Finite Group Databasebeta

← Group #146227

Character table — Group #146227

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12222244444444888888884488881616161616161616161616161616161688888888161616161616161624444488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ922222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000
χ112222222-2-2-2-22222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ122222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ132222222-2-2-2-2222-2-2-2-22222-2-222-2-20000000000000000000000002222-2-2-2-200000000
χ142222222-2-2-2-2222-2-2-2-22222-2-222-2-2000000000000000000000000-2-2-2-2222200000000
χ152222-2-2222-2-2-2-22000000002-200002222−2−2−2−22222−2−2−2−200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i200000000
χ162222-2-2222-2-2-2-22000000002-200002222−2−2−2−22222−2−2−2−20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i200000000
χ172222-2-2222-2-2-2-22000000002-20000−2−2−2−22222−2−2−2−2222200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i200000000
χ182222-2-2222-2-2-2-22000000002-20000−2−2−2−22222−2−2−2−222220000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i200000000
χ192222-2-22-2-222-2-2200000000-2200002222−2−2−2−2−2−2−2−222222i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i200000000
χ202222-2-22-2-222-2-2200000000-2200002222−2−2−2−2−2−2−2−22222−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i200000000
χ212222-2-22-2-222-2-2200000000-220000−2−2−2−222222222−2−2−2−22i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i200000000
χ222222-2-22-2-222-2-2200000000-220000−2−2−2−222222222−2−2−2−2−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i200000000
χ232222-2-2-2222222-222222222-2-2-2-2-2-2000000000000000000000000000000000000002i−2i
χ242222-2-2-2222222-222222222-2-2-2-2-2-200000000000000000000000000000000000000−2i2i
χ252222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i00
χ262222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i00
χ272222-2-2-2-2-2-2-222-22222-2-2-2-22222-2-2000000000000000000000000000000002-2000000
χ282222-2-2-2-2-2-2-222-22222-2-2-2-22222-2-200000000000000000000000000000000-22000000
χ292222-2-2-2-2-2-2-222-2-2-2-2-2222222-2-22200000000000000000000000000000000002i−2i0000
χ302222-2-2-2-2-2-2-222-2-2-2-2-2222222-2-2220000000000000000000000000000000000−2i2i0000
χ312-2-222-2-200002-2222-2-2000000002-20000000022-2-222-2-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ322-2-222-2-200002-2222-2-2000000002-20000000022-2-222-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ332-2-222-2-200002-2222-2-2000000002-200000000-2-222-2-222i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ342-2-222-2-200002-2222-2-2000000002-200000000-2-222-2-222−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ352-2-222-2-200002-22-2-22200000000-2222-2-222-2-200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ362-2-222-2-200002-22-2-22200000000-2222-2-222-2-200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ372-2-222-2-200002-22-2-22200000000-22-2-222-2-22200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ382-2-222-2-200002-22-2-22200000000-22-2-222-2-22200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ392-2-22-22-20000-222000022-2-2002-20022−2−2−2−22222−2−2−2−2222−2−222−2−2200002-2-2200000000
χ402-2-22-22-20000-222000022-2-2002-20022−2−2−2−22222−2−2−2−222−222−2−222−20000-222-200000000
χ412-2-22-22-20000-222000022-2-2002-200−2−22222−2−2−2−22222−2−22−2−222−2−220000-222-200000000
χ422-2-22-22-20000-222000022-2-2002-200−2−22222−2−2−2−22222−2−2−222−2−222−200002-2-2200000000
χ432-2-22-22-20000-2220000-2-22200-220022−2−2−2−222−2−22222−2−22−2−22−222−22-2-22000000000000
χ442-2-22-22-20000-2220000-2-22200-220022−2−2−2−222−2−22222−2−2−222−22−2−22-222-2000000000000
χ452-2-22-22-20000-2220000-2-22200-2200−2−22222−2−222−2−2−2−2222−2−22−222−2-222-2000000000000
χ462-2-22-22-20000-2220000-2-22200-2200−2−22222−2−222−2−2−2−222−222−22−2−222-2-22000000000000
χ47444444-444-4-4-4-4-400000000-4400000000000000000000000000000000000000000000
χ48444444-4-4-444-4-4-4000000004-400000000000000000000000000000000000000000000
χ4944-4-4000004i−4i00022−2222−222i2−2i22i2−2i2000000ζ+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−ζ7ζ−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+ζ7000000000000000000000000
χ5044-4-4000004i−4i00022−2222−222i2−2i22i2−2i2000000−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+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+ζ7ζ+ζ3−ζ5−ζ7000000000000000000000000
χ5144-4-4000004i−4i000−2222−2222−2i22i2−2i22i2000000ζ−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+ζ7ζ+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−ζ7000000000000000000000000
χ5244-4-4000004i−4i000−2222−2222−2i22i2−2i22i2000000−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−ζ7−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+ζ7000000000000000000000000
χ5344-4-400000−4i4i00022−2222−22−2i22i2−2i22i2000000ζ+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−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+ζ7ζ+ζ3−ζ5−ζ7000000000000000000000000
χ5444-4-400000−4i4i00022−2222−22−2i22i2−2i22i2000000−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+ζ7ζ−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+ζ7000000000000000000000000
χ5544-4-400000−4i4i000−2222−22222i2−2i22i2−2i2000000ζ−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+ζ7−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+ζ7000000000000000000000000
χ5644-4-400000−4i4i000−2222−22222i2−2i22i2−2i2000000−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−ζ7ζ+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−ζ7000000000000000000000000
χ574-44-40004i−4i0000022−22−22222i2−2i2−2i22i2000000ζ−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−ζ7ζ−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−ζ7000000000000000000000000
χ584-44-40004i−4i0000022−22−22222i2−2i2−2i22i2000000−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+ζ7−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+ζ7000000000000000000000000
χ594-44-40004i−4i00000−222222−22−2i22i22i2−2i2000000ζ+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+ζ7−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−ζ7000000000000000000000000
χ604-44-40004i−4i00000−222222−22−2i22i22i2−2i2000000−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−ζ7ζ+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+ζ7000000000000000000000000
χ614-44-4000−4i4i0000022−22−2222−2i22i22i2−2i2000000ζ−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−ζ7−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+ζ7000000000000000000000000
χ624-44-4000−4i4i0000022−22−2222−2i22i22i2−2i2000000−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+ζ7ζ−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−ζ7000000000000000000000000
χ634-44-4000−4i4i00000−222222−222i2−2i2−2i22i2000000ζ+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+ζ7ζ+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+ζ7000000000000000000000000
χ644-44-4000−4i4i00000−222222−222i2−2i2−2i22i2000000−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−ζ7−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−ζ7000000000000000000000000
χ654-4-444-440000-44-4000044-4-400-44000000000000000000000000000000000000000000
χ664-4-444-440000-44-40000-4-444004-4000000000000000000000000000000000000000000
χ674-4-44-44400004-4-444-4-400000000-440000000000000000000000000000000000000000
χ684-4-44-44400004-4-4-4-444000000004-40000000000000000000000000000000000000000

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