000000000000000000000000000002i−2i2-2000000000000
χ504-44-44-44-44i−4i004i−4i00000000000000000000000000000−2i2i-22000000000000
χ514-44-44-44-4−4i4i00−4i4i000000000000000000000000000002i−2i-22000000000000
χ524-44-44-44-4−4i4i00−4i4i00000000000000000000000000000−2i2i2-2000000000000
χ534-4-4444-4-44i−4i00−4i4i000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000
χ544-4-4444-4-44i−4i00−4i4i00000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000
χ554-4-4444-4-4−4i4i004i−4i000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000
χ564-4-4444-4-4−4i4i004i−4i00000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000
χ574-4-4-4-4444004400-4-4000-44-40400000000000000000000000000000000000
χ584-4-4-4-444400-4-40044000-4440-400000000000000000000000000000000000
χ5988-88-8-88-8000000000000000000000000000000000000000000000000000

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