Finite Group Databasebeta

← Group #417469

Character table — Group #417469

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422222222444444444444444444442444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ51111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ61111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ9111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-111-1-111-1-1
χ10111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-111-1-1-1-1-1-1-111-1-111
χ11111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1-1-111
χ12111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-111-111-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111111-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1111111-1-111-1-1
χ172222222222-2-2-2-2-2-2-2-222-2-2000022-2-2000022-2-2000000000000000000000000
χ182222222222-2-2-2-2-2-2-2-222-2-20000-2-2220000-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-222000022-2-20000-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2220000-2-222000022-2-2000000000000000000000000
χ2122222-2-2-2-2222-2-222-2-200000000000000002-22-2000022-2-202-20000000000000
χ2222222-2-2-2-2222-2-222-2-200000000000000002-22-20000-2-2220-220000000000000
χ2322222-2-2-2-2222-2-222-2-20000000000000000-22-22000022-2-20-220000000000000
χ2422222-2-2-2-2222-2-222-2-20000000000000000-22-220000-2-22202-20000000000000
χ2522222-2-2-2-22-2-222-2-22200000000000000002-2-2222-2-20000200-2000000000000
χ2622222-2-2-2-22-2-222-2-22200000000000000002-2-22-2-2220000-2002000000000000
χ2722222-2-2-2-22-2-222-2-2220000000000000000-222-222-2-20000-2002000000000000
χ2822222-2-2-2-22-2-222-2-2220000000000000000-222-2-2-2220000200-2000000000000
χ292222-2-2-222-22-22-22-22-22-22-20022000000-2-20000000000000000002-200000000
χ302222-2-2-222-22-22-22-22-22-22-200-2-200000022000000000000000000-2200000000
χ312222-2-2-222-22-22-22-22-2-22-220022000000-2-2000000000000000000-2200000000
χ322222-2-2-222-22-22-22-22-2-22-2200-2-2000000220000000000000000002-200000000
χ332222-2-2-222-2-22-22-22-222-2-2222000000-2-20000000000000000002-20000000000
χ342222-2-2-222-2-22-22-22-222-2-22-2-200000022000000000000000000-220000000000
χ352222-2-2-222-2-22-22-22-22-222-222000000-2-2000000000000000000-220000000000
χ362222-2-2-222-2-22-22-22-22-222-2-2-2000000220000000000000000002-20000000000
χ372-2-2222-22-2-2222-2-2-2-2200002-20000002-200000000002i−2i2i−2i00000000002i−2i0000
χ382-2-2222-22-2-2222-2-2-2-2200002-20000002-20000000000−2i2i−2i2i0000000000−2i2i0000
χ392-2-2222-22-2-2222-2-2-2-220000-22000000-2200000000002i−2i2i−2i0000000000−2i2i0000
χ402-2-2222-22-2-2222-2-2-2-220000-22000000-220000000000−2i2i−2i2i00000000002i−2i0000
χ412-2-222-22-22-222-22-2-22-20000002-20000002-2000000002i−2i−2i2i000000000000002i−2i
χ422-2-222-22-22-222-22-2-22-20000002-20000002-200000000−2i2i2i−2i00000000000000−2i2i
χ432-2-222-22-22-222-22-2-22-2000000-22000000-22000000002i−2i−2i2i00000000000000−2i2i
χ442-2-222-22-22-222-22-2-22-2000000-22000000-2200000000−2i2i2i−2i000000000000002i−2i
χ452-2-22-22-2-2222-2-2-2-22220000002-2000000-2200002-22-200000000000000002-200
χ462-2-22-22-2-2222-2-2-2-22220000002-2000000-220000-22-220000000000000000-2200
χ472-2-22-22-2-2222-2-2-2-2222000000-220000002-200002-22-20000000000000000-2200
χ482-2-22-22-2-2222-2-2-2-2222000000-220000002-20000-22-2200000000000000002-200
χ492-2-22-2-222-22-22-2-22-22200002-2000000-220000002-2-220000000000002-2000000
χ502-2-22-2-222-22-22-2-22-22200002-2000000-22000000-222-2000000000000-22000000
χ512-2-22-2-222-22-22-2-22-2220000-220000002-20000002-2-22000000000000-22000000
χ522-2-22-2-222-22-22-2-22-2220000-220000002-2000000-222-20000000000002-2000000
χ534444-444-4-4-44-4-444-4-4400000000000000000000000000000000000000000000
χ544444-444-4-4-4-444-4-444-400000000000000000000000000000000000000000000
χ554-4-4444-44-4-4-4-4-44444-400000000000000000000000000000000000000000000
χ564-4-444-44-44-4-4-44-444-4400000000000000000000000000000000000000000000
χ574-4-44-44-4-444-44444-4-4-400000000000000000000000000000000000000000000
χ584-4-44-4-444-444-444-44-4-400000000000000000000000000000000000000000000
χ5988-8-80000000000000000000000004i−4i00000000000000000000000000000000
χ6088-8-8000000000000000000000000−4i4i00000000000000000000000000000000
χ618-88-800000000000000000000004i−4i0000000000000000000000000000000000
χ628-88-80000000000000000000000−4i4i0000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).