Finite Group Databasebeta

← Group #131777

Character table — Group #131777

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222224444444488888888888888888888816161616161616161616161616163232
order122244444488882444888844448161616161616161616161616161616162444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-111-111-1-11111-1-1
χ9111111-111-1-1-1-1-1-11-1-111-1-11-11-11iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-11-1ii−i−ii−i
χ10111111-111-1-1-1-1-1-11-1-111-1-11-11-11iiii−i−i−i−iiiii−i−i−i−i-11-1-111-111-1−i−iii−ii
χ11111111-111-1-1-1-1-1-11-1-111-1-11-11-11−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-11-1−i−iii−ii
χ12111111-111-1-1-1-1-1-11-1-111-1-11-11-11−i−i−i−iiiii−i−i−i−iiiii-11-1-111-111-1ii−i−ii−i
χ13111111-111-1-1-1-1-1-11-1-111-1-1-11-111iiii−i−i−i−i−i−i−i−iiiii1-11-11-1-11-11ii−i−i−ii
χ14111111-111-1-1-1-1-1-11-1-111-1-1-11-111iiii−i−i−i−i−i−i−i−iiiii-11-11-111-1-11−i−iiii−i
χ15111111-111-1-1-1-1-1-11-1-111-1-1-11-111−i−i−i−iiiiiiiii−i−i−i−i1-11-11-1-11-11−i−iiii−i
χ16111111-111-1-1-1-1-1-11-1-111-1-1-11-111−i−i−i−iiiiiiiii−i−i−i−i-11-11-111-1-11ii−i−i−ii
χ172222222222-2-2-2-22222-2-2-2-22222-2000000000000000000000000-2-2000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2-200000000000000000000000022000000
χ19222222-222-22222-22-2-2-2-2222-22-2-2000000000000000000000000-22000000
χ20222222-222-22222-22-2-2-2-222-22-22-20000000000000000000000002-2000000
χ212222-2-222222222-2-22-222-2-20000-2000000000000000022-200-20000000000
χ222222-2-222222222-2-22-222-2-20000-20000000000000000-2-220020000000000
χ232222-2-22222-2-2-2-2-2-22-2-2-222000020000000000000000000220-2-200000000
χ242222-2-22222-2-2-2-2-2-22-2-2-222000020000000000000000000-2-202200000000
χ252222-2-22-2-220000-22-22000022-2-2022−2−222−2−222−2−222−2−20000000000000000
χ262222-2-22-2-220000-22-22000022-2-20−2−222−2−222−2−222−2−2220000000000000000
χ272222-2-22-2-220000-22-220000-2-222022−2−222−2−2−2−222−2−2220000000000000000
χ282222-2-22-2-220000-22-220000-2-2220−2−222−2−22222−2−222−2−20000000000000000
χ292222-2-2-222-222222-2-22-2-2-2-20000200000000000000000002-20-2200000000
χ302222-2-2-222-222222-2-22-2-2-2-2000020000000000000000000-2202-200000000
χ312222-2-2-222-2-2-2-2-22-2-2222220000-200000000000000002-2-20020000000000
χ322222-2-2-222-2-2-2-2-22-2-2222220000-20000000000000000-22200-20000000000
χ332222-2-2-2-2-2-20000222-200002-2-220i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2-2-20000222-200002-2-220−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-2-2-20000222-20000-222-20i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ362222-2-2-2-2-2-20000222-20000-222-20−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ374444444-4-4400004-4-4-400000000000000000000000000000000000000000
χ38444444-4-4-4-40000-4-44400000000000000000000000000000000000000000
χ3944-4-400400-42222−22−22000022−22000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000
χ4044-4-400400-42222−22−22000022−22000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000
χ4144-4-400400-4−22−2222220000−2222000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000
χ4244-4-400400-4−22−2222220000−2222000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000
χ4344-4-400-40042222−22−220000−2222000000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ70000000000000000
χ4444-4-400-40042222−22−220000−2222000000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ70000000000000000
χ4544-4-400-4004−22−222222000022−22000000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ70000000000000000
χ4644-4-400-4004−22−222222000022−22000000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ70000000000000000
χ474-44-4000-4404i−4i4i−4i0000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ600
χ484-44-4000-4404i−4i4i−4i000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ600
χ494-44-4000-440−4i4i−4i4i0000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ200
χ504-44-4000-440−4i4i−4i4i000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ200
χ514-4-444i−4i00002i2−2i2−2i22i200000022−22000002ζ−2ζ2ζ5−2ζ52ζ7−2ζ72ζ3−2ζ3000000000000000000000000
χ524-4-444i−4i00002i2−2i2−2i22i200000022−2200000−2ζ2ζ−2ζ52ζ5−2ζ72ζ7−2ζ32ζ3000000000000000000000000
χ534-4-444i−4i0000−2i22i22i2−2i2000000−2222000002ζ5−2ζ5−2ζ2ζ2ζ3−2ζ3−2ζ72ζ7000000000000000000000000
χ544-4-444i−4i0000−2i22i22i2−2i2000000−222200000−2ζ52ζ52ζ−2ζ−2ζ32ζ32ζ7−2ζ7000000000000000000000000
χ554-4-44−4i4i00002i2−2i2−2i22i2000000−2222000002ζ3−2ζ3−2ζ72ζ72ζ5−2ζ5−2ζ2ζ000000000000000000000000
χ564-4-44−4i4i00002i2−2i2−2i22i2000000−222200000−2ζ32ζ32ζ7−2ζ7−2ζ52ζ52ζ−2ζ000000000000000000000000
χ574-4-44−4i4i0000−2i22i22i2−2i200000022−22000002ζ7−2ζ72ζ3−2ζ32ζ−2ζ2ζ5−2ζ5000000000000000000000000
χ584-4-44−4i4i0000−2i22i22i2−2i200000022−2200000−2ζ72ζ7−2ζ32ζ3−2ζ2ζ−2ζ52ζ5000000000000000000000000
χ598-88-80008-800000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.