Finite Group Databasebeta

← Group #288352

Character table — Group #288352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888822444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-1-1-1111-1
χ12111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-1-1-11
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-11-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-1111111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-1-11111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-11111-1-111-11
χ172222222222-2-2-222-2-2-20000222200-2-200-2-200000022-2-2000000000000000000
χ182222222222-2-2-222-2-2-2000022-2-200-2-20022000000-2-222000000000000000000
χ192222222222-2-2-222-2-2-20000-2-222002200-2-2000000-2-222000000000000000000
χ202222222222-2-2-222-2-2-20000-2-2-2-20022002200000022-2-2000000000000000000
χ2122222222-2-2222-2-22-2-22222000022002200-2-200000000000000-2-20000000000
χ2222222222-2-2222-2-22-2-222220000-2-200-2-200-2-200000000000000220000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-200002200-2-20022000000000000002-20000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-20000-2-20022002200000000000000-220000000000
χ2522-2-222-2-200-2-22002002i2i−2i−2i00002-2002i−2i000000002−22−2i2i2−i2−i2000000002−2i2−i200
χ2622-2-222-2-200-2-22002002i2i−2i−2i00002-2002i−2i00000000−22−22−i2−i2i2i200000000−22−i2i200
χ2722-2-222-2-200-2-22002002i2i−2i−2i0000-2200−2i2i000000002−22−2i2i2−i2−i200000000−22−i2i200
χ2822-2-222-2-200-2-22002002i2i−2i−2i0000-2200−2i2i00000000−22−22−i2−i2i2i2000000002−2i2−i200
χ2922-2-222-2-200-2-2200200−2i−2i2i2i00002-200−2i2i000000002−22−2−i2−i2i2i2000000002−2−i2i200
χ3022-2-222-2-200-2-2200200−2i−2i2i2i00002-200−2i2i00000000−22−22i2i2−i2−i200000000−22i2−i200
χ3122-2-222-2-200-2-2200200−2i−2i2i2i0000-22002i−2i000000002−22−2−i2−i2i2i200000000−22i2−i200
χ3222-2-222-2-200-2-2200200−2i−2i2i2i0000-22002i−2i00000000−22−22i2i2−i2−i2000000002−2−i2i200
χ332-2-22-22-22222-22-2-2-2-2200002i−2i00002i−2i0000002i2i−2i−2i00002-22-200000000000000
χ342-2-22-22-22222-22-2-2-2-2200002i−2i00002i−2i000000−2i−2i2i2i0000-22-2200000000000000
χ352-2-22-22-22222-22-2-2-2-220000−2i2i0000−2i2i0000002i2i−2i−2i0000-22-2200000000000000
χ362-2-22-22-22222-22-2-2-2-220000−2i2i0000−2i2i000000−2i−2i2i2i00002-22-200000000000000
χ372-2-22-22-2222-22-2-2-222-22-22-22i−2i0000−2i2i00002-20000000000000000002i−2i000000
χ382-2-22-22-2222-22-2-2-222-22-22-2−2i2i00002i−2i00002-2000000000000000000−2i2i000000
χ392-2-22-22-2222-22-2-2-222-2-22-222i−2i0000−2i2i0000-22000000000000000000−2i2i000000
χ402-2-22-22-2222-22-2-2-222-2-22-22−2i2i00002i−2i0000-220000000000000000002i−2i000000
χ412-2-22-22-22-2-2-22-2222-222-22-2000000000000-220000000000002-2002-200000000
χ422-2-22-22-22-2-2-22-2222-222-22-2000000000000-22000000000000-2200-2200000000
χ432-2-22-22-22-2-2-22-2222-22-22-220000000000002-20000000000002-200-2200000000
χ442-2-22-22-22-2-2-22-2222-22-22-220000000000002-2000000000000-22002-200000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ464444-4-4-4-44-40004-400000000000000000000022−2222−220000000000000000000000
χ474444-4-4-4-44-40004-4000000000000000000000−2222−22220000000000000000000000
χ484444-4-4-4-4-44000-440000000004-4000000000000000000000000000000000000
χ494444-4-4-4-4-44000-44000000000-44000000000000000000000000000000000000
χ5044-4-444-4-40044-400-400000000000000000000000022−22−2222000000000000000000
χ5144-4-444-4-40044-400-4000000000000000000000000−222222−22000000000000000000
χ524-44-4-444-4004-4-4004004i−4i−4i4i0000000000000000000000000000000000000000
χ534-44-4-444-4004-4-400400−4i4i4i−4i0000000000000000000000000000000000000000
χ544-44-4-444-400-44400-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ554-44-4-444-400-44400-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ564-4-444-44-44-4000-440000000000000000000002i2−2i2−2i22i20000000000000000000000
χ574-4-444-44-44-4000-44000000000000000000000−2i22i22i2−2i20000000000000000000000
χ584-4-444-44-4-440004-4000000000000000004i−4i0000000000000000000000000000
χ594-4-444-44-4-440004-400000000000000000−4i4i0000000000000000000000000000
χ604-4-44-44-44-4-44-4444-44-400000000000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-88-88-8-88000000000000000000000000000000000000000000000000000000

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